psc final design report

Paragon Structural Consultants5029 11 th Ave NE, Seattle, WA, 98105 June 13 th , 2014 University of Washington Civil & Environmental Engineering 201 More Hall, Box 352700 Seattle, WA 98195-2700 To Whom It May Concern, Thank you for choosing Paragon Structural Consultants (PSC) for the structural design of the Civil Medical Office Building (MOB). Please find attached the final design report for the Civil MOB including the design of the gravity and lateral systems. For the structural system design, PSC chose to utilize reinforced and prestressed concrete. The main gravity system includes a one-way prestressed joist slab to carry the gravity loads and minimize deflections. The slab carries the loads to reinforced concrete girders that span between columns supported by spread footings on the soil below. For the main lateral system, special reinforced concrete shear walls are utilized to carry lateral loads from the diaphragm to the mat foundation. The penthouse design includes structural steel for quick and customizable construction. All of the design work performed by PSC was done with economy and constructability in mind to optimize the owner’s benefit. Included within the following write-up are the loads used for design, the process for designing each aspect of the structure, and a drawing package for construction. PSC appreciates your continued trust and look forward to future projects with the University of Washington. Sincerely, Albin Hovde, Project Manager Carson Baker, Gravity Lead Sam Dougherty, Drafting Lead Kyle Gysler, Foundations Lead Jean-Luc Jackson, Lateral Lead Samiah Rizvi, Analysis Lead Paragon Structural Consultants 2 | P a g e Final Design Report Civil Medical Office Building Carson Baker Samuel Dougherty Kyle Gysler Albin Hovde Jean-Luc Jackson Samiah Rizvi June 13 th , 2014 Paragon Structural Consultants 3 | P a g e TABLE OF CONTENTS List Of Figures .............................................................................................................................................. 7 List Of Tables ............................................................................................................................................. 10 1 Project Overview ................................................................................................................................ 12 1.1 Overview of Building ................................................................................................................. 12 1.1.1 Interior Partition/Architectural Plans .................................................................................. 13 1.2 Computer Programs Used ........................................................................................................... 14 2 Overview of Structural Design and Systems ...................................................................................... 14 3 Site Conditions and Geotechnical Considerations .............................................................................. 15 4 System Overview ................................................................................................................................ 16 4.1 Gravity Design Basis .................................................................................................................. 16 4.2 Capacity vs. Demand .................................................................................................................. 17 4.2.1 Conclusion .......................................................................................................................... 18 4.3 Lateral design basis ..................................................................................................................... 18 5 Material Specifications ....................................................................................................................... 19 5.1 Concrete ...................................................................................................................................... 19 5.2 Steel............................................................................................................................................. 20 6 Loads ................................................................................................................................................... 21 6.1 Dead Loads ................................................................................................................................. 21 6.2 Live Loads .................................................................................................................................. 22 6.2.1 Live Load Reductions ......................................................................................................... 22 6.2.2 Roof Live Load Reductions ................................................................................................ 23 6.3 Snow Loads ................................................................................................................................. 23 6.3.1 SEAW - Method 1............................................................................................................... 23 6.3.2 SEAW - Method 2............................................................................................................... 24 6.3.3 ASCE 7-10 Method 1 .......................................................................................................... 25 6.3.4 ASCE 7-10 Method 2 .......................................................................................................... 28 6.3.5 Snow Load Summary .......................................................................................................... 28 6.4 Wind Loads ................................................................................................................................. 29 6.4.1 Basic Wind Speed, V .......................................................................................................... 29 6.4.2 Wind Directionality Factor (K d ) .......................................................................................... 30 6.4.3 External Pressure Coefficient (C p ) ...................................................................................... 30 6.4.4 ASCE 7-10: Chapter 27 ...................................................................................................... 30 Paragon Structural Consultants 4 | P a g e 6.5 Seismic Loads ............................................................................................................................. 33 6.6 Load Combinations ..................................................................................................................... 36 6.6.1 LRFD .................................................................................................................................. 36 6.6.2 ASD ..................................................................................................................................... 36 7 SAP2000 Analysis .............................................................................................................................. 36 7.1 System Orientation ...................................................................................................................... 36 7.2 Tributary Areas ........................................................................................................................... 37 7.3 Initial Modeling .......................................................................................................................... 37 7.4 Pattern Loading ........................................................................................................................... 38 7.5 SAP2000 Output ......................................................................................................................... 39 8 One-Way Joist Slab Design ................................................................................................................ 40 8.1 Design Considerations ................................................................................................................ 40 8.1.1 One-Way Flat Slabs ............................................................................................................ 40 8.1.2 Two-Way Flat Plates and Flat Slabs ................................................................................... 41 8.1.3 Two-Way Slabs on Beams and Waffle Slabs ..................................................................... 42 8.1.4 One-Way Joist Slab ............................................................................................................. 43 8.1.5 Selection .............................................................................................................................. 44 8.2 Design Process ............................................................................................................................ 44 8.2.1 Construction Method........................................................................................................... 44 8.2.2 Section Properties ............................................................................................................... 45 8.2.3 Code Requirements ............................................................................................................. 50 8.2.4 Fire Rating .......................................................................................................................... 52 8.3 Final Design ................................................................................................................................ 53 8.3.1 Elevated Decks .................................................................................................................... 53 8.3.2 Roof Slab ............................................................................................................................ 59 8.3.3 Slab on Grade ...................................................................................................................... 60 9 Girder Design ...................................................................................................................................... 60 9.1 Design Considerations ................................................................................................................ 60 9.1.1 Girder Spanning Direction .................................................................................................. 60 9.1.2 Reinforcement Alternatives ................................................................................................ 60 9.1.3 Minimum Depth by Deflections ......................................................................................... 61 9.1.4 Deflection Limits ................................................................................................................ 61 9.1.5 Effective Width ................................................................................................................... 61 Paragon Structural Consultants 5 | P a g e 9.2 Design Process ............................................................................................................................ 62 9.2.1 Iterative Calculations .......................................................................................................... 62 9.2.2 Shear Reinforcement ........................................................................................................... 63 Final Design ............................................................................................................................................ 63 9.2.3 Bar Development ................................................................................................................ 64 10 Column Design ............................................................................................................................... 65 10.1 Design Considerations ................................................................................................................ 65 10.2 Design Process ............................................................................................................................ 65 10.3 Final Design ................................................................................................................................ 68 11 Shear Wall Design .......................................................................................................................... 70 11.1 Analysis....................................................................................................................................... 70 11.2 Design Basis ................................................................................................................................ 73 11.2.1 Boundary Element............................................................................................................... 73 11.2.2 Web Design ......................................................................................................................... 77 11.2.3 Slab Dowel Bars.................................................................................................................. 81 12 Penthouse Design (Steel/Special) ................................................................................................... 83 12.1 Penthouse 1 – NE Corner ............................................................................................................ 83 12.1.1 Assumptions ........................................................................................................................ 83 12.1.2 Design Process .................................................................................................................... 86 12.2 Penthouse 2 – Building Core ...................................................................................................... 88 12.2.1 Assumptions ........................................................................................................................ 88 12.2.2 Design Process .................................................................................................................... 88 12.3 Penthouse lateral reinforcement .................................................................................................. 90 12.3.1 Design Strategy ................................................................................................................... 90 12.3.2 Design Process .................................................................................................................... 91 13 Connection Design .......................................................................................................................... 96 13.1 Beam Column Connection .......................................................................................................... 96 13.1.1 Interior beam connection details ......................................................................................... 96 13.1.2 Exterior beam connection details ........................................................................................ 96 13.2 Column Footing Connection ....................................................................................................... 97 13.3 Penthouse anchorage system ....................................................................................................... 98 13.3.1 Design Strategy ................................................................................................................... 98 13.3.2 Design Method .................................................................................................................... 98 Paragon Structural Consultants 6 | P a g e 14 Foundation Design ........................................................................................................................ 101 14.1 Design Considerations .............................................................................................................. 101 14.2 Design Process .......................................................................................................................... 101 14.2.1 Column Footings ............................................................................................................... 101 14.2.2 Shear Wall Foundation ...................................................................................................... 102 14.2.3 Final Design ...................................................................................................................... 104 15 Codes and References ................................................................................................................... 106 Appendix A – Sample Calculations .......................................................................................................... 107 A.1 FOUNDATION Calculations......................................................................................................... 107 A.1.1 Spread Footing: Computed using loads from column at C5 ............................................ 107 A.1.2 Mat Foundation: Computed using Shear Wall along Line 6 ............................................ 108 A.2 Slab Calculations ............................................................................................................................ 110 A.2.1 Strength checks ................................................................................................................ 110 A.3 Girder Calculations ........................................................................................................................ 111 A.3.1 Computed using a typical B1 on floor 2 .......................................................................... 111 A.4 Column Calculations ...................................................................................................................... 111 A.5 Lateral analysis Calculations.......................................................................................................... 113 A.5.1 Lateral Force Method .............................................................................................................. 113 A.5.2 Stiffness Method ..................................................................................................................... 113 A.6 Connection Calculations ................................................................................................................ 114 A.6.1 Beam Foundation Connections ........................................................................................ 114 A.6.2 Beam Column Connections ............................................................................................. 115 Paragon Structural Consultants 7 | P a g e LIST OF FIGURES Figure 1-A (ASCE 1.5-1): Risk Category of Buildings for Wind, Snow, and Earthquake Loads ............. 12 Figure 1-B: Drawing S2.1L, Live Load Hatching ...................................................................................... 13 Figure 1-C: Drawing S2.2L, Live Load Hatching ...................................................................................... 14 Figure 4-A: Girder Height Allowances, Including False Ceilings and HVAC ........................................... 17 Figure 6-A (7-1 ASCE): Minimum Design Ground Snow Loads .............................................................. 25 Figure 6-B (7-7 ASCE): Drifts Formed at Windward and Leeward Steps ................................................. 27 Figure 6-C (7-2a ASCE): Slope Factor ....................................................................................................... 27 Figure 6-D: Basic Wind Speed, V (Figure 26.5-1A) .................................................................................. 30 Figure 6-E (ASCE 26.6-1): Wind Directionality Factor, K d ....................................................................... 30 Figure 6-F (ASCE 27.4-1): External Pressure Coefficient, C p ................................................................... 30 Figure 6-G (ASCE Table 27.3-1): Velocity Pressure Exposure Coefficient, K z ........................................ 31 Figure 6-H: Transverse Wind Loads (Penthouse 1 and Penthouse 2)........................................................ 32 Figure 6-I: Longitudinal Wind Loads (Penthouse 1 and Penthouse 2) ....................................................... 33 Figure 6-J: USGS Provided Output for Spectral Accelerations .................................................................. 33 Figure 6-K: Seismic Shears Distributed to Each Level of the Building ..................................................... 35 Figure 7-A: Critical Span Length for Elevated Floors (Typical) ............................................................... 37 Figure 7-B: Sample Frame at Architectural Gridline 2 from SAP2000 ...................................................... 38 Figure 7-C: Frames at Architectural Gridline 2 Showing Two Different Live Load Patterns .................... 39 Figure 7-D: Sample Output From SAP2000 ............................................................................................... 39 Figure 8-A: A One-Way Slab on Beams (Image Courtesy of Concrete Floors, by Garber) ...................... 41 Figure 8-B: A Two-Way Flat Plate Slab (Image Courtesy of Concrete Floors, by Garber) ...................... 42 Figure 8-C: A Typical Waffle Slab (Image Courtesy of Class Connection) .............................................. 43 Figure 8-D: A One-Way Joist Slab (Image Courtesy of Concrete Floors, by Garber) .............................. 44 Figure 8-E: Schematic Diagram of Typical One-Way Joist Slab Construction (Image Courtesy of Concrete Construction) ............................................................................................................................... 45 Figure 8-F: ACI Section 8.3.3 ..................................................................................................................... 46 Figure 8-G: Moments Used in Design, by Location, According to ACI Section 8.3.3 .............................. 47 Figure 8-H: Available Depths of a Standard 30” Joist Pan (Image Courtesy of CECO Concrete) ............ 47 Figure 8-I: Schematic of Load Balancing Effects ....................................................................................... 48 Figure 8-J: Magnel Diagram for the Slab above the First Interior Support ............................................... 50 Paragon Structural Consultants 8 | P a g e Figure 8-K: ACI 318 Section 8.13.2 ........................................................................................................... 50 Figure 8-L: ACI Section 8.13.3 .................................................................................................................. 50 Figure 8-M: ACI Sections 8.13.6.1 and 8.13.6.2 ........................................................................................ 51 Figure 8-N: ACI Section 7.7.2 .................................................................................................................... 51 Figure 8-O: Slab Section Detail for all Floors ............................................................................................ 53 Figure 8-P: ACI 318 Section 7.12.2.1 ......................................................................................................... 54 Figure 8-Q: ACI 318 Section 7.12.2.2 ........................................................................................................ 55 Figure 8-R: ACI 318 Section 10.5.4 ........................................................................................................... 55 Figure 8-S: ACI 318 Section 10.6.4 ............................................................................................................ 