DBDsoftPage 1 of 93 DBDsoft Top Next DBDsoft Version 2014 standard v. 0.9.0.0 – November 2014 User Manual graphic graphic Introduction Previous Top Next Introduction DBDsoft is a program developed to assist engineers in the application of the Direct displacement-based seismic design (DDBD) procedure of Priestley et al. (2007). The program is not intended as an analysis tool and instead, the software relies on the user to indicate how the design solution should be developed. To this extent, while traditional modelling information such as section dimensions and material properties are required, the strength and stiffness of elements are not specified since they should be an outcome of the design process. As the necessary performance of a building can be ensured through any one of many possible distributions of strength (and stiffness), users of DBDsoft are required to indicate the proportions of the seismic loads that will be resisted by the different elements of the load-resisting system. This very novel feature of the software recognises that inelastic seismic force distributions can be controlled through good design (see Design Strength Proportions for further details). With proportions of strength decided, the software will then compute the required design base shear and the required flexural strengths of plastic hinge zones. In this current version of DBDsoft, the engineer should then calculate the required reinforcement (reinforced concrete sections) or verify the steel profiles' capacity (steel sections) for each plastic hinge zone and optimise the design solution as desired. The task of capacity design also needs to be undertaken by the engineer, who should suitably amplify the plastic-hinge design actions indicated by the software to identify capacity design actions for all members in the structure. Users should verify the seismic performance of the design solution by using a code-compliant analysis method such as pushover analysis or non-linear time-history analyses (the permissible method will depend on the local building code requirements). We, the developers, trust that you will enjoy the benefits that this software offers. We would welcome any comments and suggestions that could improve future versions of the software. Information for Academics Previous Top Next Information for Academics In order to cite this software in publications please use the following citation: Sullivan, T.J., Bono, F., Nievas, C.I., Magni, F., Calvi, G.M. (2014) “DBDsoft: A program for the displacement-based seismic design of structures, Beta Version” EUCENTRE, www.eucentre.it. See the section on “Background” for some notes on the theory of the Direct Displacement-Based Seismic Design procedure and for a list of references where more information may be found. Contacting Us file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm Previous Top Next 11/12/2015 DBDsoft Page 2 of 93 Contacting Us If you have any suggestions for improvements, or if you would like to receive an updated version of the software, please email us at:
[email protected] Release Information Previous Top Next Release Information This version of DBDsoft is released as a trial version in order to gain feedback on the basic functioning of the program and get suggestions on possible improvements that can be implemented in the subsequent versions. The release message, viewed upon opening the software, is also shown here: Disclaimer Previous Top Next Disclaimer DBDsoft is intended to assist engineers apply the Direct Displacement-Based Design (DDBD) procedure of Priestley et al. (2007). Whilst efforts have been made to verify the accuracy and robustness of this software, no guarantees are provided that the DDBD calculations have been implemented correctly. Consequently, the EUCENTRE and the program developers take no responsibility for the consequences that any errors within the software may cause program users. Furthermore, users are advised that the DDBD procedure is not currently a code-compliant seismic design solution and therefore they should verify code-compatibility of the design solutions derived from the software by using analysis and design methods that conform with code requirements. file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm 11/12/2015 DBDsoft Page 3 of 93 About EUCENTRE Previous Top Next About EUCENTRE EUCENTRE is a non profit Foundation launched by the Italian Deparment of Civil Defence ( Dipartimento della Protezione Civile), the Italian National Institute of Geophysics and Vulcanology ( Istituto Nazionale di Geofisica e Vulcanologia), the University of Pavia ( Università degli Studi di Pavia ) and the University Institute for Superior Studies of Pavia ( Istituto Universitario di Studi Superiori di Pavia), with the aim of promoting, sustaining and overseeing training and research in the field of the reduction of seismic risk, through the following actions: § Development of applied research in the field of seismic engineering, oriented towards reaching concrete goals of evaluation and reduction of vulnerability and risk; § Development of activities useful for the definition of specific lines of public action, guidelines and regulator documents, bearing in mind the state of the art in the international scene as well; § Training personnel with strong scientific and professional capabilities in the field of seismic engineering, in particular, in the field of seismology, geology, geotechnics, behaviour of materials and structures, design of new structures, evaluation and retrofit of existing structures, even in emergency situations; § Carrying out scientific and technical consultancy at a national and international level, in the field of seismic engineering. For more information visit EUCENTRE’s