56 Figure 8-T: ACI 318 Section 11.4.6.1 ........................................................................................................ 57 Figure 8-U: ACI Section 8.13.8 .................................................................................................................. 57 Figure 8-V: ACI 318 Section 18.9.2 ........................................................................................................... 58 Figure 8-W: Alternating Tendon Stressing Schematic ............................................................................... 59 Figure 9-A (ACI 9.5-a): Minimum Thickness of Nonprestressed Beams .................................................. 61 Figure 9-B: ACI requirements for effective widths .................................................................................... 62 Figure 10-A: Example from the Architectural Plans Showing the Frames Used to Model ........................ 66 Figure 10-B: Example of the Interaction Diagram Used (Red Dot Represents Combination Test) ........... 67 Figure 10-C: Image Representing the Hoop Configuration of a Column ................................................... 68 Figure 10-D: An Example of the Tie Spacing and Splicing in a Typical Column ..................................... 69 Figure 10-E: Typical Column Section for Floors 1-4 ................................................................................. 69 Figure 10-F: Column Schedule for Civil MOB .......................................................................................... 70 Figure 11-A: Shear Wall Orientation, with Center of Rotation and Center of Mass Shown ..................... 72 Figure 11-B: Schematic of a Typical Reinforcement Layout in Shear Wall Design .................................. 73 Figure 11-C: Stress Diagram for Use in Shear Wall Design ...................................................................... 74 Figure 11-D: Typical Pattern for Boundary Elements ................................................................................ 74 Figure 11-E: PT Tendon Pass Through ....................................................................................................... 75 Figure 11-F: Transverse Reinforcement Dimensions ................................................................................. 76 Figure 11-G: Typical Web Reinforcing Schedule ...................................................................................... 78 Figure 11-H: Shear Wall Section Detail ..................................................................................................... 81 Figure 11-I: Horizontal Bar Development Length ...................................................................................... 81 Figure 11-J: Placement of Dowel Bars along Shear Wall Faces ................................................................ 83 Paragon Structural Consultants 9 | P a g e Figure 11-K: Dowel bar Callout in Slab Reinforcement Schedule ............................................................. 83 Figure 12-A: Pratt Truss I, Available by Request from Aegis Metal Framing ........................................... 84 Figure 12-B: Pratt Truss II, Available by Request from Aegis Metal Framing .......................................... 84 Figure 12-C: Pratt Truss III, Available by Request from Aegis Metal Framing ........................................ 85 Figure 12-D: Plan View of the NE Corner Penthouse (1), with Aegis Space Frame Shown ..................... 86 Figure 12-E: Plan View of Penthouse 2 with Labelled Beams, Stringers, and Columns .......................... 89 Figure 12-F: Free Body Diagram for Penthouse 1 (Both NS and EW Axes) ............................................ 92 Figure 12-G: TriPyramid Catalogue, Tension Member Selection Table (A22 Highlighted) .................... 92 Figure 12-H: TriPyramid A22 and A25 Tension Rods (Both Used for Penthouse Design) ...................... 93 Figure 12-I: B215 Jaw Assembly, Connection for A22 Tension Rods ...................................................... 93 Figure 12-J: Free Body Diagram for Penthouse 2 along the NS Axis ....................................................... 94 Figure 12-K: Free Body Diagram for Penthouse 2 along the EW Axis ..................................................... 94 Figure 12-L: TriPyramid Catalogue, Tension Member Selection Table (A25 Highlighted) ..................... 95 Figure 12-M: B230 Jaw Assembly, Connection for A25 Tension Rods .................................................... 95 Figure 13-A: Exterior Beam Connection Details ........................................................................................ 97 Figure 13-B: A Typical Column-Footing Connection ................................................................................ 98 Figure 13-C: Final Hilti Anchor Design for Penthouse 1 ........................................................................ 100 Figure 13-D: Final Hilti Anchor Design for Penthouse 2 ........................................................................ 100 Paragon Structural Consultants 10 | P a g e LIST OF TABLES Table 4-A: Worst-Case Analysis Loadings and Respective Design Capacities ......................................... 18 Table 5-A: Concrete Strength Requirements (28-day Strength, 145 pcf PCC) ......................................... 20 Table 5-B: Reinforcing Steel Reference Code (from ACI 318-11) ........................................................... 20 Table 5-C: Prestressing Strand Reference Code (from ACI 318-11)......................................................... 21 Table 6-A: Dead Loads ............................................................................................................................... 21 Table 6-B: Live Loads ................................................................................................................................ 22 Table 6-C (4-2 ASCE): Live Load Element Factor, K LL ............................................................................ 22 Table 6-D: SEAW Snow Load Analysis for King County ......................................................................... 23 Table 6-E: SEAW Method 1 Values ........................................................................................................... 24 Table 6-F (7-2 ASCE): Exposure Factor ................................................................................................... 26 Table 6-G (7-3 ASCE): Thermal Factor ..................................................................................................... 26 Table 6-H (ASCE 1.5-2): Risk Category of Structures............................................................................... 26 Table 6-I (ASCE 7-10): Method 1 Values .................................................................................................. 28 Table 6-J: Snow Load Summary ................................................................................................................. 29 Table 6-K: Wind Load Values and References .......................................................................................... 29 Table 6-L: Wind Load Calculation Spreadsheet ........................................................................................ 32 Table 6-M: Seismic Weight Calculations ................................................................................................... 35 Table 8-A (R18.3.3 ACI): Serviceability Design Requirements ................................................................ 45 Table 8-B: Minimum Equivalent Thickness of Cast-In-Place or Precast Concrete Slabs .......................... 52 Table 8-C: Fire Resistivity of Finish Materials .......................................................................................... 53 Table 8-D: d c Values for the Slab Tendon at Select Locations ................................................................... 59 Table 9-A: Concrete Beam Schedule .......................................................................................................... 64 Table 10-A: Table Defining the Splice Lengths for the Bars Used in Construction .................................. 68 Table 11-A: Comparison of Neutral Axis Depth and Boundary Element Length ...................................... 75 Table 11-B: Boundary Element Vertical Reinforcing Schedule ................................................................. 76 Table 12-A: Vulcraft Roof Deck Table for Type 1.5B, Penthouse 1 ......................................................... 85 Table 12-B: Vulcraft Roof Deck Table for Type 1.5B, Penthouse 2 .......................................................... 88 Table 12-C: Final Results for Beam Design, Penthouse 2 .......................................................................... 89 Table 12-D: Final Results for Column Design, Penthouse 2 ...................................................................... 90 Table 12-E: Penthouse 1 and Penthouse 2, Worst LRFD Load Case for Lateral Design .......................... 91 Paragon Structural Consultants 11 | P a g e Table 13-A: Exterior Beam Connection Details ......................................................................................... 96 Table 14-A: Column Footing Schedule .................................................................................................... 105 Paragon Structural Consultants 12 | P a g e 1 PROJECT OVERVIEW 1.1 OVERVIEW OF BUILDING The Civil Medical Office Building (MOB) is a 90,000 gross sq. ft. project being designed for private use. The four-story building is a brand new structure, intended as a suitable replacement for the soon to be demolished More Hall. According to the owner, the building will be used primarily for medical office space, although design considerations have been made for any medical equipment that may be introduced later. For the sake of ASCE 07-10 occupancy rating, the building is classified as a 'non-emergency' medical building: Figure 1-A (ASCE 1.5-1): Risk Category of Buildings for Wind, Snow, and Earthquake Loads The overall architectural theme for this structure is exterior brick accents, large/dominating window arrangements, and concrete tile for cladding. Also considered architectural is the Port-Cochère design, with two outer columns, and sloped roof. Finally, there are canopies which extrude from the outermost structure around the first and roof levels. The first floor canopy is meant as a functional cover, for rain, above the walkway surrounding the building. The roof level canopy is also functional, but designed as a sun screen during the summer (for the larger glass regions). Although these elements are not structural in nature, they must be accounted for when calculating the total mass of the cladding, and the way in which it is transferred to the load bearing frame. Paragon Structural Consultants 13 | P a g e 1.1.1 Interior Partition/Architectural Plans Entering the ground level of the building, there is a set of automatic sliding double-doors. Once inside, there is a vestibule and second set of identical doors. Walking into the main lobby, there is a curved architectural wall (non-structural), and important building facilities including: two private restrooms, a stairwell, two elevators, electrical room, and janitorial closet. This arrangement was critical in developing the first models of live load distribution. For the ground floor live loads, the lobby space constituted a higher load of 100 psf (fully developed loads and references can be found in Section 6.2). Below is a look at live load hatching diagram for the ground floor: Figure 1-B: Drawing S2.1L, Live Load Hatching Continuing through the main lobby, there is an exit at the rear of the building (only on the ground floor). As seen above, there is a secondary entrance to the main floor (rear only), which does not connect directly with the main lobby. At the end of this entrance is another, separate stairwell. The main lobby on floor one divides the building into two main halves using interior partition walls, allowing office space and other facilities to be built in those main areas. Floors two, three, and four each have the same core facilities as seen in floor one, except the wall partition is oriented around the core of the building (see Figure 1-C below for comparison). This essentially creates a central lobby area surrounded by a single large portion of office space. This office area can be altered and separated based on the needs of the buyer because partition wall loads were accounted for throughout the floor space. On the roof there is a penthouse structure designed to house electrical Paragon Structural Consultants 14 | P a g e equipment and utilities, which requires special design consideration (Section 12). Below is a typical live load hatch for floors 2-4: Figure 1-C: Drawing S2.2L, Live Load Hatching 1.2 COMPUTER PROGRAMS USED The following computer programs were used for structural analysis, design, drawing, and miscellaneous tasks:  AutoCAD 2013 - structural drawings and load path  SAP 2000 - structural analysis  Microsoft Office Excel - calculations  Microsoft Office PowerPoint - presentations  Microsoft Office Word - drafting technical proposal  Adobe Acrobat Pro - producing report documents  Microsoft One Drive - communication and collaboration on technical reports, and file storage  Microsoft Illustrator – simple reference images for examples  Dr. Beam – Individual beam modelling software  Dr. Frame – 2D frame modelling software 2 OVERVIEW OF STRUCTURAL DESIGN AND SYSTEMS The team at Paragon Structural Consultants has been contracted to develop and design the following critical elements: Paragon Structural Consultants 15 | P a g e  Vertical load resisting frame elements (gravity)  Post tensioned concrete slabs (one-way), reinforced and pre-stressed concrete girders, and reinforced concrete columns  Lateral load resisting system (seismic and wind)  special reinforced concrete shear walls (core wall system) During the planning and development of this structure, the PSC team worked closely with the ASCE 07- 10 standards, and ACI manual for concrete construction (occasionally PCI for reference). Every important decision was referenced with supporting code (the preliminary standards and assumptions of which will be included as well). The load path of the building is intended to carry the self-weight of the structure into the supporting soils in a safe and effective manner. The specific direction and design of the load path for the Civil MOB is highlighted, in detail, in the Structural Drawings (S1.2-S1.5). Essentially, the slabs on each floor are designed in a one way fashion, such that loads are distributed from the middle of the slab in each direction to the nearest perpendicular girder. From the top down, the slabs will distribute loads directly to the girders (based on tributary area and loads in psf), which will in turn send those combined loads into the supporting columns. The loads from each floor accumulate in this fashion, and are sent down through the structural members into the foundations. One important factor for consideration is the central shear wall system being designed for lateral loads. Not only does this shear wall core resist the lateral loads, including wind and seismic, but also some of the gravity load. The boundary elements of the shear walls will act as columns to carry the gravity load from the girders to the foundation. The distribution of the gravity load is also based on the tributary area and orientation of the shear walls (including the location and types of the connections). 3 SITE CONDITIONS AND GEOTECHNICAL CONSIDERATIONS The geotechnical soil profile is primarily dense sandy gravel, penetrating to a depth of about 75 feet. The primary consulting geotechnical engineer has recommended that the following parameters be used for foundation design:  Seismic Site Classification: D  Shallow foundations with an allowable bearing pressure of 12,000 psf  Coefficient of friction: 0.35 Since the site conditions are favorable for the structure, shallow foundations will provide the necessary support. These footings will only need to be placed a few feet under the soil grade. The foundation design will consist of spread footings to transfer column loads and continuous strip footings to transfer lateral loads. The slab on grade thickness will be minimal, since the soil can provide adequate strength. Paragon Structural Consultants 16 | P a g e 4 SYSTEM OVERVIEW 4.1 GRAVITY DESIGN BASIS This segment introduces the gravity resisting frame system of the Civil Medical Office Building. The critical elements which affect the design strategy include the following:  Tributary area (dead loads, self-weight, and live loads),  Slab design (one-way, post tensioned, and reinforced concrete),  Girder design (pre-stressed concrete with reinforcement),  Column design (reinforced concrete), and  Foundation design (reinforced concrete, spread footings and strip footings). The tributary area is a simple tool used to distribute dead loads throughout the load resisting frame. The PSC process for dead loads started with the self-weight of the floor slabs (floors 2-4), being distributed by one-way action to perpendicular girders. These girders resist their own self weight, along with the dead load from the slab, and transfer them to the columns between which they span. External beams run in plane with the girders, parallel to the slab, along the perimeter of the building (only in the N-S direction). These beams resist the weight of the external cladding, along with their own self weight. Finally, the girder/beam system will distribute loads to the columns, which run continuously from the bottom floor to the roof level. They accept the combined loads from the slab, girders, beams, and their own self weight. On the ground level, the weight of the columns is distributed into spread footings, allowing the combined loads to effectively be distributed into the soils below. The slab was the first member to be considered, and was vital to the design of subsequent members (girders, columns, and footings). Due to the governing span length of 33 feet in the N-S orientation, PSC engineers found that post-tensioned slab design was necessary. After many iterations, PSC concluded that a one-way slab with post-tensioned ribs was the most economical and effective design to span the critical length. The one-way slab is a simple design, allowing a less complicated flow of load path from slab to girder (vs. two-way slab). Also, the post tensioned ribs provided the moment arm to allow a high bending capacity, which is key (deflections will ultimately govern a thin slab design). For an in-depth analysis of the PSC slab design, please refer to Section 8 of this document. In order to distribute the weight of the slab effectively, PSC chose to use perpendicular reinforced girders between the columns (in the E-W direction). Since the ends of the slabs tie in directly to the sides of the girders (i.e. the top of slab is parallel with top of girder), PSC engineers were able to let the girder depth govern the overall floor height limitations. The girder depth was the only size limiting factor when accounting for false ceiling height (approx. 10 feet), and HVAC (approx. 2 feet). This meant that there was about 3 feet of vertical space to accommodate the girder design, as shown in the figure below: Paragon Structural Consultants 17 | P a g e Figure 4-A: Girder Height Allowances, Including False Ceilings and HVAC For constructability purposes, PSC engineers also wanted the girder design width to be less than the column dimension. With these constraints in mind, iterations were done with specially prepared Excel spreadsheets, in order to find the lightest possible member that could support the area of simple reinforcement required. The columns were the next step in the gravity resisting frame design. This meant that the iterative process included both girder design and column design in a repeating loop. Once a suitable width dimension for columns was found, the PSC team went back to design the girder’s width to be less than (or equal to) that size. It was important to find the smallest column cross section possible (while still meeting requirements of strength and maximum reinforcement). In order to effectively distribute the massive weight of the building into the soils below, it was critical for PSC to analyze them using geotechnical calculations, in order to design the most effective foundation. After finding the total load of the building under gravity, the same idea of tributary area was used to determine the load path from the columns into the ground. Then, engineers found the dimensions of the spread footings based on the worst possible column load case. Also included in the foundation design is the strip footing, which is required below the shear wall concrete core of the building. This footing is limited by the worst case lateral load scenario (from either wind or seismic). 4.2 CAPACITY VS. DEMAND Before capacity design was completed for all of the critical members in the gravity system, PSC engineers used SAP to determine if the system would be capable of withstanding any potential demand. This step was critical to the iterative process, and can be highlighted by the following fundamental principle: (4-1) Paragon Structural Consultants 18 | P a g e The capacity calculations for each member do not account for the continuity between them, which creates frame stiffness and additional moment resistance. After entering all the factored loads into SAP2000, along one of the 2D girder/column frames, it capacity and demand values could be compared. Further iterations allowed for closer values, until a final design choice was made. In order to begin analysis using programs like Excel, and SAP2000, PSC engineers first had to finalize the tributary area calculations. Starting with a tributary area concept drawing, architectural plans were used to precisely measure the various tributary areas and their effect on the gravity frame (member by member). The lists seen in Tables 6-A (Dead Loads) and 6-B (Live Loads) indicate the different types of loads considered. By adding each of these categories into an Excel spreadsheet, PSC engineers were able to generate a map of where all the loads were going, and develop cross sectional load paths for each of the eight girder locations (running E-W). These cross sections became critical for the SAP models in 2 dimensions. 4.2.1 Conclusion Based on the analysis using Excel and SAP2000 as described above, PSC determined that the capacity of the members designed is greater than the demand required. Table 4-A shows the worst case scenario results for the columns and girders. Further details of SAP Analysis may be found in Section 7. The degree to which the members were optimized was only constrained by time and budget, as well as constructability concerns. Table 4-A: Worst-Case Analysis Loadings and Respective Design Capacities 4.3 LATERAL DESIGN BASIS For the lateral design of this building, PSC decided to use a special reinforced concrete shear wall. A special reinforced concrete shear wall (SRCSW) is a concrete wall that has been designed to transfer the lateral loads induced in a structure, by acting as a deep cantilever beam. This concrete shear wall is considered “special” because of the level of detailing and the expected ductility/performance it will provide for resisting lateral loading. The two main components in a SRCSW are the web and the boundary zone. The web portion of the shear wall is filled with light vertical and transverse steel, which is determined by the shear demand on the wall. The boundary zone is filled with heavy vertical and transverse steel, determined by the moment acting on the shear wall, and provides most of the flexural capacity (similar to a wide flange beam). The walls in the Civil MOB are considered to be squat walls because of the short height of the building, and have been designed as standard single walls. The following sections will highlight the process of finding the analysis and demand of the shear walls in the Civil MOB. Paragon Structural Consultants 19 | P a g e 5 MATERIAL SPECIFICATIONS 5.1 CONCRETE Typical mix components are shown in the list below, along with their code of reference. Specific load resistance requirements are indicated by the design team at Paragon (in member design sections) to be used by the concrete mix contractor (who will develop specific percentages for final mix design). In the event that strength requirements vary significantly, different mixes may be utilized in order to reduce cost (while still meeting the minimum strength requirements). Depending on the cost/benefit of multiple mix design versus single mix design (meeting the highest governing stress requirement), the contractor(s) may decide which method is best suited for the Civil MOB project. The following is a list of typical concrete components, the combination of which will vary based on specific needs, proprietary mix design, and overall structural strength requirements: A. Cement a. ASTM C150: Portland Cement b. ASTM C595: Blended hydraulic cement i. Type IS: Portland blast-furnace slag cement ii. Type IP: Portland/pozzolan cement c. ASTM C618: Fly ash and natural pozzolan d. ASTM C845: Expansive hydraulic cement e. ASTM C989: Ground, granulated, blast-furnace slag cement (concrete and mortar) f. ASTM C1157: Hydraulic cement g. ASTM C1240: Silica fume B. Admixtures a. ASTM C494: Water reducers and strength/set accelerators, etc. b. ASTM C1017: increase concrete flow with low water content C. Aggregate: a. ASTM C29: Bulk volume of coarse aggregate per unit volume of concrete. b. ASTM C33: Normal weight aggregate c. ASTM C330: Light weight aggregate D. Air Content: a. City of Seattle: Requires minimum of 4.5% to maximum of 7.5% for concrete structures. b. ACI 211.1: Provides a table of air entrainment required, based on desired slump and building exposure rating. i. Mild Exposure: Concrete not exposed to freezing conditions or chemicals (most likely range since majority of concrete will be interior, and cladding protects exterior columns as well). E. Water Content: a. ASTM C1602: Mixing water used in the production of hydraulic cement concrete i. Slump: determined primarily by the water content, and water to cement ratio Paragon Structural Consultants 20 | P a g e The following table shows the general expectations in terms of concrete strength requirements, based on a 28-day cure period. PSC have chosen to use conservative values. Based on the specific load resistance calculations, Table 6-A below provides a list of the resulting strength requirements for each member in the design: Table 5-A: Concrete Strength Requirements (28-day Strength, 145 pcf PCC) ELEMENT TYPE f'c (psi) Gravity/Lateral Frame Columns (interior, wall, and corner) 6000 PT Floor Slab, One-Way (levels 2, 3, 4 and roof) 6000 Girders (prestressed and reinforced) 6000 Core Walls (lateral load resisting system) 6000 Additional Slab-on-Grade 3000 Spread Footings (columns) and Mat Footings (walls) 4000 Architectural (Port-Cochère, roof atrium, etc.) 4000 5.2 STEEL Although the primary design focus for the Civil MOB structural project is concrete construction, steel prestressing, post tensioning, and reinforcement is key to the final design strength. Table 6-B shows some typical steel reinforcement, based on code designations: Table 5-B: Reinforcing Steel Reference Code (from ACI 318-11) Reinforcing Member Reference Code Standard Grade 60 Rebar ASTM A615 Welded/Threaded Grade 60 Rebar ASTM A706 (AWS D1.4 for welds) Deformed Reinforcing Bars Carbon Steel ASTM A615 Low Alloy Steel ASTM A706 Stainless Steel ASTM A955 Welded Wire Fabric Smooth ASTM A185 Deformed ASTM A497 Paragon Structural Consultants 21 | P a g e Note: Materials considered under this specification are available in Grades 40, 60 and 75. For the sake of Civil MOB, all rebar specified will be assumed to be Grade 60. Also critical to structural members is the use of prestressed and post-tensioned concrete. Typical expectations for the prestressing include: 7 wire strands (diameter of 0.5 in.), f py =245 ksi, f pu =270 ksi, and E s =28,500 ksi. Table 6-C below lists the various types of typical strand and the corresponding code: Table 5-C: Prestressing Strand Reference Code (from ACI 318-11) Prestressing Strand Reference Code Wire (low relaxation) ASTM A421 (Supplement S1) Strand ASTM A416 High-Strength Bar ASTM A722 Note: PT strand is available in Grades 250 and 270. For the PT member design specified in this report, all strands are assumed to be Grade 270 (ksi). 6 LOADS 6.1 DEAD LOADS The dead loads were estimated by assuming initial sizes for structural members including the columns, girders, and slab. The initial column size was determined by comparing the Civil MOB building to similar 4-story buildings in the Seattle area. Also, the weight of exterior cladding was determined by the architectural plans. The shear walls were assumed to resist the lateral load demand based on LRFD load cases, and as a result they are thicker than the walls and partitions used for transferring planar loads. The slab was assumed to be 6 inches deep to take into account the dead and live loads that it will carry, with reference to similar structures/designs. The table below is a simple list of all the different dead loads accounted for: Table 6-A: Dead Loads Load Type Description Uniform psf Slab Self-weight Calculated using normal weight concrete 75 Partition Walls Gypsum/Insulation 20 Exterior Walls, Floor 1 4 in. brick veneer with glass 20 Exterior Walls, Floor 2-4 Concrete panel with glass 30 Mechanical/Electrical HVAC and electrical wiring 5 Ceiling Suspended gypsum on metal lath 5 Penthouse Walls Steel panel 20 Paragon Structural Consultants 22 | P a g e 6.2 LIVE LOADS Live loads were determined from ASCE 7-10 Table 4-1. The unreduced values for the live loads are included in the following table: Table 6-B: Live Loads Load Type Description Uniform psf Office ASCE Table 4-1 50 Lobbies and first floor corridor ASCE Table 4-1 100 Corridors, Floors 2-4 ASCE Table 4-1 80 Stairs, Floors 2-4 ASCE Table 4-1 100 Penthouse Mechanical ASCE Table 4-1 125 Roof ASCE Table 4-1 20 6.2.1 Live Load Reductions Uniform live loads were reduced in accordance with ASCE 7-10. Except for roof live loads, uniform live loads were reduced using methods in section 4.7 using equation 4.7-1. ( √ ) (6-1) Tributary areas were calculated for all members and their respective live load element factors, K LL , were determined from Table 4-2 (shown below): Table 6-C (4-2 ASCE): Live Load Element Factor, K LL Paragon Structural Consultants 23 | P a g e 6.2.2 Roof Live Load Reductions Uniform roof live loads were reduced using section 4.8 from ASCE 7-10. Equation 4.8-1 was used to reduce the live loads. (6-2) R 1 was determined as follows: (6-3) R 2 was determined as follows: (6-4) However, for all cases R 2 was taken to be 1, because the roof was not pitched. 6.3 SNOW LOADS Snow loads were calculated according to both the recommendations provided by WABO-SEAW and ASCE 7-10 provisions. Each of those methods are highlighted below. 6.3.1 SEAW - Method 1 According to SEAW Snow Load Analysis found in Appendix A, the recommended ground snow load for the Seattle Area under an elevation of 350 ft is 20 psf. This table is reproduced in the figure below. The elevation for the Civil MOB at ground level is 106 feet according to geographic data provided by the Veloroutes website. These recommended loads are conservatively higher than given from calculations from known elevations and the isolines. Per SEAW recommendation two, a 30 percent reduction may be applied to this ground load to determine the roof snow load. Finally, the UBC Appendix suggests adding an additional 5 psf for flat roofed systems to account for increased load, resulting from a rain storm following a snow storm (producing a rain on snow effect). Table 6-D: SEAW Snow Load Analysis for King County Paragon Structural Consultants 24 | P a g e Table 6-E: SEAW Method 1 Values Value Reference (WABO-SEAW August 2000) Seattle 20 SEAW Appendix A Roof Reduction Factor 0.7 SEAW Analysis and Recommendation 4 Flat Roof Factor 5 UBC Appendix The values are thus computed in the following manner: Flat Roofs (20 * 0.7) + 5 = 19 psf Sloped Roofs (20 * 0.7) + 0 = 14 psf 6.3.2 SEAW - Method 2 SEAW Recommendation one suggests that a minimum uniform roof snow load of 25 psf may be used in the case that no other more conservative loadings are suggested, due to localized weather phenomenon, particular geographic features, or the presence of other historical weather data. The SEAW recommendation of 5 psf for flat roofed structures may again be applied in order to be conservative. The values are thus computed in the following manner: Paragon Structural Consultants 25 | P a g e Flat Roofs 25 + 5 = 30 psf Sloped Roofs 25 + 0 = 25 psf 6.3.3 ASCE 7-10 Method 1 The ASCE 7-10 chapter 7 guidelines provide a more thorough and rigorous method of calculating roof snow loads. The basic formula for roof snow loads is given by equation 7.3-1 and is shown below: (6-5) The factors used in this equation are explained in ASCE 7-10 section 7.2 and 7.3, and the criteria is used subsequently. 6.3.3.1 Ground Snow Loads (pg) ASCE Figure 7-1 shows the design ground snow loads PSC used. Since the Civil MOB has an elevation of 106 feet, the value of 15 psf was chosen. Figure 6-A (7-1 ASCE): Minimum Design Ground Snow Loads 6.3.3.2 Exposure Factor (Ce) In order to compute the Exposure Factor, the Terrain Category and Surface Roughness categories must first be determined according to guidelines established in Section 26.7. The Civil MOB site is in an urban area with numerous obstructions as large as, or larger than, single family dwellings, and has a mean roof height of greater than 30 ft (9.1 m). Thus, both Surface Roughness B and Exposure B categories apply. The Civil MOB roof is partially exposed due to it being surrounded by higher structures. Utilizing these pieces of information and ASCE Table 7-2 given below, the Exposure Factor is given as 1.0: Paragon Structural Consultants 26 | P a g e Table 6-F (7-2 ASCE): Exposure Factor 6.3.3.3 Thermal Factor (Ct) The thermal factor may be found by ASCE Table 7-3. The Civil MOB falls under the category of "All Structures Except as Indicated Below" and thus has a value of 1.0: Table 6-G (7-3 ASCE): Thermal Factor 6.3.3.4 Importance Factor (Is) The risk category for the Civil MOB is categorized as type II in accordance with Table 1.5-1, and thus the Snow Importance factor is given as 1.0 from Table 1.5-2. These two tables are reproduced below: Table 6-H (ASCE 1.5-2): Risk Category of Structures Paragon Structural Consultants 27 | P a g e 6.3.3.5 Drifts on Lower Roofs Snow drifts on lower roofs must be calculated to consider both windward drifts as well as leeward drifts. A visual representation of these is provided in ASCE Figure 7-7: Figure 6-B (7-7 ASCE): Drifts Formed at Windward and Leeward Steps Leeward drifts and windward drifts are computed in accordance with Section 7.7.1. These drift surcharges are controlling when they occur over areas which are framed by short members. Considering that there are no shorter members framed under areas susceptible to snow surcharges, drift loads can be ignored for the Civil MOB. 6.3.3.6 Sloped Roofs Section 7.4 details the provisions required for sloped roofs under ASCE 7-10. As C t is 1.0, the roof is categorized as a warm roof under Section 7.4.1. The roof slope factor may be found by Figure 7-2a. The slope of the northeast penthouse roof is 4/12 (ft), which results in a roof slope factor C s of 0.8; thus, reduction is permitted given the grade of slope on the roof. Figure 6-C (7-2a ASCE): Slope Factor Paragon Structural Consultants 28 | P a g e 6.3.3.7 Rain-On-Snow Surcharge Loads As with the SEAW White Paper, the ASCE 7-10 requires an additional load of 5 psf to be added where p g is less than 20 psf (to account for rain-on-snow loads). This additional load is only to be applied when drift and unbalanced loads are not considered. The values used to compute snow loads are summarized in the following table: Table 6-I (ASCE 7-10): Method 1 Values Value Reference (ASCE 7-10) Ground Snow Load, p g 15 Figure 7-1 Surface Roughness B Section 26.7.2 Exposure Category B Section 26.7.3 Exposure Factor, C e 1.0 Table 7-2 Thermal Factor, C t 1.0 Table 7-3 Risk Category II Table 1.5-1 Snow Importance Factor I s 1.0 Table 1.5-2 Roof Slope Factor C s 0.8 Figure 7-2a 6.3.3.8 Final Calculations The values are thus computed in the following manner: Flat Roofs (0.7 * 1.0 * 1.0 * 1.0 * 15) + 5 = 15.5 psf Sloped Roofs (0.7 * 1.0 * 1.0 * 1.0 * 15) * 0.8 = 8.4 psf 6.3.4 ASCE 7-10 Method 2 Low-slope roofs have an additional load condition according to section 7.3.4, which states that where p g is 20 psf or less, a minimum roof snow load p m is to be computed. The value p m is calculated by multiplying the Snow Importance Factor I s by the Ground Snow Load p g . This results in the following load case: (6-6) 6.3.5 Snow Load Summary The results of all calculations are given in the table below: Paragon Structural Consultants 29 | P a g e Table 6-J: Snow Load Summary Uniform Load Methods Flat Roof (psf) Sloped Roof (psf) SEAW Method 1 19 14 SEAW Method 2 30 25 ASCE 7-10 Method 1 15.5 8.4 ASCE 7-10 Method 2 15 N/A While the SEAW recommendations are not legal documents, their recommendations are conservative and will be used for simplicity. Thus, for all flat roofs a uniform value of 30 psf will be used; while for sloped roofs a value of 25 psf will be used. Following the frame design, drift calculations can be reconsidered on a case by case basis. 6.4 WIND LOADS Wind loads were calculated using the directional method in accordance with ASCE 7-10. For calculations, the building was simplified to an average roof elevation of 60 feet and 3 foot parapets along the perimeter. The penthouse was treated as a rooftop structure and the building was assumed to be fully enclosed. Included below are the values used to compute the lateral loading at each floor and the references used to obtain the values: Table 6-K: Wind Load Values and References Value Reference (ASCE 7-10) Risk Category II Table 1.5-1 Basic Wind Speed, V 110 mph Figure 26.5-1A Wind Directionality Factor, K d 0.85 Table 26.6-1 Exposure Category B Section 26.7.3 Topographic Factor, K zt 1.0 seattle.gov Enclosure Classification Enclosed Gust Effect Factor, G 0.85 Section 26.9.1 6.4.1 Basic Wind Speed, V The basic wind speed for the Civil MOB was determined to be 110 mph from ASCE 7-10, based on the location and risk category for the building. Paragon Structural Consultants 30 | P a g e Figure 6-D: Basic Wind Speed, V (Figure 26.5-1A) 6.4.2 Wind Directionality Factor (Kd) The wind directionality factor takes into account the chance that the wind is not blowing directly onto one face of the building: Figure 6-E (ASCE 26.6-1): Wind Directionality Factor, K d 6.4.3 External Pressure Coefficient (Cp) The external pressure coefficient accounts for the size of building, and how the wind affects each side of the building. For windward walls, C p = 0.8, and for leeward walls, C p = -0.3. Figure 6-F (ASCE 27.4-1): External Pressure Coefficient, C p 6.4.4 ASCE 7-10: Chapter 27 The following wind loads were determined using the method provided in ASCE 7-10: Chapter 27. Paragon Structural Consultants 31 | P a g e 6.4.4.1 Velocity Pressure Exposure Coefficient (Kz) A list of the velocity pressure exposure coefficients were determined from ASCE 7-10 based on the height of the building and the exposure category: Figure 6-G (ASCE Table 27.3-1): Velocity Pressure Exposure Coefficient, K z 6.4.4.2 Velocity Pressure (qz) The windward velocity pressures were determined up the height of the building using equations provided by ASCE 7-10. The leeward velocity pressure was taken at the roof of the building given by ASCE 27.3- 1: (6-7) 6.4.4.3 Wind Pressure (p) Wind pressures could then be determined from the velocity pressures, the gust effect factor, and the external pressure coefficients. For windward and leeward pressures: p = q G C p – q i (GC pi ) (6-8) For parapet pressure: p = qp (GC pn ) (6-9) Where q p is taken at the roof of the building and (GC pn ) is determined to be 1.5 (Section 27.4.5) 6.4.4.4 Final Wind Loads From the wind pressures, the lateral loads could be distributed to each level based on tributary widths. These lateral loads will transfer through the diaphragm to the shear walls and then into the footings. Paragon Structural Consultants 32 | P a g e Below is the excel spreadsheet used to compute the wind loads with the final loads determined at each level for wind blowing in both the transverse and longitudinal directions: Table 6-L: Wind Load Calculation Spreadsheet Loads from a wind blowing in the transverse direction: Figure 6-H: Transverse Wind Loads (Penthouse 1 and Penthouse 2) Loads from a wind blowing in the longitudinal direction: V (mph) Kd Kzt G GCf Cp GCpn Cp (Lee.) Assume internal pressures cancel 110 0.85 1.12 0.85 1 0.8 1.5 -0.3 Transverse Longitudinal T L w (k/ft) w (k/ft) w (k/ft) w (k/ft) 2.64 1.17 -1.48 -0.65 2.87 1.27 -1.48 -0.65 3.06 1.35 -1.48 -0.65 3.24 1.43 -1.48 -0.65 3.52 1.55 -1.48 -0.65 3.75 1.66 -1.48 -0.65 3.94 1.74 -1.48 -0.65 8.69 3.84 9.91 4.38 -7.27 -3.21 10.10 4.46 -7.27 -3.21 Transverse Longitudinal T (ft) L (ft) Level F (k) F (k) 231 102 2 64.26 28.38 3 72.41 31.97 Af2 (sf) Af2 (sf) Af1 (sf) Af1 (sf) 4 78.31 34.58 1750 546 357.489 346.656 Roof 55.59 24.54 Pent. 2 8.96 8.69 Pent. 1 43.87 13.69 17.0 42.9 43.7 Parapet (63 ft) 14.0 0.93 23.9 25.1 26.2 27.4 0.89 60 12.4 13.2 16.2 15.2 16.8 18.3 19.5 20.6 22.4 20 25 30 40 50 0.66 0.7 0.76 0.81 0.85 Height above ground level, z (ft) Exposure B Kz Velocity Pressure qz (psf) -31.5 -31.5 70 80 0.57 0.62 -6.4 -6.4 -6.4 0-15 25.1 37.6 -6.4 -6.4 -6.4 WINDWARD LEEWARD Wind Pressure p (psf) -6.4 Wind Pressure p (psf) 11.4 Paragon Structural Consultants 33 | P a g e Figure 6-I: Longitudinal Wind Loads (Penthouse 1 and Penthouse 2) 6.5 SEISMIC LOADS Seismic loads and drift limits were determined in accordance with ASCE 7-10. The following information was provided by the consulting geotechnical engineer, and was used to determine the spectral accelerations from the USGS website. Site Coordinates: 47.65278 o , 122.3053 o Soil Classification: Site Class “D” (Dense Sand) Risk Category: II Figure 6-J: USGS Provided Output for Spectral Accelerations Paragon Structural Consultants 34 | P a g e After the spectral accelerations were determined, the approximate fundamental period for the structure could be compared to the periods for the design response spectrum. Those values are calculated below. T o = 0.2 S D1 /S DS = 0.2*(0.499/0.859) = 0.116 s (6-10) T S = S D1 /S DS = (0.499/0.859) = 0.581 s (6-11) Values to find Approximate Period (ASCE 7-10 Table 12.8-2): C t = 0.02, x = 0.75 Approximate Fundamental Period (ASCE 7-10 Eqn. 12.8-7): T a = C t h n x =0.02(60) 0.75 = 0.431 s (6-12) The structure’s approximate fundamental period falls in between T 0 and T S on the design response spectrum, so the building was designed using the spectral acceleration S DS . Seismic Importance Factor (ASCE 7-10 Table 1.5-2): I e = 1.00 The response modification coefficient was determined based on the special reinforced concrete shear wall system. Response Modification Coefficient (ASCE 7-10 Table 12.2-1): R = 6 The total base shear for the structure was calculated using the seismic response coefficient shown below. This had to be checked, so as not to exceed equation 12.8-3 from ASCE 7-10 (for structures with an approximate period less than the long-period transition period). Base Shear (ASCE 7-10 Eqn. 12.8-1, 12.8-2): V = C s W (6-13) C s = S DS /(R/I e ) = 0.859/(6/1) = 0.143 < Cs = S D1 /T(R/I e ) = 0.190 OK (6-14) Below is the excel spreadsheet that was used to calculate the seismic weight at each level, and the total seismic weight of the building. A base shear could then be determined using this seismic weight and the seismic response coefficient. Finally, the base shear could be distributed up the height of the structure to determine the lateral load from each floor. Paragon Structural Consultants 35 | P a g e Vertical Distribution (ASCE 7-10 Eqn. 12.8-11, 12.8-12): (6-15) C vx = w x h x k /∑ w i h i k (6-16) Table 6-M: Seismic Weight Calculations Figure 6-K: Seismic Shears Distributed to Each Level of the Building Paragon Structural Consultants 36 | P a g e 6.6 LOAD COMBINATIONS 6.6.1 LRFD Load combinations used for member design include (ASCE 7-10 2.3.2): 1. 1.4D 2. 1.2D + 1.6L + 0.5(Lr or S or R) 3. 1.2D + 1.6(Lr or S or R) + (L or 0.5W) 4. 1.2D + 1.0W + L + 0.5(Lr or S or R) 5. 1.2D + 1.0E + L + 0.2S 6. 0.9D + 1.0W 7. 0.9D + 1.0E Load combinations expected to govern the design: 1.2D + 1.6L + 0.5(Lr or S or R) 1.2D + 1.0W + L + 0.5(Lr or S or R) 1.2D + 1.0E + L + 0.2S 6.6.2 ASD Load combinations used for foundation stability/design includes: 1. D 2. D+L 3. D+(L r or S or R) 4. D+0.75L+0.75(L r or S or R) 5. D+(0.6W or 0.7E) 6. D+0.75L+0.75(0.6W)+0.75(L r or S or R) 7. D+0.75L+0.75(0.7E)+0.75S 8. 0.6D+0.6W 9. 0.6D+0.7E 7 SAP2000 ANALYSIS Due to the complex nature of a concrete gravity system and the interactions between the beams and columns, SAP2000 was required for analysis. Using SAP2000 allowed for easier iterations of the design process, as changes could be easily made and it would continuously update. The following section discusses how PSC utilized SAP2000. 7.1 SYSTEM ORIENTATION In order to accurately determine the tributary area for design of slab, girders, and columns, PSC first had to decide on the orientation of the one-way slab system. Since post-tensioning was planned for the slab system, it made sense to choose the one-way orientation of the slab to run N-S. This was important for Paragon Structural Consultants 37 | P a g e two reasons: (1) the slab bays would all be consistent in length, so a single critical design (end-bay) would allow for a uniform slab to cover the entire floor space, and (2) in the E-W direction, there are two 44’ critical spans near the entrance of the building which would cause unacceptable deflections in a PT slab. By spanning the shorter 33’ length with PT slab, PSC could instead design simply reinforced girders perpendicular to the slab which are capable of spanning 44’. See the simple plan illustration below for reference: Figure 7-A: Critical Span Length for Elevated Floors (Typical) 7.2 TRIBUTARY AREAS The tributary area calculations were critical in finding the appropriate load path between structural members. It was also used to distribute the loadings on each floor to the beams and columns for the SAP2000 analysis. In general, the following steps were used to assemble the tributary area diagram: A. Determine the combined loading from SIDL, live load, and self-weight of the slab B. Divide the slab into tributary areas, whereby loads are going from slab to girders (one-way), slab to shear walls, and slab to perimeter beams (very small trib.) C. Divide the girders and perimeter beams to distribute the loads from girder to columns D. Take the column loads down into the footings, then into the soils 7.3 INITIAL MODELING Since the slabs were determined to run in the N-S direction, the girders supporting the slab needed to run in the E-W direction. Frames were then set up along the E-W architectural gridlines in SAP2000 and Paragon Structural Consultants 38 | P a g e initial sizes for the beams and columns were estimated. Below is a sample frame used to model the beam and column interactions along architectural gridline 2: Figure 7-B: Sample Frame at Architectural Gridline 2 from SAP2000 Connections between the beams and columns were modeled as fixed connections, and end length offsets were introduced to account for the rigidity in the beam-column connection. Supports were also modeled as fully restrained between the base columns and the footings. 7.4 PATTERN LOADING After the models were set up, loads were applied to each girder based on each respective tributary area, and loads were applied to certain joints to account for loads (such as exterior walls running in the N-S direction, and penthouse columns). Load combinations were also introduced to identify the controlling case for different members. To account for the uncertain nature of live loads, pattern loading was also considered. This allowed for the development of moment envelopes for each member, so that all possible combinations of live loads were accounted for. Below are two examples of how the pattern loading was applied to the frame at gridline 2: Paragon Structural Consultants 39 | P a g e Figure 7-C: Frames at Architectural Gridline 2 Showing Two Different Live Load Patterns One of the important considerations for the SAP analysis that must addressed is the likelihood of pattern loads being different on each floor. Although this specific analysis may create deviation in the range of worst case demand combination, the difference is not significant enough to warrant this method. With the worst case loads distributed to all of the floors, PSC engineers can develop a conservative design that is not excessively over-built. 7.5 SAP2000 OUTPUT Maximum moments and axial forces were obtained using the SAP2000 outputs from different load cases and used to design both beams and columns. Below is a sample output for the frame along gridline 2 with maximum moments and axial forces: Figure 7-D: Sample Output From SAP2000 Paragon Structural Consultants 40 | P a g e 8 ONE-WAY JOIST SLAB DESIGN The primary slab design for the More Hall MOB required several design iterations due to architectural and loading constraints placed on the design. Ultimately, a one-way post-tensioned joist slab was designed that carries floor live and dead loads to simply reinforced concrete girders, under the code provisions provided by ACI 318. The complete design process is detailed below. 8.1 DESIGN CONSIDERATIONS Several different types of floor slabs were considered in the slab design process. The primary factors considered in design included:  Span  Loading  Deflections  Efficiency  Constructability The most typical span between columns is roughly 33 feet, which necessitates a thoughtful design in order to efficiently span the length. While a slab design may efficiently use materials, if the formwork or reinforcing plans are exceedingly complicated or unusual, they may prove less practical. Additionally, if contractors are familiar with certain slab designs, they are likely to be preferred. The following floor types were considered: 8.1.1 One-Way Flat Slabs The simplest option which was first considered was a simple monolithic and uniform thickness, one-way slab, spanning the distance between girders. The advantages are that the length perpendicular to the span may be unlimited, and that a one-way slab requires fewer supports in comparison with two-way slabs. Additionally primary reinforcement is only needed in the direction of the span. While secondary temperature steel is placed to control cracks from shrinkage, it is ignored when determining the load- carrying capacity of the slab. Using a Magnel Diagram to analyze a one way slab for a 33 ft span, it was discovered that the slab would need to be 14 inches thick in order to satisfy stress limits and balance the self-weight and SIDL loadings. Also, this slab would transfer a self-weight load of 5.8 kips/ft to each girder. This load is enormous and impractical, and would require girders of significant size to support it. Paragon Structural Consultants 41 | P a g e Figure 8-A: A One-Way Slab on Beams (Image Courtesy of Concrete Floors, by Garber) 8.1.2 Two-Way Flat Plates and Flat Slabs A two-way slab would provide flexural reinforcing in both directions and allow load to be transferred to girders on all four sides, as seen in Figure 8.b. This would allow the slab to be thinner and lighter. As with one-way joist slabs, two-way flat plate slabs are easily constructed since the formwork is simple and minimal. Additionally two-way slabs are often the most efficient designs in terms of conserving story height, as there are no intermediary beams required. However, two-way flat plates are heavy because they do not use materials efficiently. Often two-way slabs require extra reinforcing or thickened sections around columns to minimize punching shear effects; these slabs are known as flat slabs. Furthermore significant amounts of prestressing are often required to minimize deflections. The advantages of two way flat plates lessen with large span lengths, and thus a two-way flat plate slab would not prove economical for the Civil MOB (which has spans up to 44ft in length). As flat slab solutions were not viable, beamed and joisted slabs were then considered: Paragon Structural Consultants 42 | P a g e Figure 8-B: A Two-Way Flat Plate Slab (Image Courtesy of Concrete Floors, by Garber) 8.1.3 Two-Way Slabs on Beams and Waffle Slabs A two-way flat slab on beams is designed such that loads are transferred to beams spanning between columns on all sides, as depicted in Figure 8-C. A waffle slab refines this concept by adding intermediate beams between columns. These slabs perform excellently given deflection constraints, are efficient in their use of material and height, and can be architecturally elegant. However these slabs come at the cost of constructability. While standard formwork is available for waffle slabs in the form of joist pans, they are labor intensive due to precise specifications for prestressing strand, reinforcing bar, stirrup, and joist pan placement. At 15 feet, the Civil MOB has a tall and spacious floor height, thus the benefit gained from the slightly shorter slab height due to a waffle slab are inconsequential. Additionally two-way waffle slabs are not commonly used, and thus their construction is a less familiar process for laborers. While a waffle slab could be designed for all spans necessary for the Civil MOB project, the additional construction costs outweigh the savings due to an efficient use of materials. Paragon Structural Consultants 43 | P a g e Figure 8-C: A Typical Waffle Slab (Image Courtesy of Class Connection) 8.1.4 One-Way Joist Slab When intermediary beams are added to a one-way slab design they are referred to as joists. These joists are cast with the floor slab, and create a one-way joist slab as depicted in Figure 8-D. The addition of joists provides a means of creating a large moment arm, without the inefficiency of a flat slab. These slabs may be factory precast, or cast in place using joist pans. Formwork for these slabs is readily available. One-way joist slab are more easily designed and constructed than waffle slabs because primary reinforcement and pre-stressing strand runs in only one direction. This simplifies calculations of stresses, deflections, and creep. Additionally they are more commonly used in practice, thus construction is more familiar. Paragon Structural Consultants 44 | P a g e Figure 8-D: A One-Way Joist Slab (Image Courtesy of Concrete Floors, by Garber) 8.1.5 Selection Based on the previous considerations, a one-way joist slab was selected as the best design. Joist slabs may be readily designed to span the 33ft length required, and require no intermediary supports (regardless of bay length). The joist allows for a large depth and thereby moment arm, which permits the span to support heavier loads. The deep joist also allows for a more flexible tendon profile, as the banded tendons can move up and down within the joist. This flexibility allows the slab to balance dead load, to minimize camber and deflection, by varying the location of the prestressing. Finally, the availability of formwork and the relative ease of construction of one-way joists, in comparison to waffle slabs, both streamline the construction process and allow for a less labor-intensive design. Having established the structural slab type, the slabs were then designed based on stress and strength calculations. 8.2 DESIGN PROCESS 8.2.1 Construction Method Precast joists may be constructed as tees and double tees, or hollow core sections. The advantages to precasting include mass production to minimize costs, better quality control, and simplified prestressing (by utilizing pretensioning). However, precasting requires that sections be transported on site via truck, and due to the size of the sections required and the restraints of the site location, these precast options were dismissed. Thus the slabs for the Civil MOB were designed to be cast in place slabs. When joists are cast in place, they are formed through the use of industry standard reusable joist pans, which are readily available for construction use. While there are multiple manufacturers and suppliers of these joist pans, their dimensions are standardized. Cast in place slab design should be done in accordance with available joist pans for constructability. Joists come in two primary widths, namely 30” and 20”. While both larger and smaller sizes are available, these two categories comprise the bulk of the joist pans commonly used. These forms are aligned end to end and separated by a specified distance to create the joist profile required. The forms are supported by wood planks on stringers which are shored up to a specified floor height. Once in place, tendons and reinforcing steel are placed within the forms. Finally Paragon Structural Consultants 45 | P a g e concrete is poured, and after curing, the forms are stripped and reused. A schematic of this setup is depicted in Figure 8-E: Figure 8-E: Schematic Diagram of Typical One-Way Joist Slab Construction (Image Courtesy of Concrete Construction) 8.2.2 Section Properties 8.2.2.1 Design Assumptions In accordance with ACI, the slab is designed as a prestressed flexural member under class U conditions, in accordance with ACI Chapter 18.3. Table R18.3.3 summarizes the design requirements for various concrete classes. Class U was chosen because the design is meant to be operating within cracking stress limits. Table 8-A (R18.3.3 ACI): Serviceability Design Requirements Paragon Structural Consultants 46 | P a g e Slab design adhered to the ACI Moment Coefficient method found in ACI 318 Section 8.3.3. This method of analysis conservatively approximates the moments and shears as opposed to performing a complete slab analysis. These are strictly used for slab design, and do not apply to column design (which requires a frame analysis). The requirements for use of this method are reproduced below: Figure 8-F: ACI Section 8.3.3 For this design, the requirements of using the ACI Moment Coefficient method are all satisfied. The Civil MOB has seven 33 foot spans (8.3.3a and 8.3.3b), and is under uniformly distributed loads throughout (8.3.3c). The unfactored live load, at 240 lb/ft, is a fraction of the unfactored dead load at 323 lb/ft. (8.3.3d). Finally members are prismatic, as the cross-section remains constant along the span (8.3.3e). Having satisfied all requirements, the ACI Moment Coefficients were then used as design criteria. The specific values used in design are the following:  Positive Moment  End Span – Discontinuous end integral with support -  Interior Span -  Negative Moment  Exterior Support – Support is a column -  Note: Though the majority of the slab is supported by girders spanning between columns, some portion of the slab runs into the columns, and so this value was selected to be conservative.  First Interior Support – More than two spans -  Other Interior Supports -  Shear  First Interior Support -  Other Interior Supports - These values were determined from ACI 318 Section 8.3.3. Paragon Structural Consultants 47 | P a g e A diagram depicting the moments used in design is given in Figure 8-G: Figure 8-G: Moments Used in Design, by Location, According to ACI Section 8.3.3 8.2.2.2 Joist Size The strength of the slab is determined by its section properties. When more strength is required, joists can be made deeper, or the spacing between joists can be reduced. Initially a slab height of 4.5 inches and a joist spacing of 2 feet on center (using 20” joist pans) were selected based on previous effective designs. However it was determined that there would be insufficient width to fit the shear reinforcement and banded tendons were needed to balance the load. The design was modified to use joists spaced 3 feet on center, using 30” joist pans. Once this was selected, it was necessary to determine the required depth of the joists. The available dimensions for 30” wide joist pans are depicted in Figure 8-H: Figure 8-H: Available Depths of a Standard 30” Joist Pan (Image Courtesy of CECO Concrete) Based on the moment coefficients, the critical case moment exists over the first interior column. This negative moment, equal to , was the value used in design. Although other values are seen over other columns throughout the building, this value controls the joist size design of the slab. While other slabs could be designed throughout the building in accordance with the differing moments, these would require different formwork, and thus the renting of different joist pans. For simplicity in design and construction, a single slab was designed for use across the building. To account for the different stress patterns, the tendon profile was adjusted (rather than changing the slab size). Paragon Structural Consultants 48 | P a g e 8.2.2.3 Load Balancing Load Balancing is the practice of choosing a tendon profile which creates a prestressing force, in order to balance the external loads placed on the slab. The tendon sag creates an upward force exerted across the beam. When placed correctly, this upward force is equal and opposite to that of the equivalent gravity loads. This results in zero net moment and thus, zero net curvature. The only remaining stresses are uniform throughout the cross-section. This effect is shown in Figure 8-I: Figure 8-I: Schematic of Load Balancing Effects It is common practice to balance 80 percent of dead loads placed on the beam. Using a Magnel Diagram, superimposed with balanced stresses due to 80 percent of the dead load, a tendon profile was created in order to properly balance the slab throughout the building. 8.2.2.4 Stress Analysis When designing prestressed members, stress limits are typically analyzed first under service conditions, then strength requirements are checked using factored loads (to ensure the design is satisfactory). The Magnel Diagram is a visual representation of the stress limits within a beam or slab, and is used to simplify the design process. The diagram is used to determine which stress limits control the design, and to more easily determine the appropriate cross section and prestressing force. The Magnel Diagram plots four different stress limits which provide a linear relationship between the eccentricity of the tendon profile (e p ) and the stress due to prestressing (1/f 0i ). The four inequalities are given below: Paragon Structural Consultants 49 | P a g e (8-1) (8-2) (8-3) (8-4) When these four inequalities are plotted on the same graph the designer is able to adjust various parameters to determine an appropriate design for a slab. Using an excel spreadsheet, a Magnel Diagram was created to determine the height of the joists. The height was varied until a balance of joist depth and an appropriate amount of prestressing required to balance the load was found. It was concluded that a joist depth of 16”, a joist width of 6”, and a center to center spacing of 36” would be sufficient for all design cases. Three 0.5” diameter tendons (sheathed to 0.62”) are banded in each joist, with a total prestressing of 85 kips per rib. The Magnel diagram used to determine the most critical design is given in Figure 8-J. The shaded area indicates the combinations within the concrete stress limits. This design was then repeated throughout the structure for simplicity. Paragon Structural Consultants 50 | P a g e Figure 8-J: Magnel Diagram for the Slab above the First Interior Support 8.2.3 Code Requirements Once a working section was established, it needed to be checked under the special provisions included in ACI 318 Section 8.13, which places additional constraints on joist design. The requirements are detailed in the following sections. 8.2.3.1 ACI 318-8.13.2 Rib width must not be less than 4”, and the depth must not be more than 3.5 times the rib width (see figure 8-K below). The slabs used throughout the Civil MOB utilize joists which are designed at a minimum width of 6”, and have a depth of 16”. The depth to width ratio of the joists is 2.7, which is within the code requirements: Figure 8-K: ACI 318 Section 8.13.2 8.2.3.2 ACI 318-8.13.3 Code requirements set the clear spacing between ribs to be no more than 30”. Clear spacing utilized in the Civil M.O.B. is set at exactly 30”, the maximum allowed by the ACI code: Figure 8-L: ACI Section 8.13.3 8.2.3.3 ACI 318-8.13.6 The ACI code places special restrictions on joists utilizing removable forms. Slab thickness is limited to of the clear spacing between joists, and must also be at least two inches. Additionally, temperature and shrinkage reinforcement must adhere to the requirements found in section 7.12. The slab thickness is 3” for the Civil M.O.B. on all elevated decks. This value exceeds both the 2.5” requirement specified by the clear spacing ratio and the 2” minimum requirement. Normal reinforcement satisfies requirements set by 7.12, and is detailed in a later section. Paragon Structural Consultants 51 | P a g e Figure 8-M: ACI Sections 8.13.6.1 and 8.13.6.2 8.2.3.4 ACI 318-7.7.2c Clear cover for cast in place prestressed concrete slabs and joists is limited to ¾” when not exposed to earth or weather, as is the case for the Civil MOB. Figure 8-N: ACI Section 7.7.2 Paragon Structural Consultants 52 | P a g e 8.2.4 Fire Rating The minimum slab thickness necessary to achieve a two hour fire rating under the 2012 International Fire Code Section 721.2.1.1 for carbonate concrete construction is 4.6”. IFC Table 721.2.1.1 summarizes the code requirements and has been reproduced below. Table 8-B: Minimum Equivalent Thickness of Cast-In-Place or Precast Concrete Slabs Through the utilization of 7/8” gypsum panels in the ceiling suspended below the floor slab, a fire rating can be achieved without the need for a 4.6 inch slab under the provisions in IFC Section 721.2.1.4: SLABS WITH GYPSUM WALLBOARD OR PLASTER FINISHES: The fire-resistance rating of cast-in-place or precast concrete slabs with finishes of gypsum wallboard or plaster applied to one or both sides shall be permitted to be calculated in accordance with the provisions of this section. Utilizing the provisions of IFC Section, the floor slab may be reduced to up to half of the depth specified in Table 721.2.1.1. The Civil MOB slab was reduced in depth to 3” which is greater than the value of 2.3” required. Modification of the slab thickness significantly reduces the self-weight of the slab section. This reduction would require at least 40 minutes of fire-resistance from the gypsum panels. Selection of specific finish type may be made from IFC Table 721.2.1.4(2) which is listed below: Paragon Structural Consultants 53 | P a g e Table 8-C: Fire Resistivity of Finish Materials 8.3 FINAL DESIGN 8.3.1 Elevated Decks Based on the requirements and analysis discussed in section 8.2, it was determined that a slab design with 6” wide and 16” deep joists at 3 feet on center with a 3” topping slab would be sufficient under stress analysis and code requirements. A diagram of the design is given in figure 8-P: Figure 8-O: Slab Section Detail for all Floors Paragon Structural Consultants 54 | P a g e 8.3.1.1 Strength Checks Strength requirements must be computed as an additional design procedure for prestressed concrete members. Calculations utilize the following equations. (8-5) (8-6) (8-7) ( ) (8-8) The value for d p was computed assuming the minimum cover as specified in ACI 318 Section 7.7.2c and a #4 stirrup. The factored nominal moment capacity of the section was found to be 83.25 kip-ft. Ultimate maximum factored moment demand was computed at 76.34 kip-ft. Sample calculations of this process are available in Appendix A. 8.3.1.2 Temperature and Shrinkage Reinforcement Despite the load balancing procedure described in section 8.2.2.3, thermal and shrinkage effects still occur in the slab. In order to prevent thermal and shrinkage cracks from forming in the concrete, additional reinforcement is required. ACI Section 7.12.2.1 governs the design of this reinforcing steel, and is given in Figure 8-P: Figure 8-P: ACI 318 Section 7.12.2.1 Paragon Structural Consultants 55 | P a g e By selecting grade 60 rebar, the minimum area of steel required for temperature and shrinkage reinforcement is given by the following equation: The A c mentioned refers to gross slab area, and does not include the area of the rib. For a given 1 foot section of the Civil MOB slab, the minimum require reinforcement is calculated as follows: ( ) Spacing requirements for the temperature and reinforcing steel are given in several sections in the ACI 318 code (each requirement must be checked). ACI 318 Section 7.12.2.2 provides general spacing requirements for all slab types, as listed in Figure 8-Q: Figure 8-Q: ACI 318 Section 7.12.2.2 Since the Civil MOB slab has a thickness of 3”, the minimum of five times the thickness at 15 in governs the maximum reinforcement spacing. ACI 318 Section 10.5.4 lists special provisions for structural slabs, as displayed in Figure 8.R: Figure 8-R: ACI 318 Section 10.5.4 Under this requirement, the spacing maximum is listed as three times the thickness, which further limits the spacing to 9”. The final requirement is given in ACI 318 Section 10.6.4, shown below in Figure 8-S: Paragon Structural Consultants 56 | P a g e Figure 8-S: ACI 318 Section 10.6.4 Using ACI equation 10-4 and values for clear cover (c c ) of 0.75” and f s at 40,000 ksi, the spacing is computed using the two equations listed as follows: ( ) ( ) ( ) ( ) While the minimum of these results is 12”, the spacing limits are still governed by ACI Section 10.5.4 at 9”. If No. 4 bars are used at the maximum recommended spacing of 9”, this results in a reinforcing area of .266 in 2 / ft. This value is significantly larger than the 0.0648 in 2 /ft detailed above. Rather than using smaller bars, a selection of welded wire fabric was made. Using size W2.9 at 4” wire fabric gives a reinforcing area of 0.087 in 2 /ft, which meets the reinforcing requirement. 8.3.1.3 Shear Reinforcement One way joists are very efficient at resisting shear, due to their section properties. Accounting for this, ACI 318 Section 11.4.6.1c waives the minimum shear reinforcement requirement such that is not required, as described in the following figure: Paragon Structural Consultants 57 | P a g e Figure 8-T: ACI 318 Section 11.4.6.1 Despite these recommendations, the shear capacity for the slabs was checked to ensure proper resistance. The shear demand is given by ACI 318 Section 8.3.3, and is most critical at the first interior support. The recommended ACI equation is given as: (8-9) Computed a distance d away from the support, this value was calculated to be 9725 lbs. The nominal shear strength provided by the concrete, V c is allowed to be increased by 10% from typical values using the equations from ACI Chapter 11. This increased value is used in the calculations of shear capacity for the slab. Figure 8-U: ACI Section 8.13.8 The shear capacity of the concrete is found utilizing ACI equation 11-3 from ACI 318-11.2.1.1: √ (8-10) Paragon Structural Consultants 58 | P a g e When multiplied by 1.1 per the ACI 318-8.13.8 provision, the shear capacity of the concrete was found to be 18,020 lb using this formula. This value is greater than the 9,725 lb demand, and thus the recommendation to waive the requirement of minimum shear steel is justified. 8.3.1.4 Additional Reinforcement ACI requires a minimum area of bonded reinforcing steel for all flexural members with unbonded tendons in ACI 318 Section 18.9.2. Following the provided equation, the area of flexural steel was computed to be 0.31 in 2 in the joist cross section, and 0.51 in 2 in the top slab cross section. To satisfy this requirement, two No. 4 bottom bars (which together have an area of 0.4 in 2 ) were added on bottom at midspan, (total length 2L/3 centered at midspan). Additionally, No. 4 bars at maximum spacing of 9” were added to the top slab to extend L/3 out from the girder lines. While these No. 4 bars alone are more than sufficient to satisfy the requirements of Section 18.9.2, they are used for their simplicity in construction and high availability. Figure 8-V: ACI 318 Section 18.9.2 8.3.1.5 Tendon Profile The tendon profile varies throughout the slab in order to correctly balance the external loads. This profile was determined by using a Magnel diagram, and computed using the correct ACI moment coefficients from ACI 318 Section 8.3.3. While leaving the section profile and the effective post tensioning stress unchanged, the location of the tendon is adjusted in accordance with the changing moments. This profile is demonstrated in Figure 8.W: Figure 8.W: Typical Tendon Profiles Showing Parabolic Designs Based on Moment Diagrams Paragon Structural Consultants 59 | P a g e The depth of the tendon profile was computed at each midspan and end, as seen in the post-tension plan drawings. These dimensions are measured from the bottom of the slab, and are summarized in Table 8-D: Table 8-D: d c Values for the Slab Tendon at Select Locations LOCATION d c (in) Exterior Column 16.0 End Midspan 9.0 First Interior Column 17.5 Other Midspans 9.5 Other Interior Columns 17.0 Because tendons span the length of the building, frictional losses are considerable. As the tendons travel in their duct, they lose stress due to friction because the tendon rubs along the side of the duct. These losses equate to 75 percent less prestressing force, varying from live to dead ends of the strand. If all tendons are stressed in the same orientation, the stress variation at either end of the building is significant. To minimize this disparity, tendons should be sequentially stressed at opposite ends to better equilibrate the frictional losses throughout the slab. This sequence is to be repeated throughout the building, and is displayed in Figure 8.W. Tendons marked in red are the live pulling ends. Figure 8-W: Alternating Tendon Stressing Schematic 8.3.2 Roof Slab While a design for a more slender roof slab system was designed, it utilized 14” joists. The design was not significantly different from the elevated floor slabs, apart from the shorter joist height. However Paragon Structural Consultants 60 | P a g e construction of these joists would require additional, different sized joist pans. It was determined that using the same design for the elevated decks on the roof slab would be simpler for constructability and still conservative. Thus the design provided for floors 2-4 will also be used on the roof. 8.3.3 Slab on Grade The slab on grade is designed based on geotechnical concerns and loading patterns. The soil is stiff and sandy, minimizing the flexural effects in the slab. Loading for the slab on grade is limited to 120 psf of uniformly distributed, combined service loads. Additionally, satisfactory historical performance has been observed for slabs with similar conditions and loading requirements (designed at 4” thick). Under these considerations, the Civil MOB was designed with a 4” slab on grade. The placing of reinforcing steel is in accordance with ACI 7.12.2.1, which governs shrinkage and temperature reinforcement for slabs. Control joints will be saw-cut 1.5" deep along column gridlines and at centerlines between columns, with each panel roughly 16' x 16' square. This is to limit the cracking in the concrete slab to designated locations. 9 GIRDER DESIGN 9.1 DESIGN CONSIDERATIONS Similarly to the design of the slab, the primary factors considered in the design of girders included:  Span  Loading  Deflections  Efficiency  Constructability 9.1.1 Girder Spanning Direction In the sequence of Civil MOB's load path, the girders transmit the forces from the one-way joist slabs to the columns. Often, girders span in a bay's longer dimension and the slab connected to the girders span in a bay's shorter dimension. Civil MOB's PT slab spans in the N-S direction, and the bays are all 33 feet long; whereas, the E-W perimeter spans are 32, 26, and 32 feet in length. Though it may seem that girders should span in the N-S direction, the building's longest spans are 44 feet in the E-W direction, located at the lobby entrance of the building. 9.1.2 Reinforcement Alternatives In general, it is preferable that post-tensioned strand run in only one direction of the building. This is to prevent complex calculation of the interactive forces that result from Poisson's effect, when the building experiences compressive forces in perpendicular directions. These resultant forces can lead to severe Paragon Structural Consultants 61 | P a g e cracking in slabs. To prevent such cracking, it was decided to avoid placing post-tensioned strand in the E-W direction. To avoid using post-tensioned girders, the girders were designed as reinforced concrete members running in the E-W direction. A particular advantage of Civil MOB is the large floor heights, having an average height of 14’-8”. A common concern for reinforced concrete girders is the possibility of large member depth. However, with the large floor heights, deeper girders were not an issue. 9.1.3 Minimum Depth by Deflections The girders were designed to make use of ACI Table 9.5(a). This table specifies that there is a minimum thickness for girders/beams where the deflections do not need to be checked. PSC was able to use this table because the floors had enough clearance to allow for this minimum thickness of the girders to be achieved. Below is the table from ACI that was used. The girders were considered one end continuous in the outside bays and two ends continuous in the middle bay: Figure 9-A (ACI 9.5-a): Minimum Thickness of Nonprestressed Beams 9.1.4 Deflection Limits Beam deflections are a crucial part of analysis that must be checked based on the ACI 318-11 code and PCI Manual, Section 4. Beam deflection limits are: 1. Live Limit = L/360 - floors not supporting or attached to nonstructural elements and likely to be damaged by large deflections (Table 9.5A, ACI) 2. Total Limit = L/480 - roof or floor construction supporting or attached to nonstructural elements likely to be damaged by large deflections (Table 9.5A, ACI) By designing the flexural members (slabs and girders) to fall within these ACI limits, PSC engineers were able to avoid calculating deflections for each member. 9.1.5 Effective Width For girders built integrally with the slab, it is permitted to use an effective width from the slab in the flexural stiffness of the girder. These effective widths were determined using ACI section 8.12 for T- beam construction. Paragon Structural Consultants 62 | P a g e Figure 9-B: ACI requirements for effective widths For all girders, the effective width was limited by the thickness of the slab. 9.2 DESIGN PROCESS 9.2.1 Iterative Calculations The design process of the girders was an iterative one, utilizing SAP2000 and Excel. SAP2000 was used to develop the demand on the girders, while Excel was used to design members capable of providing sufficient capacity. The Excel spreadsheet assisted the iterative process because it could quickly calculate member strength as the member geometry and applied moments were updated. Moment values were obtained from the continuously updated SAP2000 model and added into the spreadsheet. The spreadsheet utilized calculations as follows: (9-1) ( √ ) (9-2) (9-3) (9-4) With an area of steel obtained, A s , the bar choice and number of bars were selected for each girder. As beams and girders were designed, their dimensions would be slightly modified, thereby changing their self-weight (SW) loading. This SW was then inputted into SAP2000, the resultant moment was collected, Paragon Structural Consultants 63 | P a g e and a new iteration of beam or girder was designed. This process was repeated until the demands and capacities converged on a given member dimension and reinforcement layout. 9.2.2 Shear Reinforcement Shear reinforcement is designed based on of ACI 318-11 code, which specifies both an upper and a lower limit for area of steel required. The upper and lower limits are used to make certain that, in the event of an overload, failure would be ductile. The difference here is that minimal shear reinforcement may let the concrete fail suddenly in tension, whereas too much shear reinforcement may let the girder fail when the crushing point of the concrete is reached. The design procedure was carried out as follows: Figure 9.c: ACI 11.2.1.1 (9-5) ( ) (9-6) ( ) ( √ ) (9-7) ( ) (( ) ( ) ) (9-8) ( ( ) ( ) ) (9-9) Shear reinforcement was designed utilizing single-hoop #4 ties. FINAL DESIGN This iterative process was performed for each beam type to determine beam dimensions and reinforcement selection and layout: Paragon Structural Consultants 64 | P a g e Table 9-A: Concrete Beam Schedule CONCRETE BEAM SCHEDULE MARK Size Width X Depth (in) Bottom Bars Top Bars Stirrups Continuous Continuous B1 16" x 22" (3) #9 (6) #9 #4 @ 11" B2 16" x 20" (2) #9 (5) #9 #4 @10" B3 16" x 34" (5) #9 (7) #9 #4 @ 16" B4 16" x 20" (2) #9 (2) #9 #4 @ 10" B5 20" x 22" (2) #9 (4) #9 #4 @ 11" B6 18" x 26" (6) #9 (12) #9 #4 @ 16" B7 12" x 18" (4) #8 (8) #8 #4 @ 14" B8 12" x 12" (4) #8 (6) #8 #4 @ 6" B9 12" x 16" (4) #8 (6) #8 #4 @ 8" B10 12" x 30" (2) #7 (2) #7 #4 @ 8" As seen in the Concrete Beam Schedule, Table 9-A, beam designs varied throughout the building per loading differences. See the structural drawing package for locations of beam marks throughout each floor plan. 9.2.3 Bar Development The development of flexural tension reinforcement in the girders was performed using ACI chapter 12. Once the stirrups for the girders were determined for shear strength, the development lengths for the flexural reinforcement could be calculated. These lengths were determined using ACI equation 12-1: ( √ ( ) ) (9-10) Where K tr is calculated using ACI equation 12-2: (9-11) Paragon Structural Consultants 65 | P a g e After the development lengths were calculated, the locations of the cut offs for the rebar needed to be checked. To find the theoretical cut off point, the capacity of the girders was reduced to account for less tension steel. For all girders, at least two bars were carried along the top and bottom per ACI section 21.2.2. Only the 44’ girder had 3 bars carried through the cutoff point, to account for ACI section 12.11.1. The capacity of the bars that carried through was checked with the demand along the girders to find where the cutoff point. This theoretical cutoff point (TCOP) was then modified using stipulations in ACI chapter 12 to find the actual cutoff points. One final check was to make sure that the flexural reinforcement was not cutoff in an area where the shear demand was greater than two-thirds the shear capacity per ACI 12.10.5.1. After all of these checks, the final cutoff points were determined for the flexural reinforcement. Sample calculations for the cutoff points can be found in Appendix A, and visual examples can be found in the girder drawings. 10 COLUMN DESIGN 10.1 DESIGN CONSIDERATIONS Columns are designed to carry axial force, bending moment and shear. For the Civil MOB, the building was designed based on the gravity loads applied to each floor. In buildings, the columns around the perimeter have relative small tributary area; therefore, they are designed for both bending moment and axial force. However, for Civil MOB, the interior columns controlled because of the bigger tributary area. They were designed for axial force and then checked for moment. Rectangular columns were chosen for Civil MOB because they fit better to rectangular shear and partition walls. They contain longitudinal bars to resist moment and compression and transverse reinforcement to confine the core concrete and resist shear. The longitudinal bars were designed for a 1-3 percent reinforcement ratio. The ties required are No. 4 ties for No. 11 or smaller longitudinal bars. The column system was designed as a seismic frame system, so additional transverse reinforcement was added to confine the core and prevent inelastic reversed bending. Interaction diagrams are widely used for designing columns because no equations exist that relate moment and axial force at failure to the column size and reinforcing pattern. The axial and bending strengths of columns are interlinked because both loadings produce axial stress in the concrete and longitudinal bars. Many different combinations of axial force and bending moments that will cause failure can be drawn on a plot. The curve connects all of the combinations (M, P) that cause failure. Any point (M, P) closer to the origin, corresponds to a loading that will not cause failure. As long as the column design falls within the failure curve, it is acceptable. 10.2 DESIGN PROCESS The Civil MOB gravity design was an iterative process that started by finding the demand in SAP2000. The building was first divided into eight bays, according to the architectural reference lines. The appropriate loads, which include slab weight, girder weight, dead, live and snow load, were applied. After running the program, the loads were found from the load combinations listed earlier. The max load was found using load combination 1.2D + 1.6L +0.5S on the first floor column of the fifth architectural Paragon Structural Consultants 66 | P a g e reference line. This makes sense because line 5 has one of the longest girders attached which contributes to the column with the most loading. Figure 10-A: Example from the Architectural Plans Showing the Frames Used to Model Next, the preliminary column sizes were found using a limit on demand. The original ACI limit on demand is P u = φ0.85f’ c A g , where φ=0.65, f’ c is the concrete strength, and A g is the gross area for the column. PSC used P u = 0.4f’ c A g to keep axial load less than 40 percent of the capacity and to ensure there would not be a compression failure. Using this equation, the preliminary column size was found to be a 22” by 22” square. See Appendix A for calculations. After finding the preliminary column size, each load and moment combination was checked using an interaction diagram. For example, a load was entered into the interaction diagram, and the appropriate amount of rebar was entered to maintain the demand. The rebar capacity was also checked through moments; if the moment caused by the longitudinal bars was greater than the demand that accompanied the load, then the reinforcement was acceptable. The reinforcement ratio had to be between 1-3 percent because it helps reduce congestion in the beam-column joint. Paragon Structural Consultants 67 | P a g e Figure 10-B: Example of the Interaction Diagram Used (Red Dot Represents Combination Test) Once the longitudinal reinforcement was found, the next step was to find the hoop configuration and tie spacing. PSC referred to Chapter 21 of the ACI Manual – Earthquake Resisting Structures, then found the appropriate tie spacing and hoop configuration based on Section 21.3. These requirements applied to intermediate moment frames, forming part of the seismic-force-resisting system. While the building frame does not act as an intermediate moment frame, use of these requirements is conservative. The ties used were No. 4 in size for our reinforcement. ACI states that the ties need to be at least No. 3 for longitudinal bars No. 10 or smaller, however using No. 3 ties is not common. Following ACI 21.5.3.2, hoops shall be provided at a spacing of s 0 over a length of l 0 measured from the joint face. The spacing of s 0 shall not exceed the minimum of d/4, six times the diameter of the smallest primary flexural reinforcing bars, and 6”. Length l 0 shall not be less than the max of one-sixth the clear span of the column and the maximum dimension of the column. Using ACI 21.3.5.4, the spacing of the transverse reinforcement outside of length l 0 should conform to ACI 21.13.3.2, which states that members with factored gravity axial forces exceeding A g f’ c /10 shall not exceed the smallest of six diameters of the smallest longitudinal bar enclosed and 6”. Since the majority of the loads applied exceed the equation mentioned previously, the spacing follows this ACI rule. The area required for hoop configuration was calculated by the equation given in ACI 21.6.4.4 as the total area of the hoop reinforcement should not be less than , where s is the spacing of ties, b c is the width of the column, f’ c is the concrete strength, and f yt is the yield strength of the transverse bar. The bending of the hoops and the extension of the hoops need to be at least 6 times the diameter of the hoop being used. See Appendix A for calculations. Paragon Structural Consultants 68 | P a g e Figure 10-C: Image Representing the Hoop Configuration of a Column The last step for column design is splicing. According to common practice for an intermediate moment frame, PSC decided to splice halfway up the column. Following ACI 12.17 Splice Requirements for Columns and 12.16 Splices of Deformed Bars in Compression, the compression lap splice length should be 0.0005f y d b for f y of 60000 psi or less. Once the lap splice length is confirmed, the slope of the inclined portion of the offset bar is found by ACI 7.8.1.1 as the slope should not exceed 1/6. 10.3 FINAL DESIGN PSC determined that the final design is a 22” by 22” column with three types of reinforcing: 8 No. 8’s, 8 No. 9’s, and 8 No. 10’s. Each column is confined with 4 No. 4 hoop ties at 8” spacing within the joint, occurring for a length of l 0 =30 inches (from the joint face in both directions). The spacing increases to 16”, then decreases back down to 8” again, when the columns need to be spliced. The splicing lengths are as follows: for No. 8 bars – 30”, No. 9 bars – 34”, No. 10 bars = 38.1”. Table 10-A: Table Defining the Splice Lengths for the Bars Used in Construction Bar Splice length No. 8 30” No. 9 33.84” = 34” No. 10 38.1” = 38” Paragon Structural Consultants 69 | P a g e Figure 10-D: An Example of the Tie Spacing and Splicing in a Typical Column Figure 10-E: Typical Column Section for Floors 1-4 Paragon Structural Consultants 70 | P a g e Figure 10-F: Column Schedule for Civil MOB 11 SHEAR WALL DESIGN 11.1 ANALYSIS There are many ways to determine the distribution of lateral loads to the wall. The main methods used by PSC were the lateral forces method and stiffness method. The lateral force method calculates the shear forces induced in each wall due to their lateral forces, V x and V y . Since there is an eccentricity between the center of mass (CM) and center of rigidity (CR), the total lateral force V x would be distributed to all walls in proportion to their stiffness. There will also be an additional force generated by torsion, as a result of this eccentricity. The two expressions for shear found in a wall that has its strong axis perpendicular to the lateral force V x include: [ ∑ ] (11-1) [ ] ( ) (11-2) I yj : the moment of inertia of the wall. I yn : is the sum of the moment of inertias that have their strong axis perpendicular to the lateral force V x . T x , T y : the torsion resisted by each wall in the floor plan. Paragon Structural Consultants 71 | P a g e The torsion resistance is related to the lateral stiffness of the wall in terms of bending about its strong axis, multiplied by the distance in the x or y direction to the CR, as measured perpendicular to the weak axis of the wall. For Equation 11-2, α = 0.3 to reflect the low probability of having the maximum lateral forces acting simultaneously in both directions. This is called the response-spectrum procedure. Response-spectrum analysis is used to determine the total design displacement and the total maximum displacement that will include 100 percent of ground motion in the critical direction (the direction in which the lateral force is applied) and 30 percent of the ground motion in the horizontal direction. The max displacement can be calculated as the sum of these two displacements (ASCE 7). The torsional stiffness, K t , is calculated for all walls in the floor system and can be calculated as the sum of the torsional resistance from each wall multiplied by their distance to the CR. This stiffness can be expressed as: ∑ ∑ (11-3) Once the results from Eq. 11-1 and Eq. 11-2 are combined, the total shear resisted by walls with their strong axis perpendicular to the lateral force V x will be obtained. Walls that have their strong axis perpendicular to the lateral force V y will go through a similar process. See Appendix A for calculations. The shear in each wall for the Civil MOB was found by this lateral force method and then checked with the stiffness method. After the shear forces were found, the walls were designed. In terms of the stiffness method, the main idea is to use the stiffness of each wall to figure out how much shear is placed on each wall (based on displacement). The main equation for this method is: , where P is the force applied, k is the stiffness, and is the displacement of the wall. However, there are other factors to this equation. The seismic force is applied at the center of mass, which is not at the same point as the center of rigidity. Because the centers act in separate locations, there will be a moment applied on the building, which results in torsional effects. As a result, the building is subjected to load and moment, which results in a rotation/displacement. Another important aspect to consider is the eccentricity between the center of mass and center of rigidity. This results in an incidental and accidental eccentricity. Incidental eccentricity is the difference between the center of mass and center of rigidity. The accidental torsion is taken as 5 percent of the maximum building dimension perpendicular to the force vector under consideration (ASCE 7). Basically, the moment arm is the length of the eccentricity (incidental and accidental) that will result in the worst combination. The equation used for the stiffness method is essentially a matrix: [ ] [][ ] where P is the total lateral load applied on the building, M is the eccentric moment which will be applied on the center of rigidity, is the displacement of the building, and θ is the rotation due to the torsion. The stiffness of the system was determined by calculating the deflection limit, which for a multi-story building is as follows: (11-4) Paragon Structural Consultants 72 | P a g e Therefore making the stiffness: (11-5) Where h is the height of the wall, A w is the wall area (t x l w ) and I is the flexural moment of inertia. For walls with aspect ratios (h w /l w ) less than 3, the effect of shear deformations become more significant; therefore, it is recommended to use a modified moment of inertia to reflect the importance of shear deformation. The value used is a recommended equation from the PCA Design Handbook: (11-6) Where h is the height of the wall, A w is the wall area (t x l w ) and I x is the strong axis moment of inertia. At this point, the stiffness was found for each wall. Using sum of forces and sum of moments, the unknowns and θ were found. Each force was defined by stiffness and displacement (with or without rotation). For the Civil MOB structure, there are walls in both the N-S and E-W directions (see figure below). Figure 11-A: Shear Wall Orientation, with Center of Rotation and Center of Mass Shown To find the shear on the walls in the E-W direction, the force was applied at the CM with the 5 percent eccentricity which will cause a rotation: ∑ (11-7) ( ) ( ) Where k 1,2 represents each member stiffness, and x 1,2 are the distances of the walls from the CR. Paragon Structural Consultants 73 | P a g e ∑ (11-8) Where F 3 , F 4 , and F 5 are factors of rotation, for example: (11-9) After solving for and θ, the forces are determined by iteration. MATLAB was used to find the displacement and rotation. See Appendix A for calculations. 11.2 DESIGN BASIS Because the design of shear wall boundary elements controls the design of the shear wall as a whole, they are designed before the web steel is selected. Designs were derivative of the moment analysis described in Section 11.1. 11.2.1 Boundary Element The boundary element is a portion along a structural wall strengthened by longitudinal and transverse reinforcement. ACI requires special boundary elements in highly compressed regions. The longitudinal reinforcement in boundary elements must be tied by transverse reinforcement that satisfies ACI codes 7.10.5. 11.2.1.1 Moment Capacity The longitudinal reinforcement concentrated in the boundary element helps to increase the nominal moment strength of the shear wall. When calculating the nominal moment strength, the vertical reinforcement in the web is usually ignored because it does not contribute to M n , and is found based on shear. The following figure is a schematic of the typical reinforcement layout in a shear wall. As seen, the majority of the reinforcement can be found in the flange section to resist moment: Figure 11-B: Schematic of a Typical Reinforcement Layout in Shear Wall Design The critical load case for evaluating the nominal moment strength of a wall includes the tension force for the boundary element in tension and a factored axial load. This will minimize the nominal wall moment Paragon Structural Consultants 74 | P a g e strength. Summing the moment about the compression force in Figure 11-C leads to the following expression: ( ) ( ) (11-10) Where A s is the total area of longitudinal steel in the boundary element. Below is a typical stress diagram, which provides a simplified view of the forces and lever arm: Figure 11-C: Stress Diagram for Use in Shear Wall Design 11.2.1.2 Longitudinal Steel Design Unlike traditional concrete beam design, it is not common to place the entirety of the flexural reinforcement at the extreme end of the shear wall. Additional considerations, including congestion and development concerns require a deviation from classical beam design regarding the placement of the longitudinal reinforcement. The typical longitudinal bar pattern used in the Civil MOB across all shear walls is shown in Figure 11-D. When additional moment capacity is required, and thus more longitudinal steel is required, the pattern is extended to allow for additional bars: Figure 11-D: Typical Pattern for Boundary Elements Paragon Structural Consultants 75 | P a g e It is preferable to limit the compression zone of the shear wall to within the extents of the boundary zone. This is achieved by designing the boundary length to exceed the neutral axis depth at each shear wall. A comparison of the neutral axis depth with the boundary length of each shear wall is given in Table 11-A. Table 11-A: Comparison of Neutral Axis Depth and Boundary Element Length BOUNDARY ELEMENT VERTICAL REINFORCING DETAILS WALL C na L be N 35" 52" S 32" 40" E 32" 46" W3 21" 46" W4 15" 40" As horizontal bars providing reinforcement to the web develop within the boundary element, it is common to design the boundary zone to accommodate the development length of the horizontal bars. Discussion of the design of the horizontal bars is provided in Section 0. Multiple slab tendons pass through the boundary element of the shear wall along architectural line 6 at all levels with elevated decks, as depicted in Figure 11-E. The bundles passing through the wall are comprised of bands of three 0.5” tendons (sheathed to 0.62”). These must be permitted to pass through the shear wall. In addition, dowel bars must past through or hook into the shear wall on the same vertical plane as the post-tension strand. To accommodate this, it is necessary to provide adequate spacing between longitudinal bars, to ease constructability and minimize consolidation issues which may arise when pouring in congested regions. Figure 11-E: PT Tendon Pass Through Utilization of multiple rows of longitudinal bars additionally allows for more crossties to be used per layer. This increases the area of shear reinforcement, and thus increases the permitted vertical spacing between reinforcement layers. In order to maintain a desired cross-sectional area of shear reinforcement per layer, the size of the longitudinal bars was decreased to maintain a minimum of seven rows, which provides adequate shear reinforcement and ample spacing. Section 11.2.1.3 gives further discussion of crosstie design. The longitudinal reinforcing was designed based on these considerations, and to provide Paragon Structural Consultants 76 | P a g e the sufficient moment capacity in accordance with equation (11-10). The longitudinal reinforcing schedule is provided in Table 11-B: Table 11-B: Boundary Element Vertical Reinforcing Schedule BOUNDARY ELEMENT VERTICAL REINFORCING SCHEDULE WALL REINFORCING L be N (22) #11 @ 6" 52" S (18) #11 @ 6" 40" E (20) #10 @ 6" 46" W3 (20) #9 @ 6" 46" W4 (18) #7 @ 6" 40" 11.2.1.3 Crossties Crossties and hoop ties provide confinement to the concrete by creating shear reinforcement. ACI Section 21.6.4.4 determines the necessary minimum reinforcement based on properties of the concrete strength and hoop grade, as given in Equation (11-11) below: ( ) (11-11) This equation must be satisfied in both cross-sectional directions of the rectangular boundary element. The variable denotes the dimension perpendicular to the tie legs, which is included in the formula for , the total cross-sectional area of rectangular hoop reinforcement. These values are depicted in Figure 11-F: Figure 11-F: Transverse Reinforcement Dimensions Paragon Structural Consultants 77 | P a g e Using values of 6 ksi for and 60 ksi for the hoop grade allows for a spacing of 6” between layers of transverse reinforcement for all shear walls. If this is determined to be inadequate by the contractor, for constructability concerns, grade 80 bars may be substituted to increase the spacing to 8” between layers for all shear walls. 11.2.2 Web Design The goals in web design are to develop a wall which provides strength and ductility under the factored lateral loads, and to avoid shear failure of the wall due to brittle behavior. ACI provides two ways to prevent this behavior: capacity design, which is to design the shear capacity to be greater than flexural capacity, and the use of a lower φ factor in shear design to provide an extra factor of safety. The web of the wall provides the majority of the shear capacity and can be approached in a similar way to the web of a wide-flange beam. Due to the large amount of concrete area resisting the shear forces, shear walls often require light vertical and transverse steel. Lateral loads parallel to the plane of the wall are resisted in two ways: cantilever action for slender walls (where bending deformation is dominant) and truss action for squat walls (where shear deformation is dominant). ACI chapter 21.9 provides a means of determining which of these deflections will control in seismic design by finding the aspect ratio of the wall. Classifications are determined by a ratio of vertical height of the wall to the transverse length of the wall ( ) with further classifications by ratio of the length to width of the wall ( ). All of the walls in Civil MOB are defined as a “wall”, as opposed to a “wall pier”. This is because their ratios are larger than 2.0, and their ratios are larger than 6.0 (ACI Table R21.9.1). Accordingly, all walls shall be designed to be limited by shear rather than flexure. 11.2.2.1 Shear Capacity To determine how much reinforcement is required in the web of the wall to resist shear, it is necessary to find the shear capacity of the concrete alone. ACI equations 11-1, 11-1, 11-4 in sections 11.1 and 11.2 are given as: (11-12) (11-13) √ (11-14) V c is defined as the nominal shear strength of concrete subject to axial compression, and V s is the steel reinforcement in the shear wall. In equation (11-14), and are defined as the thickness of the wall and , respectively. All shear walls are 24” thick (b w ), but have varying lengths (l w ). Since varies per wall, each wall in Civil MOB will have its own concrete shear resistance. Paragon Structural Consultants 78 | P a g e ACI defines three shear categories that relate factored shear loads to the shear capacity of the concrete. If , minimum steel may be used in the wall (as defined in ACI chapter 14.3); if , the vertical reinforcement of the web must be increased to prevent shear cracks (a function of the horizontal reinforcement in the web as defined in ACI 11.9.9); if , horizontal reinforcement must be designed to accompany the concrete shear capacity in resisting the applied shear load (with vertical reinforcement once again being a function of horizontal reinforcement as defined in ACI 11.9.9). In Civil MOB, every wall fell under one of the last two categories. For an example calculation of shear wall web reinforcement in these two categories, see the calculations in section 0. 11.2.2.2 Reinforcement Design Once the shear capacity of the concrete, V c , and the respective shear category has been determined, web reinforcement for the shear wall can be designed according to the ACI design procedures. Calculations for walls in the category and the category are shown below. In the calculation sequence, certain steps include references to relevant ACI codes. These references are quite numerable and were therefore identified in the form of an example calculation. Figure 11-G: Typical Web Reinforcing Schedule Figure 11-G displays the web reinforcing schedule for all shear walls in Civil MOB. The following calculations demonstrate how equivalent web reinforcing was selected for all walls. When designing web reinforcement, the goal was to maintain equal bar sizes and similar spacing values for consistency between shear walls. It should be noted that all of the walls in Civil MOB are 24” thick. ACI states that walls thicker than 10” need be reinforced with two curtains of reinforcement (one per wall face), as shown in Figure 11-H. As an example of walls falling within the category, design of the northwestern shear wall, of dimensions 24” thick and 16’ long (W3 in the structural plans), is shown below as per ACI 11.9.9. √ √()() () and therefore .  Paragon Structural Consultants 79 | P a g e The minimum ratio of horizontal (transverse) reinforcement (ρ t ) in this category of walls is limited to 0.0025 and the maximum spacing is limited to the smallest of and 18”, controlled by 18”. () . Assuming #8 bars and two curtains of reinforcement, , () . Therefore, two curtains of #6 bars at 12” spacing were chosen. Vertical (longitudinal) reinforcement is a function of the ratio of longitudinal reinforcement, per ACI 11.9.9. The minimum longitudinal reinforcement ratio is 0.0025. ( ) ( ) ( ) ( )  Therefore, 0.0025 was used. As a final verification of seismic sufficiency, ACI 21.9.4 states that V n of special structural walls shall not exceed ( √ ), where for all Civil MOB shear walls. Accordingly, ()()()(√ () .  Therefore, 2 curtains of #6 bars at 12” spacing were chosen. These calculations were performed for all walls falling within the category. As an example of walls falling within the category, design of the northern shear wall, of dimensions 24” thick and 28’ long (N in the structural plans), is shown below per ACI 11.9.9. Paragon Structural Consultants 80 | P a g e , therefore .  ACI section 11.9.9.1 provides equation (11-29) for V s : ()()() Assuming #6 bars and 2 curtains of reinforcement, , () . Maximum spacing is 18”. Therefore, 2 curtains of #6 bars spaced at 12” were chosen. Vertical (longitudinal) reinforcement is a function of the ratio of longitudinal reinforcement, per ACI 11.9.9. The minimum longitudinal reinforcement ratio is 0.0025. ( ) ( ) ( ) ( )  () As a final verification of seismic sufficiency, ACI 21.9.4 states that V n of special structural walls shall not exceed ( √ ), where for all Civil MOB shear walls. Accordingly, ()()()(√ () .  Therefore, 2 curtains of #6 bars spaced at 12” were chosen. The final design for the shear walls can be seen in Figure 11-H. Paragon Structural Consultants 81 | P a g e Figure 11-H: Shear Wall Section Detail The horizontal bars in the web need to run the full length of the web to sufficiently develop at the ends. Rather than hook the bars and increase congestion at the internal edge of the boundary element, the horizontal bars run into the boundary element and have sufficient length for development. These bars are No. 6 bars for all walls, and have a development length in. The minimum boundary element length is found in the southwest shear wall at 40”, so the horizontal bars can properly develop in all boundary elements. This horizontal bar development is depicted in Figure 11-I: Figure 11-I: Horizontal Bar Development Length For constructability purposes, a splice occurs between the central horizontal bars and the hooked horizontal bars at the ends, as seen in Figure 11-H. This splice length needs to be at least the development length of the No. 6 bars, which is 14” (as previously stated). There is ample room in the web for this development, so the location of the splice is left for the contractor to decide. 11.2.3 Slab Dowel Bars When lateral loads are applied on a building, the forces are often not applied directly to the lateral load resisting systems. As a result, intermediate structural components of a building are designed to transmit lateral forces to the lateral load resisting systems. In the case of Civil MOB, the slabs and their diaphragm Paragon Structural Consultants 82 | P a g e were used to transmit forces from the entirety of the structure to the shear walls. Accordingly, some sort of shear friction is necessary between the slabs and shear walls to ensure that the interface between these members is capable of withstanding the significant shear forces experienced in seismic loading. Dowel bars were designed to properly connect the slabs to the shear walls, capable of transmitting shear forces on the building to the shear walls. As mentioned above, sufficient shear friction must be provided for the slab-wall interface. Following ACI 11.6.4, the shear capacity of reinforcement perpendicular to the plane of such an interface is defined as: (11-15) Where A vf is the area of steel perpendicular to the plane of the interface that, in this case, connects slab to shear wall, and µ is the coefficient of friction between surfaces. ACI states that this coefficient of friction may be taken as 1.4 if the concrete of the connection is poured monolithically, 1.0 if the interfacial surfaces are roughened to ¼”, or 0.6 if the interfacial surfaces are not roughened. A conservative assumption was made that the concrete would be poured non-monolithically between slab and shear wall, and that the contractor would intentionally roughen the interfacial surfaces. Although the shear wall and slab could be poured simultaneously due to their equivalent f’ c , the option was made available for the contractor to pour the members separately. To find the necessary area of dowel reinforcement connecting the slab to each shear wall, the following calculation was performed for each shear wall. This example calculation will be performed for the northern wall: ⁄ ⁄ ()() There are 2 faces per wall along which dowel bars can be placed and the length of the northern wall is 334”. Assuming #5 bars, ( ) ()( ) Therefore, #6 dowel bars spaced at 6” were chosen. For proper development, these #6 bars need at least 14” of straight length, or 7” if a standard 90 hook of 9” (12d b ) is used. These hooks may bend vertically or horizontally in the shear wall while the straight end of the bars may develop straight into the slabs. These dowel bars must run along every face of each shear wall, framing each wall face into the intersecting slab. A hook at the end of the dowel bar is only necessary if there is an opening on the other side of the shear wall, as seen in Figure 11-J. If there is no opening, the dowel may run through the wall and gain development in straight length on the other side. This decision was left to the contractor as they may choose to hook dowel bars to solve congestion issues. Details are specified in the structural plans, as seen in Figure 11-K. Paragon Structural Consultants 83 | P a g e Figure 11-J: Placement of Dowel Bars along Shear Wall Faces Figure 11-K: Dowel bar Callout in Slab Reinforcement Schedule 12 PENTHOUSE DESIGN (STEEL/SPECIAL) The two penthouse structures shown on the roof of the Civil MOB have been designed using steel members. Although this is a departure from the reinforced concrete/PT used throughout our structure, in this application steel design was most economical. This is especially relevant for the center (core) penthouse, which houses electrical equipment and a thicker slab section. Choosing a slender, steel frame system to hang cladding from, which was also capable of spanning 33 feet, was ultimately the priority. 12.1 PENTHOUSE 1 – NE CORNER 12.1.1 Assumptions The corner penthouse located on the roof of the Civil MOB is intended as an architectural accent. The diamond shaped roof and elevated corner design serves to break the continuity of the roof edge. For the sake of structural integrity, it was important that PSC design the structural frame to withstand both gravity and lateral loads. Detailed below is the design for gravity resistance, using LRFD Paragon Structural Consultants 84 | P a g e method. The lateral system design will come in the form of an update, which will be included in the final design report. The diamond shaped roof will be developed using a prefabricated space truss system from Aegis, in the form of a series of five Pratt style trusses (each shown below). This design is appropriate simply because ceiling height under this architectural penthouse is not important (the area is enclosed), allowing for a flat bottom design for each truss cross section: Figure 12-A: Pratt Truss I, Available by Request from Aegis Metal Framing The first custom truss, named cross section I for drawing/reference purposes, forms the peak of the diamond shaped roof. By utilizing a Pratt truss system, PSC was able to satisfy the maximum span length for the roof deck of choice (discussed further below). The next truss profile, which is implemented 5.5 feet away from either side of the middle truss, is named cross section II: Figure 12-B: Pratt Truss II, Available by Request from Aegis Metal Framing Paragon Structural Consultants 85 | P a g e The third and final truss required to frame the diamond shaped roof is named cross section III, and can be found in the figure below: Figure 12-C: Pratt Truss III, Available by Request from Aegis Metal Framing With the roof framing complete, a roof deck was chosen based on the Steel Deck Institute sizing/strength requirements. Nucor Steel Company offers a line of roof deck called Vulcraft, whose charts allowed us to simply select a roof deck based on the total factored psf that the sheets would experience. For the sake of the roof, the unbraced length (based on the custom fabricated truss system), is approximately 6 feet. Total load demand for the roof, assuming a flat surface (conservative): () ( ) () () Based on Vulcraft charts, for a three-span roof section, we chose to use B19 roof deck. Although the value is extremely close to max allowable, PSC found that the design is safe due to the large degree of conservation in choosing a flat roof. See the figure below for reference: Table 12-A: Vulcraft Roof Deck Table for Type 1.5B, Penthouse 1 Paragon Structural Consultants 86 | P a g e With a 3-span system that has such close gap spacing (about 6 feet), the roof deck will have capacity greater than the demand of factored gravity loads. This added capacity is acceptable for the following reasons:  The geometry of the truss system lends itself to five truss cross sections, since the similarity between these truss profiles is maximized (see figures above).  The cantilever sections at the ends of each roof surface will be accounted for with the additional capacity.  Being slightly conservative in deck gauge will not add a significant amount of weight relative to other members. After choosing the roof deck material, and having calculated the LRFD loads on the gravity frame, PSC was prepared to perform an individual design analysis for the beams/columns. 12.1.2 Design Process Below is a simple plan of the steel structural design for the gravity frame, with the space truss system accounted for (all members are assumed to be pinned for analysis): Figure 12-D: Plan View of the NE Corner Penthouse (1), with Aegis Space Frame Shown Paragon Structural Consultants 87 | P a g e 12.1.2.1 Beam Design With the Aegis space frame and Vulcraft roof deck chosen, the total loads can be determined for the beams/columns. Due to the simplicity of the geometry, PSC treated all loads in terms of psf, and divided the tributary area into quarters for each beam. The calculation is as follows: ( ⁄ ) ( ) ( ) () () ⁄ ⁄ After entering these values into Dr. Beam, the resulting . Since the beams are all laterally braced at their midpoints by the roof truss, the design (AISC Table 3-1) and (all four beams were designed for the worst case length of 33 ft). Using the beam design methods in the AISC manual, PSC has decided to select W8x24 members for the exterior beams. This design is very slightly conservative, but is the smallest member which acts in Zone 2. This decision was made over smaller, Zone 3 members to utilize the full yield capacity of the material. The final capacity vs. demand results as: 12.1.2.2 Column Design For the column design, the tributary calculations were simply taken from the line loads on the beams, plus the beam self-weight. Also included was the weight of the cladding, which was hung from the exterior of the frame. The new total psf for these combined loads is shown below: [ ⁄ () () ⁄ ()] Using AISC Table 4-4, PSC chose an HSS section capable of supporting this load down a axial span. The final design choice for these columns will be Square HSS 4x4x1/4. This member meets the capacity vs. demand requirements in the following way: Although there is a degree of additional capacity available in the 4x4 HSS design, this size member is most commonly available. It is therefore recommended that the columns be built in the 4x4 dimension, rather than 3.5x3.5 or smaller. Also, in terms of constructability and anchor design for both penthouse 1 and penthouse 2, it makes sense to prescribe the same HSS column dimension/thickness for both penthouses, based on the worst case scenario. As long as the variance between capacity and demand is less significant than the cost savings and constructability gains, the additional capacity is welcome. ( ) ( ) Paragon Structural Consultants 88 | P a g e 12.2 PENTHOUSE 2 – BUILDING CORE 12.2.1 Assumptions The center penthouse exists at the core of the Civil MOB roof, and acts as an enclosed facility for electrical equipment. This penthouse is only 1/3 enclosed by a roof deck, while the remaining section is open with cosmetic walls. Similar to Penthouse 1, the gravity resisting structure was designed using traditional steel member analysis, assuming all connections pinned. For continuity purposes, the frame spans 3 bays (33’ each) in the N-S direction, and only 1 bay (26’) in the E-W direction. The 33’ span was critical in terms of the uncovered sections (no roof), because there were no intermediate supports to lower the effective length (L b ). Similar to Penthouse 1, Vulcraft Roof Deck was chosen from the Nucor Catalogue, based on the same total factored load of 48 psf (previously calculated). For the bay which required roof deck, the material was intended by the architects to span in the E-W direction, so stringers were designed to reduce the span from 26’ to multiple lengths of 9’. This allowed PSC to select a material type based on Steel Deck Institute sizing, as shown below (note that this penthouse has 3 spans, requiring selection from further down in the chart): Table 12-B: Vulcraft Roof Deck Table for Type 1.5B, Penthouse 2 12.2.2 Design Process The design process for Penthouse 2 followed the same general process for Penthouse 1, with a few differences. Below is shown a figure of the general plan view for Penthouse 2, with designed members shown. The rightmost bay was framed separately due to the increased loads resulting from the roof deck. The remaining two bays were simple beam and column frames, with no bracing required. Paragon Structural Consultants 89 | P a g e Figure 12-E: Plan View of Penthouse 2 with Labelled Beams, Stringers, and Columns 12.2.2.1 Beam Design The rightmost bay was designed first, and independently of the rest of the structure. This is due to the intermediate stringers which act to brace beams C. Also, the orientation of these stringers serves to support the Vulcraft Roof Deck at intervals of approximately 9 feet (for the sake of selecting the Roof Deck grade). These members were designed using the beam method highlighted for Penthouse 1, which can be referenced as needed. The results for beams are as follows: Table 12-C: Final Results for Beam Design, Penthouse 2 Beam Design Moment (k*ft) Member W-Section Analysis Zone Demand Capacity A W12x45 3 103 107 B W8x35 3 69 74 C W12x35 2 192 195 D W12x40 3 84 86 E W8x35 3 64 74 F W8x31 3 64 77 It is important to note that there is a difference between members D and F, resulting in different demand values. The bay height for member D is 20.7 feet, resulting in a larger surface area of cladding to add to the total dead load. For the member F, the bay height is only 15.7 feet. Since this is not immediately obvious in the plan view and table, it is worth noting. Paragon Structural Consultants 90 | P a g e 12.2.2.2 Column Design The column design, just like the beams and stringers for Penthouse 2, continued with the previously shown standard method for AISC steel design (see Penthouse 1 calculation example, section 14.1.2.2). A simple tributary analysis was made, based on the plan drawings seen in figure 14.c, and the total loads per column were determined. Based on the analysis, the columns were grouped into pairs for ease of design. For the sake of constructability, PSC decided to remain consistent between Penthouse 1 and Penthouse 2 by using square, HSS4x4 for both (being that this member size is readily available). The final design results are shown below: Table 12-D: Final Results for Column Design, Penthouse 2 Column Design Axial Load (kips) Member Square HSS Section Demand Capacity C1 HSS4x4x1/4 24 48 C2 HSS4x4x1/4 26 28 C3 HSS4x4x1/4 22 28 C4 HSS4x4x1/4 17 48 ( ) The following results include the point loads on the gravity frame resulting from the Penthouse 2 design: ( ), ( ), ( ), ( ) 12.3 PENTHOUSE LATERAL REINFORCEMENT 12.3.1 Design Strategy Having completed the primary gravity resisting steel frames for both Penthouse 1 and Penthouse 2, the dead loads were finalized for use in lateral design. The self-weight of the final members was added into the seismic spreadsheet for lateral loads since the calculation requires an accurate dead load (wind is dependent upon penthouse dimensions, which has not changed). With these lateral loads determined for each penthouse, the design process for lateral bracing could be started (for further details on the lateral calculations, refer to sections 6.4-6.5). Although PSC engineers anticipated that wind loads would govern the penthouse lateral system design, it turned out that earthquake loads provided the critical value. After cross checking all the values and calculations in both spreadsheets, this turns out to be accurate. The reason is simply due to the large spans and relatively heavy members needed to carry the gravity system for each penthouse. Also, the structural steel roof deck and fireproofing system adds considerable mass where it is needed. Ultimately, Paragon Structural Consultants 91 | P a g e while these penthouse designs have sizeable mass (causing earthquake lateral loads to be considerable), they are not over-conservative or too expensive for the architectural/structural needs of the Civil MOB. In terms of lateral reinforcement for the steel framed penthouse system, PSC chose to use a tension only steel rod design. The reasons this steel rod/cable system was chosen includes the following:  they are inexpensive and straightforward  they are lightweight, and weatherproof (excellent for roof/penthouse framing)  since the lateral system is designed to carry tension only, there is no complex modelling needed  they are capable of spanning large lengths between gravity elements 12.3.2 Design Process The two cases which were considered for the lateral penthouse design are: 1. 0.9D + 1.0W 2. 0.9D + 1.0E As previously stated, the critical case for both penthouse systems ended up being the seismic combination. The most important numbers for consideration are shown below: Table 12-E: Penthouse 1 and Penthouse 2, Worst LRFD Load Case for Lateral Design Unfactored Loads (k) Factored Loads (k) Combined (k) Pent. 1 Dead Wind Earthquake Dead (0.9) Wind (1.0) Earthquake (1.0) Lateral F(x) Vertical F(y) Case 1 31.83 4.5 28.65 4.5 4.5 28.65 Case 2 31.83 17.5 28.65 17.5 17.5 28.65 Pent. 2 Case 1 26.3 22 23.67 22 22 23.67 Case 2 26.3 32.5 23.67 32.5 32.5 23.67 Note: Worst case for each penthouse is shown in bold under ‘Combined’ segment. For both structures, seismic was the controlling LRFD load case. 12.3.2.1 Penthouse 1 Design In the case of each penthouse, the plan was to have a crossing X pattern, tension only rod design. For Penthouse 1, all four walls were designed to have tension rods; whereas, with Penthouse 2, only four out of eight walls needed lateral bracing. Using free body diagrams, PSC engineers were able to isolate each crossing tension rod (while ignoring the other rod in compression), and place the 1.0E lateral load as well as the 0.9D vertical load. Due to the simplicity of the member interaction, the vertical dead load did not contribute in any way to the demand on the tension rod (in axial load analysis). This is because all members were assumed to be pin-pin, and the fact that rods only carried tension. While this method is simple, it proved to be more than adequate for the penthouse lateral system. Paragon Structural Consultants 92 | P a g e Below is an example of the free body diagram for Penthouse 1, using Dr. Beam for analysis: Figure 12-F: Free Body Diagram for Penthouse 1 (Both NS and EW Axes) It should be noted that only half of the total lateral load was placed on each brace, since there will actually be two separate tension braces working in the same plane. The same analysis was done for the NS bracing, and the EW bracing for each penthouse. Fortunately, Penthouse 1 is nearly symmetrical in the length of each perpendicular axis, so the more critical length of 33’ was used for the design of both axes’ tension rods. TriPyramid makes a comprehensive catalogue of different tension rod/cable designs, including various fittings for attachment to the gravity system. Based on the axial demand of 18.4 kips in tension, the following table allows PSC engineers to choose a product: Figure 12-G: TriPyramid Catalogue, Tension Member Selection Table (A22 Highlighted) Paragon Structural Consultants 93 | P a g e For all four walls of Penthouse 1, the cross bracing will be 0.5” diameter A22 type tension rods, which are capable of carrying 21.6 kips without yielding. For this selection, B215 adjustable jaw assemblies will be used at both ends, allowing contractors to tighten the rod system from either end (as needed). Below are two images of the specifics for this selection: Figure 12-H: TriPyramid A22 and A25 Tension Rods (Both Used for Penthouse Design) Figure 12-I: B215 Jaw Assembly, Connection for A22 Tension Rods 12.3.2.2 Penthouse 2 Design The second penthouse was designed using the same general method as penthouse 1, although the critical loads are slightly larger (being a three-bay penthouse with more mass in structural steel, roof, and cladding). Even with the larger penthouse, only four walls of tension reinforcement were needed. The two figures below are representative of the reinforcement along each axis (lateral, and transverse): Paragon Structural Consultants 94 | P a g e Figure 12-J: Free Body Diagram for Penthouse 2 along the NS Axis Figure 12-K: Free Body Diagram for Penthouse 2 along the EW Axis Paragon Structural Consultants 95 | P a g e With representative axial demands for each axis based on a sample frame (shown above), the appropriate tension rod and fitting could again be chosen from the TriPyramid catalogue: Figure 12-L: TriPyramid Catalogue, Tension Member Selection Table (A25 Highlighted) Interestingly, the differences in geometry between the lateral and transverse axes of Penthouse 2 did not significantly affect the axial demands in the tension rods. Both cases fall just under the requirements for 0.75”, A25 tension rods (yields at 39 kips). Figure 12-M: B230 Jaw Assembly, Connection for A25 Tension Rods Paragon Structural Consultants 96 | P a g e 13 CONNECTION DESIGN 13.1 BEAM COLUMN CONNECTION 13.1.1 Interior beam connection details Detailing beam-column joints requires careful attention. Beam bars must thread through column longitudinal bars, leaving enough space for concrete to pour without causing voids. Also, it is important for beam and column longitudinal reinforcement to be anchored correctly, so that the joint can resist moments. Inside interior joints, the beam reinforcement usually extends through the joint, and is anchored in the adjacent beam span. The reinforcement is cut off at its developmental length (for a No. 9 bar, the developmental length is 16 inches which is established by using ACI 12.3.2). 13.1.2 Exterior beam connection details For exterior joints, the top beam bars usually end in a hook and the hook is embedded in the beam- column joint. The standard is to use a 90˚ hook in normal-weight concrete with the length at least √ (13-1) Which is within the confined core of the column. After the length of the extension into the joint is established, the diameter and the extension of the rebar after the bend are established using ACI 7.1.3. The bottom beam bars also end in a hook about 4.5 inches from the edge of the column. The minimum distance between the furthest extended bar and the edge of the column is 2 inches. Table 13-A: Exterior Beam Connection Details Which bar? Spacing from top of beam Spacing from end of joint Spacing from beginning of column Diameter of bend Extension of bend 1 st row compression bars 1.5 in 2 in 20 in 9 in 14 in 2 nd row compression bars 1.5 + 1 (No. 9)db = 2.628 = 3 in 2 in + 2 (No. 9)db = 4.408 =5 in 18 in 9 in 14 in 1 st row tension bars 20.5 in = 20 in 2 in + 3 (No. 9)db = 5.6 = 6 in 16 in 9 in 14 in Paragon Structural Consultants 97 | P a g e Figure 13-A: Exterior Beam Connection Details 13.2 COLUMN FOOTING CONNECTION A column applies a concentrated load on the footing. This load is transmitted by bearing stresses in the concrete and by stresses in the dowels or column bars that cross the joint. Typically column bars stop at end of column and dowels are used to transfer loadings. Dowels are used because it is awkward to embed the column steel in the footing and it is difficult in locating it accurately. According to ACI 15.8.2.1, the area of reinforcement should not be less than 0.005Ag, where Ag is the gross area of the column. Once the area of reinforcement is found, there needs to be a cut off for the distance the dowels extend into the column and footing. The dowels extend into the column at a distance equal to the greater of the compression developmental length of a No. 8 bar (the longitudinal bar in the column) and the compression lap splice of the dowels. The dowels extend into the footing at a distance equal to the compression development length of the dowel (ACI 15.8.2.3 and ACI 12.3.2). The hook diameter and extension length of the dowel is found after referring to ACI 7.2.1 for the diameter of the bend and ACI 7.1.3 for the extension of the hook. The connection for the foundation is designed to use four No. 7 dowels. The dowels extend into the columns for 26 inches, which is the lap splice length of a No. 7 bar (ACI 12.16.1). The dowels extend into the footing for 17 inches, which is the compression development length of the dowel. Paragon Structural Consultants 98 | P a g e Figure 13-B: A Typical Column-Footing Connection 13.3 PENTHOUSE ANCHORAGE SYSTEM 13.3.1 Design Strategy With the structural systems for each penthouse complete (both gravity and lateral), PSC engineers were only left with the challenge of anchoring them to the building roof. Having designed the primary Civil MOB structure to be concrete only (simply reinforced and prestressed), a special design was needed to allow connection detailing between the penthouse columns, and Civil MOB roof. In terms of penthouse structural design, the gravity resisting frame and lateral load resisting frame were both assumed to be pin only members. When designing the anchors to resist loads in a fixed end capacity, the connections are redundant, and therefore conservative. 13.3.2 Design Method For the penthouse anchorage design, proprietary software was used by permission of the company Hilti (Profis Anchor Design 2.4.7). This software is open source, allowing PSC design engineers to model the steel/concrete interface in great detail. The method is straightforward, and can be highlighted in the following steps: Paragon Structural Consultants 99 | P a g e 1. Start by selecting the anchor plate dimensions (standard 0.5” thick ASTM F 1554 steel) 2. Indicate the concrete base material at the interface, which is 6000 psi, and how much pad height will be used above the roof slab top (7 inches for both penthouse structures) 3. Indicate whether seismic design is necessary, which models the interface as follows: a. Concrete assumed to be cracked under seismic loading b. Reinforcement for tension and shear both condition B c. Edge reinforcement: ≥No. 4 bar with stirrups d. Hilti proprietary grout/epoxy used to elevate anchor plate 1.25 inches above pad (f c =15,000 psi) 4. Enter the anchor reaction forces, which PSC engineers took from Dr. Frame (based on worst LRFD load case) 5. Select steel strength modelling parameters (based on ACI 318 for this design) 6. With all input complete, the software will run and determine factors such as pullout strength, concrete breakout strength, shear load, tension load, etc. 7. Select the Anchor type and diameter, and number of fasteners (heavy square head, gr. 105 used for both penthouses) 8. Minimize dimensions to maximize efficiency (also automated by the software) For each penthouse, the anchors were designed based on the worst case support reactions. Since these Hilti anchors are proprietary and custom made, a single design for each penthouse is reasonable. The results/output of the Hilti software can be found in Appendix A.5 Connection Details, including exact materials and design dimensions. The visual representation of each penthouse anchor can be seen in the following two figures: Paragon Structural Consultants 100 | P a g e Figure 13-C: Final Hilti Anchor Design for Penthouse 1 Figure 13-D: Final Hilti Anchor Design for Penthouse 2 Paragon Structural Consultants 101 | P a g e 14 FOUNDATION DESIGN 14.1 DESIGN CONSIDERATIONS The foundation for Civil MOB will consist of spread footings, designed to carry the gravity load from the columns to the soil, and mat foundations under the shear walls to resist lateral loading. The underlying soil was determined by geotechnical consultants to consist of dense sand with an allowable bearing pressure of 12,000 psf. Since the sand is dense and stiff, long term settlements will not be an issue, and therefore do not need to be checked. 14.2 DESIGN PROCESS The process for designing the foundations is listed below. See Appendix C.1 for sample calculations. 14.2.1 Column Footings To begin the design of the column footings, the axial loads from the columns were determined. These axial loads were provided by the SAP 2000 output, and checked by hand for each frame model. The column loads were grouped according to their relative magnitudes, at which point the footings could be designed for each specific load group. 14.2.1.1 Sizing for bearing To size the base of each column, unfactored loads were used per ASD (the controlling load combination was D + L). This load combination was divided by the allowable bearing pressure of the soil to achieve a base area. Each footing was made square and the lengths were rounded up to the nearest half foot. The following equation was used to find the required area, A req , for bearing where P D+L is the unfactored load from the column and q all is the allowable bearing pressure: (14-1) 14.2.1.2 Sizing for shear The depth of each footing is required to resist any shear failures, and for this analysis, two types of shear failures were checked: one-way shear and punching shear. One-way shear, or beam shear, was determined by modeling the footing as a cantilevered beam, treating the column as a support. The shear strength was expected to occur at a distance d (footing depth) away from the support. This is due to the concrete tending to fail in diagonal tension cracks. The other type of shear failure checked was punching shear. This could be caused by a high point load from the column being transferred to the soil over a large area of footing. The concrete again would fail in diagonal tension cracks on all four sides of the column. A critical section of failure was determined by Paragon Structural Consultants 102 | P a g e averaging all four sloped sides to check the strength resisting punching shear. Only the concrete in the footing was be used to resist shear, since it is less expensive to make the footing a little deeper than to add any shear steel. To check shear, factored loads were used from LRFD. The controlling load combination was 1.2D + 1.6L + 0.5S. In all cases, punching shear controlled the depth of each footing. The shear strength of the concrete was determined as follows: () √ (14-2) It was determined that the footings needed to be deeper to account for the development length of the transfer dowels that connect the columns to the footings. This minimum depth for the connection was determined to be two feet. 14.2.1.3 Flexural Reinforcement Finally, flexural reinforcement was computed for the footings. This was determined by modeling the footing as a cantilever from the edge of the column and using the simplified moment capacity method for concrete beams (which assumes a lever arm of 0.9 times the distance from the upper most compressive face to the center of the flexural steel). By making this assumption, the area of flexural reinforcement that is required to resist the moment could be determined from the following equation: (14-3) Where F y is the yield strength of the steel and A s is the area of required steel. The area of flexural reinforcement determined from this method was checked to satisfy the minimum requirements for reinforcement based on the width of the footing. 14.2.2 Shear Wall Foundation To begin the design of the mat foundations, the critical lateral loads on the building were determined to be seismic. This is due to the building site being located in a seismically active area with lower wind speeds. Next, the tributary area for each shear wall was determined based on the orientation of each slab and girder with the wall, to find the axial loads acting on that wall. The dead load from the tributary area and weight of the footing are required to resist the over-turning and eccentric bearing (caused by the earthquake forces distributed on each floor). The first step in designing the shear wall foundation is to estimate an initial size for the footing. This cannot be done the same way as it was for the column footings, simply because the size needs to be much larger to resist overturning than it does to resist bearing. This final size was determined by checking overturning, eccentric bearing, punching shear, and beam shear. Ultimately, flexural reinforcement was determined based on the size of the footing. Paragon Structural Consultants 103 | P a g e 14.2.2.1 Size for overturning The first check on the shear wall foundation was for overturning. The foundation is required to resist 75 percent of the overturning moment due to seismic loads per ACI. The equivalent lateral loads distributed to each floor were multiplied by their distance from the footing to obtain the total overturning moment. This overturning was assumed to be resisted by the weight of the wall, footing, and the building dead loads. These vertical loads were multiplied by half the length of the footing to get the resisting moment. Since the weight of the wall and the building dead loads were fixed, only the footing dimensions could be increased to achieve a downward force large enough to resist the overturning. The critical ASD load combination for overturning is 0.6D + 0.7E, since it causes the largest ratio of earthquake load to dead load. 14.2.2.2 Size for eccentric bearing The next step is to check eccentric bearing on the footing, so as not to allow failure of the supporting soil. This eccentricity is cause by the lateral seismic forces inducing a moment on the footing, and is found by dividing the applied moment by the vertical dead load (as seen below). (14-4) This eccentricity was checked to see if it was outside the kern of the footing, and if there was any net tension on the soil. The soil, however, does not resist any tension forces. Instead, the length of compression and the maximum compressive stress was found at the extent of the footing: (14-5) (14-6) This maximum compressive stress cannot exceed the allowable bearing pressure of the soil, which ultimately governs the size of the footing. Once again, the ASD load combination of 0.6D + 0.7E was the critical load case. 14.2.2.3 Check for shear For the mat foundation, shear failures need to be checked although they would not likely govern the size of the footing because of the footing depth needed to provide sufficient resistance to the overturning and eccentric bearing. Again, the two types of shear that needed to be checked are beam shear and punching shear and they would be checked using factored loads from LRFD. For beam shear, the length of the footing in bending was modeled as a cantilever beam from the edge of the wall footing interface. This shear demand was taken at a distance of d (depth of the footing) from the support due to diagonal tension cracking. Similar to column footings, only the depth of the mat Paragon Structural Consultants 104 | P a g e foundation will resist the shear, providing a minimum depth of the foundation. This minimum was checked against the depth needed to resist overturning and eccentric bearing, and was found to have sufficient capacity. For punching shear, the first step was to compute the total shear demand. The largest axial force was found at one end of the wall, and this was conservatively assumed to act over the entire length of the wall. The critical section for shear failure resistance was taken around the perimeter of the wall at a distance of . Only the shear strength of the concrete was used to resist the shear demand, and the calculated depth of the footing was found to have enough shear capacity to resist punching. 14.2.2.4 Flexural Reinforcement For flexural reinforcement in the shear wall foundations, the ends of the footings were modeled as cantilever beams from the wall/footing interface. Similar to column footings, the area of steel required was found using the same method of multiplying a lever arm of 0.9 times the depth of the footing. The ultimate moment value was calculated from the factored LRFD loads, and the flexural reinforcement was sized to meet the maximum spacing requirement of 18 inches per ACI 15.10.4 (for mat foundations). The minimum reinforcement required was also checked and added to the foundations in the transverse direction. Similarly, minimum reinforcement was also required at the top face of the foundation, due to the bending caused by shear wall uplift. 14.2.3 Final Design The column footings are grouped below into four different sizes. The location of each footing type can be found in the foundation plan. Each footing was labeled in a way which makes it easier to see footing dimensions on the foundation plan. The shear wall footings have been broken up into two different sizes, because the individual footings around the three North shear walls can be combined into one. The reason for this is that they are all large enough to cause significant overlap. After designing individual footings, there was only a couple feet of soil left between the East and West shear walls. PSC engineers decided that it would be easier to dig this soil out and fill it with concrete, rather than attempt to use it for formwork. These footings were also labeled in a similar fashion to the column footings, again to make it more convenient to see them on the foundation plan. Paragon Structural Consultants 105 | P a g e Table 14-A: Column Footing Schedule FOOTING SCHEDULE MARK SIZE DEPTH BOTTOM REINF TOP REINF F5 5’-0” x 5’-0” 2’-0” (5) #7 EW - F6 6’-0” x 6’-0” 2’-0” (6) #7 EW - F7 7’-0” x 7’-0” 2’-0” (7) #8 EW - F8 8’-0” x 8’-0” 2’-2” (8) #8 EW - F28x50 28’-0” x 50’-0” 6’-0” (22) #6 LONG (34) #6 SHORT (20) #6 LONG (34) #6 SHORT F50x67 50’-0’ x 67’-0” 6’-0” (34) #6 LONG (53) #6 SHORT (34) #6 LONG (53) #6 SHORT Paragon Structural Consultants 106 | P a g e 15 CODES AND REFERENCES The following materials have been referenced for this project: A. ACI 318-11 Building Code Requirements for Structural Concrete B. ASCE 7-10 Minimum Design Loads for Buildings and Other Structures C. AISC Steel Construction Manual (14e) D. ASTM Standards in Building Codes, (46e) E. PCI Design Handbook, Precast and Prestressed Concrete (7e) F. Foundation Design: Principles and Practices (2e) - Donald P. Coduto G. Reinforced Concrete: Mechanics and Design (6e) - James K. Wight, James G. MacGregor H. Prestressed Concrete Analysis and Design: Fundamentals (3e) - Antoine E. Naaman I. Seattle Building Code, 2012 - Department of Planning and Government J. Vulcraft Roof Deck Catalogue - Nucor Steel Company K. Aegis Roof/Space Truss Catalogue - Design and Fabrication Company L. CECO Concrete Construction Company - Concept to Completion Materials (PT and Simple RC) Paragon Structural Consultants 107 | P a g e APPENDIX A – SAMPLE CALCULATIONS A.1 FOUNDATION CALCULATIONS A.1.1 Spread Footing: Computed using loads from column at C5 A.1.1.1 Controlling Load Combinations:  ASD: D + L = 761 kips  LRFD: 1.2D + 1.6L + 0.5S = 927 kips A.1.1.2 Size for Bearing: √ √ A.1.1.3 Size for One-Way Shear: ( ) ( ) (√ ) √ () ( ) Paragon Structural Consultants 108 | P a g e A.1.1.4 Size for Punching Shear: ( ( ) ) ( ( ) ( ) ) ( ) ( ) √ () √ A.1.1.5 Flexural Reinforcement: ( ) ( ) ( ) ⁄ () Check minimum steel: A.1.2 Mat Foundation: Computed using Shear Wall along Line 6 A.1.2.1 Controlling Loads  Dead Load: 854 kips  Seismic: 1043 kips o Floor 2 : 111 kips Paragon Structural Consultants 109 | P a g e o Floor 3: 225 kips o Floor 4: 338 kips o Roof: 369 kips ( ) ( ) ( ) A.1.2.2 Overturning Moment ASD: 0.6D + 0.7E ∑ ( ) ( ) GOOD A.1.2.3 Eccentric Bearing ∑ ( ) ( ) GOOD A.1.2.4 Beam Shear LRFD: qu = 1.5*qmax = 1.5*11.39 = 17.1 ksf (1.5 ~ average load factor) Paragon Structural Consultants 110 | P a g e ( ) ( ) ( ) ( ) √ √ ⁄ GOOD A.1.2.5 Flexural Reinforcement ( ) ( ) GOOD A.2 SLAB CALCULATIONS A.2.1 Strength checks A.2.1.1 Factored Moment Demand – values used over first interior column LRFD: ( ) ( ) ( ) () A.2.1.2 Factored Moment Capacity – values used over first interior column ( ) Paragon Structural Consultants 111 | P a g e ( ) ( ) A.3 GIRDER CALCULATIONS A.3.1 Computed using a typical B1 on floor 2 A.3.1.1 Bar Cutoff Points for bottom reinforcement ( √ ( ) ) ( √ ( ) ) { { } } { { } ( ) A.4 COLUMN CALCULATIONS Preliminary column size: φ0.85f’cAg = Pu  0.4f’cAg = Pu Pu = max load before live load envelopes and live load reduction = 1152 k Ag = = ( ) = 480 in 2 Preferred a square column; to find dimensions from Ag, square root Ag. Final design: 22” by 22” column Sample calculation to find reinforcement ratio: where ρ is reinforcement ratio and the ideal reinforcement ratio lies between 1-3% For 1.5% reinforcement: Paragon Structural Consultants 112 | P a g e To find number of bars, divide by area of bar of preferred bar: No. of bars Sample calculation for spacing for seismic: ACI 21.5.3.2 s 0 = min (d/4, 6d b , 6) For No. 8 bar: s 0 = min (5.5, 6, 6) – spacing is 5.5 inches or less – using 4 inches Sample calculation for length measured from joint face, l 0 : l 0 = max (l c /6, h c , 18) For 14’ 8” bay (l c ): l 0 = max (29.3, 22, 18) – length is 30 inches Sample calculation for spacing outside of lengthl 0 for seismic: ACI 21.13.3.2 s = min (6d b , 6) For No. 8 bar: s = min (6, 6) – spacing is 6 inches Sample calculation for area required for hoop configuration: ACI 21.6.4 (for seismic) A sh = To find number of hoop ties using No. 4 ties: No. of bars Sample calculation for hoop extensions: ACI 21.5.3 3 in ≤ 6d b For No. 4 tie: 3 in ≤ 6(0.5) – extension is 3 inches Sample calculation for splice length: ACI 12.16.1 0.0005f y d b where f y is 60000 psi and d b is No. 8 – 1 in, No. 9 – 1.128 in, No. 10 – 1.27 in For No. 8 bar: 0.0005 x 60000 psi x 1 = 30” Paragon Structural Consultants 113 | P a g e A.5 LATERAL ANALYSIS CALCULATIONS A.5.1 Lateral Force Method Finding shear for Wall 1 (strong axis in N-S direction - force applied in the E-W direction) V x = V y = 2095 kips I 1 = 68309457 in 4 H w = 520.8” A w = 7348 in 2 I mod = = 37943287 in 4 ∑ ∑ [ ∑ ] [ ] ( ) Eccentricities: e y and e x - See CM and CR calculations. e y = 17.8’ = 213.6” e x = 16.25’ = 195” Torsion caused by the lateral loads as follows: T x = 2095 k x 213.6” = 447364 k-in T y = 2095 k x 195” = 409154 k-in ∑ ∑ ∑ (Walls perpendicular to N-S direction) ∑ (Walls perpendicular to E-W direction) K t = 3.27E+13 [ ∑ ] [ ] ( ) [ ] () [ () () ] ( ()) A.5.2 Stiffness Method Finding Shear for Wall 1 (strong axis in N-S direction – force applied in E-W direction): ( ) ( ) ( ) ( ) Paragon Structural Consultants 114 | P a g e ( ) (∑ ) [ ] [ ∑ ∑ ] [ ] A w = l x t; l = length = 27.8’ x 12 = 334”, t = thickness = 22”; A w = 7348 in 2 h = height of wall = 528” (the height of the wall where force is applied – not the top because that will be too conservative) E = 57√(f’c) = 4415 ksi; I = bh 3 /12  using I mod = = 37943287 in 4 K 1,2 (just taking flexural into account) = 3415 k/in [ ] [ ∑ ∑ ] [ ] Δ = 0.04 in; θ=0.000002553 ( ) A.6 CONNECTION CALCULATIONS A.6.1 Beam Foundation Connections Area of reinforcement for dowels (ACI 15.8.2.1): A s = 0.005A g A g is the gross area of the column A s = 0.005 x 22 2 = 2.42 in 2 To find how many dowels to use, choose a bar size. Try a No. 7 dowel: No. of bars = = = 4 bars Cut off for distance the dowels extend into column (ACI 12.16.1): Lap splice length of a No. 7 bar: 0.0005f y d b 0.0005 x 60000 psi x 0.845 in = 26.25 in Paragon Structural Consultants 115 | P a g e The dowels extend into the column for 26 inches Cut off for distance the dowels extend into foundation (ACI 12.3.2): Compression developmental length of the dowel: √ = √ ( ) = 16.6 in = 17 in A.6.2 Beam Column Connections A.6.2.1 Exterior joints: The standard is to use a 90˚ hook in normal-weight concrete with the length at least √ (ACI 12.7.5.1) Sample calculation for No. 8 bar: √ Sample calculation for diameter bend and extension (ACI 7.1.3): For No. 9 bar: Diameter bend: 8d b = 9.024 = 9 in Extension after bend: 12d b = 13.536 = 14 in A.6.2.2 Interior joints: Sample calculation of development length for compression members (ACI 12.3.2): Compression developmental length of a No. 9 bar: √ = √ () = 15.49 in = 16 in www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 1 6/9/2014 Specifier's comments: 1 Input data Anchor type and diameter: Heavy Square Head ASTM F 1554 GR. 105 7/8 Effective embedment depth: h ef = 4.724 in. Material: ASTM F 1554 Proof: design method ACI 318-08 / CIP Stand-off installation: without clamping (anchor); restraint level (anchor plate): 2.00; e b = 1.250 in.; t = 0.500 in. Hilti Grout: CB-G EG, epoxy, f c,Grout = 14939 psi Anchor plate: l x x l y x t = 10.000 in. x 10.000 in. x 0.500 in.; (Recommended plate thickness: not calculated) Profile: Square HSS (AISC); (L x W x T) = 4.000 in. x 4.000 in. x 0.125 in. Base material: cracked concrete, 6000, f c ' = 6000 psi; h = 7.000 in. Reinforcement: tension: condition B, shear: condition B; edge reinforcement: > No. 4 bar with stirrups Seismic loads (cat. C, D, E, or F) no Geometry [in.] & Loading [lb, in.lb] www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 2 6/9/2014 2 Load case/Resulting anchor forces Load case: Design loads Anchor reactions [lb] Tension force: (+Tension, -Compression) Anchor Tension force Shear force Shear force x Shear force y 1 1542 4375 4375 0 2 1542 4375 4375 0 3 1542 4375 4375 0 4 1542 4375 4375 0 max. concrete compressive strain: - [‰] max. concrete compressive stress: - [psi] resulting tension force in (x/y)=(0.000/0.000): 6167 [lb] resulting compression force in (x/y)=(0.000/0.000): 0 [lb] Tension 1 2 3 4 x y 3 Tension load Load N ua [lb] Capacity ffff N n [lb] Utilization bbbbN = N ua / ffff N n Status Steel Strength* 1542 43312 4 OK Pullout Strength* 1542 49224 4 OK Concrete Breakout Strength** 6167 27072 23 OK Concrete Side-Face Blowout, direction ** N/A N/A N/A N/A * anchor having the highest loading **anchor group (anchors in tension) 3.1 Steel Strength N sa = n A se,N f uta ACI 318-08 Eq. (D-3) f N steel ≥ N ua ACI 318-08 Eq. (D-1) Variables n A se,N [in. 2 ] f uta [psi] 1 0.46 125001 Calculations N sa [lb] 57750 Results N sa [lb] fsteel f N sa [lb] N ua [lb] 57750 0.750 43312 1542 3.2 Pullout Strength N pN = yc,p N p ACI 318-08 Eq. (D-14) N p = 8 A brg f ' c ACI 318-08 Eq. (D-15) f N pN ≥ N ua ACI 318-08 Eq. (D-1) Variables yc,p A brg [in. 2 ] f ' c [psi] 1.000 1.47 6000 Calculations N p [lb] 70320 Results N pn [lb] fconcrete f N pn [lb] N ua [lb] 70320 0.700 49224 1542 www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 3 6/9/2014 3.3 Concrete Breakout Strength N cbg = ( A Nc A Nc0 ) yec,N yed,N yc,N ycp,N N b ACI 318-08 Eq. (D-5) f N cbg ≥ N ua ACI 318-08 Eq. (D-1) A Nc see ACI 318-08, Part D.5.2.1, Fig. RD.5.2.1(b) A Nc0 = 9 h 2 ef ACI 318-08 Eq. (D-6) yec,N = ( 1 1 + 2 e ' N 3 h ef ) ≤ 1.0 ACI 318-08 Eq. (D-9) yed,N = 0.7 + 0.3 ( c a,min 1.5h ef ) ≤ 1.0 ACI 318-08 Eq. (D-11) ycp,N = MAX ( c a,min c ac , 1.5h ef c ac ) ≤ 1.0 ACI 318-08 Eq. (D-13) N b = k c l √f ' c h 1.5 ef ACI 318-08 Eq. (D-7) Variables h ef [in.] e c1,N [in.] e c2,N [in.] c a,min [in.] yc,N 4.724 0.000 0.000 ∞ 1.000 c ac [in.] k c l f ' c [psi] 0.000 24 1 6000 Calculations A Nc [in. 2 ] A Nc0 [in. 2 ] yec1,N yec2,N yed,N ycp,N N b [lb] 406.96 200.88 1.000 1.000 1.000 1.000 19090 Results N cbg [lb] fconcrete f N cbg [lb] N ua [lb] 38674 0.700 27072 6167 www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 4 6/9/2014 4 Shear load Load V ua [lb] Capacity ffff V n [lb] Utilization bbbbV = V ua / ffff V n Status Steel Strength* 4375 18018 25 OK Steel failure (with lever arm)* 4375 6384 69 OK Pryout Strength** 17500 54144 33 OK Concrete edge failure in direction ** N/A N/A N/A N/A * anchor having the highest loading **anchor group (relevant anchors) 4.1 Steel Strength V sa = n 0.6 A se,V f uta ACI 318-08 Eq. (D-20) f V steel ≥ V ua ACI 318-08 Eq. (D-2) Variables n A se,V [in. 2 ] f uta [psi] 1 0.46 125001 Calculations V sa [lb] 34650 Results V sa [lb] fsteel feb f V sa [lb] V ua [lb] 34650 0.650 0.800 18018 4375 4.2 Steel failure (with lever arm) V M s = aM · M s L b bending equation for stand-off M s = M 0 s ( 1 - N ua f N sa ) resultant flexural resistance of anchor M 0 s = (1.2) (S) (f u,min ) characteristic flexural resistance of anchor ( 1 - N ua f N sa ) reduction for tensile force acting simultaneously with a shear force on the anchor S = p (d) 3 32 elastic section modulus of anchor bolt at concrete surface L b = z + (n)(d 0 ) internal lever arm adjusted for spalling of the surface concrete f V M s ≥ V ua ACI 318-08 Eq. (D-2) Variables aM f u,min [psi] N ua [lb] f N sa [lb] z [in.] n d 0 [in.] 2.00 125001 1542 43312 1.500 0.500 0.875 Calculations M 0 s [in.lb] ( 1 - N ua f N sa ) M s [in.lb] L b [in.] 9865.410 0.964 9514.241 1.938 Results V M s [lb] fsteel f V M s [lb] V ua [lb] 9821 0.650 6384 4375 www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 5 6/9/2014 4.3 Pryout Strength V cpg = k cp [( A Nc A Nc0 ) yec,N yed,N yc,N ycp,N N b] ACI 318-08 Eq. (D-31) f V cpg ≥ V ua ACI 318-08 Eq. (D-2) A Nc see ACI 318-08, Part D.5.2.1, Fig. RD.5.2.1(b) A Nc0 = 9 h 2 ef ACI 318-08 Eq. (D-6) yec,N = ( 1 1 + 2 e ' N 3 h ef ) ≤ 1.0 ACI 318-08 Eq. (D-9) yed,N = 0.7 + 0.3 ( c a,min 1.5h ef ) ≤ 1.0 ACI 318-08 Eq. (D-11) ycp,N = MAX ( c a,min c ac , 1.5h ef c ac ) ≤ 1.0 ACI 318-08 Eq. (D-13) N b = k c l √f ' c h 1.5 ef ACI 318-08 Eq. (D-7) Variables k cp h ef [in.] e c1,N [in.] e c2,N [in.] c a,min [in.] 2 4.724 0.000 0.000 ∞ yc,N c ac [in.] k c l f ' c [psi] 1.000 - 24 1 6000 Calculations A Nc [in. 2 ] A Nc0 [in. 2 ] yec1,N yec2,N yed,N ycp,N N b [lb] 406.96 200.88 1.000 1.000 1.000 1.000 19090 Results V cpg [lb] fconcrete f V cpg [lb] V ua [lb] 77348 0.700 54144 17500 5 Combined tension and shear loads bN bV z Utilization bN,V [%] Status 0.228 0.685 5/3 62 OK bNV = b z N + b z V <= 1 6 Warnings • Load re-distributions on the anchors due to elastic deformations of the anchor plate are not considered. The anchor plate is assumed to be sufficiently stiff, in order not to be deformed when subjected to the loading! • Condition A applies when supplementary reinforcement is used. The Φ factor is increased for non-steel Design Strengths except Pullout Strength and Pryout strength. Condition B applies when supplementary reinforcement is not used and for Pullout Strength and Pryout Strength. Refer to your local standard. • ACI 318 does not specifically address anchor bending when a stand-off condition exists. PROFIS Anchor calculates a shear load corresponding to anchor bending when stand-off exists and includes the results as a shear Design Strength! • Checking the transfer of loads into the base material and the shear resistance are required in accordance with ACI 318 or the relevant standard! Fastening meets the design criteria! www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 6 6/9/2014 Coordinates Anchor in. Anchor x y c -x c +x c -y c +y 1 -3.000 -3.000 - - - - 2 3.000 -3.000 - - - - 3 -3.000 3.000 - - - - 4 3.000 3.000 - - - - 7 Installation data Anchor plate, steel: - Anchor type and diameter: Heavy Square Head ASTM F 1554 GR. 105 7/8 Profile: Square HSS (AISC); 4.000 x 4.000 x 0.125 in. Installation torque: -0.009 in.lb Hole diameter in the fixture: d f = 0.938 in. Hole diameter in the base material: - in. Plate thickness (input): 0.500 in. Hole depth in the base material: 4.724 in. Recommended plate thickness: not calculated Minimum thickness of the base material: 6.776 in. Cleaning: No cleaning of the drilled hole is required 1 2 3 4 2.000 6.000 2.000 2 . 0 0 0 6 . 0 0 0 2 . 0 0 0 x y 5.000 5.000 5 . 0 0 0 5 . 0 0 0 www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 1 6/9/2014 Specifier's comments: 1 Input data Anchor type and diameter: Heavy Square Head ASTM F 1554 GR. 105 1 1/8 Effective embedment depth: h ef = 4.724 in. Material: ASTM F 1554 Proof: design method ACI 318-08 / CIP Stand-off installation: without clamping (anchor); restraint level (anchor plate): 2.00; e b = 1.250 in.; t = 0.500 in. Hilti Grout: CB-G EG, epoxy, f c,Grout = 14939 psi Anchor plate: l x x l y x t = 11.106 in. x 11.184 in. x 0.500 in.; (Recommended plate thickness: not calculated) Profile: Square HSS (AISC); (L x W x T) = 4.000 in. x 4.000 in. x 0.250 in. Base material: cracked concrete, 6000, f c ' = 6000 psi; h = 7.000 in. Reinforcement: tension: condition B, shear: condition B; edge reinforcement: > No. 4 bar with stirrups Seismic loads (cat. C, D, E, or F) no Geometry [in.] & Loading [lb, in.lb] www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 2 6/9/2014 2 Load case/Resulting anchor forces Load case: Design loads Anchor reactions [lb] Tension force: (+Tension, -Compression) Anchor Tension force Shear force Shear force x Shear force y 1 5171 8125 8125 0 2 5171 8125 8125 0 3 5171 8125 8125 0 4 5171 8125 8125 0 max. concrete compressive strain: - [‰] max. concrete compressive stress: - [psi] resulting tension force in (x/y)=(0.000/0.000): 20682 [lb] resulting compression force in (x/y)=(0.000/0.000): 0 [lb] Tension 1 2 3 4 x y 3 Tension load Load N ua [lb] Capacity ffff N n [lb] Utilization bbbbN = N ua / ffff N n Status Steel Strength* 5171 71531 8 OK Pullout Strength* 5171 76978 7 OK Concrete Breakout Strength** 20682 31548 66 OK Concrete Side-Face Blowout, direction ** N/A N/A N/A N/A * anchor having the highest loading **anchor group (anchors in tension) 3.1 Steel Strength N sa = n A se,N f uta ACI 318-08 Eq. (D-3) f N steel ≥ N ua ACI 318-08 Eq. (D-1) Variables n A se,N [in. 2 ] f uta [psi] 1 0.76 125001 Calculations N sa [lb] 95375 Results N sa [lb] fsteel f N sa [lb] N ua [lb] 95375 0.750 71531 5171 3.2 Pullout Strength N pN = yc,p N p ACI 318-08 Eq. (D-14) N p = 8 A brg f ' c ACI 318-08 Eq. (D-15) f N pN ≥ N ua ACI 318-08 Eq. (D-1) Variables yc,p A brg [in. 2 ] f ' c [psi] 1.000 2.29 6000 Calculations N p [lb] 109968 Results N pn [lb] fconcrete f N pn [lb] N ua [lb] 109968 0.700 76978 5171 www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 3 6/9/2014 3.3 Concrete Breakout Strength N cbg = ( A Nc A Nc0 ) yec,N yed,N yc,N ycp,N N b ACI 318-08 Eq. (D-5) f N cbg ≥ N ua ACI 318-08 Eq. (D-1) A Nc see ACI 318-08, Part D.5.2.1, Fig. RD.5.2.1(b) A Nc0 = 9 h 2 ef ACI 318-08 Eq. (D-6) yec,N = ( 1 1 + 2 e ' N 3 h ef ) ≤ 1.0 ACI 318-08 Eq. (D-9) yed,N = 0.7 + 0.3 ( c a,min 1.5h ef ) ≤ 1.0 ACI 318-08 Eq. (D-11) ycp,N = MAX ( c a,min c ac , 1.5h ef c ac ) ≤ 1.0 ACI 318-08 Eq. (D-13) N b = k c l √f ' c h 1.5 ef ACI 318-08 Eq. (D-7) Variables h ef [in.] e c1,N [in.] e c2,N [in.] c a,min [in.] yc,N 4.724 0.000 0.000 ∞ 1.000 c ac [in.] k c l f ' c [psi] 0.000 24 1 6000 Calculations A Nc [in. 2 ] A Nc0 [in. 2 ] yec1,N yec2,N yed,N ycp,N N b [lb] 474.25 200.88 1.000 1.000 1.000 1.000 19090 Results N cbg [lb] fconcrete f N cbg [lb] N ua [lb] 45069 0.700 31548 20682 www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 4 6/9/2014 4 Shear load Load V ua [lb] Capacity ffff V n [lb] Utilization bbbbV = V ua / ffff V n Status Steel Strength* 8125 29757 28 OK Steel failure (with lever arm)* 8125 12261 67 OK Pryout Strength** 32500 63096 52 OK Concrete edge failure in direction ** N/A N/A N/A N/A * anchor having the highest loading **anchor group (relevant anchors) 4.1 Steel Strength V sa = n 0.6 A se,V f uta ACI 318-08 Eq. (D-20) f V steel ≥ V ua ACI 318-08 Eq. (D-2) Variables n A se,V [in. 2 ] f uta [psi] 1 0.76 125001 Calculations V sa [lb] 57225 Results V sa [lb] fsteel feb f V sa [lb] V ua [lb] 57225 0.650 0.800 29757 8125 4.2 Steel failure (with lever arm) V M s = aM · M s L b bending equation for stand-off M s = M 0 s ( 1 - N ua f N sa ) resultant flexural resistance of anchor M 0 s = (1.2) (S) (f u,min ) characteristic flexural resistance of anchor ( 1 - N ua f N sa ) reduction for tensile force acting simultaneously with a shear force on the anchor S = p (d) 3 32 elastic section modulus of anchor bolt at concrete surface L b = z + (n)(d 0 ) internal lever arm adjusted for spalling of the surface concrete f V M s ≥ V ua ACI 318-08 Eq. (D-2) Variables aM f u,min [psi] N ua [lb] f N sa [lb] z [in.] n d 0 [in.] 2.00 125001 5171 71531 1.500 0.500 1.125 Calculations M 0 s [in.lb] ( 1 - N ua f N sa ) M s [in.lb] L b [in.] 20967.592 0.928 19451.989 2.063 Results V M s [lb] fsteel f V M s [lb] V ua [lb] 18863 0.650 12261 8125 www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 5 6/9/2014 4.3 Pryout Strength V cpg = k cp [( A Nc A Nc0 ) yec,N yed,N yc,N ycp,N N b] ACI 318-08 Eq. (D-31) f V cpg ≥ V ua ACI 318-08 Eq. (D-2) A Nc see ACI 318-08, Part D.5.2.1, Fig. RD.5.2.1(b) A Nc0 = 9 h 2 ef ACI 318-08 Eq. (D-6) yec,N = ( 1 1 + 2 e ' N 3 h ef ) ≤ 1.0 ACI 318-08 Eq. (D-9) yed,N = 0.7 + 0.3 ( c a,min 1.5h ef ) ≤ 1.0 ACI 318-08 Eq. (D-11) ycp,N = MAX ( c a,min c ac , 1.5h ef c ac ) ≤ 1.0 ACI 318-08 Eq. (D-13) N b = k c l √f ' c h 1.5 ef ACI 318-08 Eq. (D-7) Variables k cp h ef [in.] e c1,N [in.] e c2,N [in.] c a,min [in.] 2 4.724 0.000 0.000 ∞ yc,N c ac [in.] k c l f ' c [psi] 1.000 - 24 1 6000 Calculations A Nc [in. 2 ] A Nc0 [in. 2 ] yec1,N yec2,N yed,N ycp,N N b [lb] 474.25 200.88 1.000 1.000 1.000 1.000 19090 Results V cpg [lb] fconcrete f V cpg [lb] V ua [lb] 90137 0.700 63096 32500 5 Combined tension and shear loads bN bV z Utilization bN,V [%] Status 0.656 0.663 5/3 100 OK bNV = b z N + b z V <= 1 6 Warnings • Load re-distributions on the anchors due to elastic deformations of the anchor plate are not considered. The anchor plate is assumed to be sufficiently stiff, in order not to be deformed when subjected to the loading! • Condition A applies when supplementary reinforcement is used. The Φ factor is increased for non-steel Design Strengths except Pullout Strength and Pryout strength. Condition B applies when supplementary reinforcement is not used and for Pullout Strength and Pryout Strength. Refer to your local standard. • ACI 318 does not specifically address anchor bending when a stand-off condition exists. PROFIS Anchor calculates a shear load corresponding to anchor bending when stand-off exists and includes the results as a shear Design Strength! • Checking the transfer of loads into the base material and the shear resistance are required in accordance with ACI 318 or the relevant standard! Fastening meets the design criteria! www.hilti.us Profis Anchor 2.4.7 Input data and results must be checked for agreement with the existing conditions and for plausibility! PROFIS Anchor ( c ) 2003-2009 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan Company: Specifier: Address: Phone I Fax: E-Mail: | Page: Project: Sub-Project I Pos. No.: Date: 6 6/9/2014 Coordinates Anchor in. Anchor x y c -x c +x c -y c +y 1 -3.782 -3.822 - - - - 2 3.782 -3.822 - - - - 3 -3.782 3.822 - - - - 4 3.782 3.822 - - - - 7 Installation data Anchor plate, steel: - Anchor type and diameter: Heavy Square Head ASTM F 1554 GR. 105 1 1/8 Profile: Square HSS (AISC); 4.000 x 4.000 x 0.250 in. Installation torque: -0.009 in.lb Hole diameter in the fixture: d f = 1.205 in. Hole diameter in the base material: - in. Plate thickness (input): 0.500 in. Hole depth in the base material: 4.724 in. Recommended plate thickness: not calculated Minimum thickness of the base material: 6.974 in. Cleaning: No cleaning of the drilled hole is required 1 2 3 4 1.771 7.564 1.771 1 . 7 7 0 7 . 6 4 4 1 . 7 7 0 x y 5.553 5.553 5 . 5 9 2 5 . 5 9 2