website www.eucentre.it Background Previous Top Next Background Seismic design in current codes is based on force (and hence acceleration) rather than displacement, essentially as a consequence of the historical developments of an understanding of structural dynamics and, more specifically, of the response of structures to seismic actions and the progressive modifications and improvement of seismic codes worldwide. In the first decades of the last century, after several major earthquakes, such as Messina (Italy, 1908), Kanto (Japan, 1925), Napier (New Zealand, 1932), and Long Beach (USA, 1933) the first design codes started being developed. These codes were essentially prescribing specific detailing and construction rules and in cases the application of some lateral inertia forces. Typically, and possibly in analogy with some kind of wind design, a value of about 10% of the building weight applied as a vertically distributed lateral force was required, regardless of building period. This initial force-based approach has been essentially retained with the progressive increasing of understanding of the significance of structural dynamic characteristics, that lead to period-dependent design lateral force levels in most seismic design codes, and even when it became clear that many structures had survived earthquakes capable of inducing inertia forces many times larger than those corresponding to their structural strength, if a linear response was assumed. This apparent inconsistency was explained after the first simple inelastic time-history analyses had been performed, and the concept of ductility introduced, to reconcile the anomaly of survival with inadequate strength. In the seventy’s, relationships between ductility and force-reduction factor were developed, introducing the well known concepts of “equal displacement”, “equal energy” and “equal force” approximations, that appeared to be appropriate to estimate the “real” structural response as a function of linear response and period of vibration of the structures. Since then, ductility has been considered the fundamental parameter to estimate appropriate “force reduction factors”, to be used to determine the design lateral force levels. Much research effort was therefore directed to determining the available ductility capacity of different structural systems, performing extensive experimental and analytical studies to determine their safe displacement capacity. It is now clear that this approach is implicitly assuming displacement capacity, and not force capacity, as the basis for design. However, the design process is still carried out in terms of required strength in essentially all codes of practice around the world and displacement capacity, if directly checked at all, is only a final product of the design procedure. This brief summary of the history of seismic design indicates that initially design was purely based on strength, or force considerations. However, as demonstrated by Priestley (1993) and Priestley et al. (2007) there are several conceptual drawbacks associated with the use of force-based methods in seismic design. With reference to the design of a RC file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm 11/12/2015 htm 11/12/2015 .DBDsoft Page 4 of 93 building possessing three walls A. a brief review of some of the problems with force-based design can be made. the force-based approach makes a prediction of the elastic forces of the structure and uniformly reduces these by a behaviour factor to obtain inelastic design forces. It is clear that the shear in Walls A & C is only one-quarter that for Wall B in the elastic state. code methods divide elastic forces by a force-reduction factor which is set in proportion to the ductility capacity of the structure. However. can be shown to involve: The use of ductility capacity dependent force-reduction factors. Figure 1. at the design displacement of the system. it is evident that the ductility capacity could not be developed in all the walls simultaneously. This point suggests that the use of force-reduction factors that are based on ductility capacity is inappropriate. As mentioned above. it is evident that the system ductility demand is actually lower than the ductility capacity of the critical element. such that at the design displacement. For example. The difficulty in defining the system ductility for mixed structural systems. file:///C:/Users/User/AppData/Local/Temp/~hh512C. illustrated in Figure 1. In order to obtain design force levels. Interestingly. the actual ductility demand for a structural system will typically be smaller than the ductility capacity of the structure. It is clear that in controlling non-structural deformations the system ductility is less than the ductility capacity of the long stiff Wall B and considerably less than the shorter flexible Walls A & C. whereby the yield displacement of the system would typically be obtained through a bi-linear representation of the system response. suppose that Wall B shown in Figure 1 only had a ductility capacity of three. the elastic force distribution can be very different to the inelastic force distribution. This point demonstrates that force reduction factors cannot be easily set for mixed structural systems. The amount by which it is lower depends on the mixed system considered and larger differences could be expected for different mixed systems. This point demonstrates that elastic analyses using the initial stiffness are inappropriate for predictions of inelastic force distributions. The main issues associated with current force-based design methods. its ductility capacity had been reached. However. The force distributions predicted through the use of the elastic stiffness for analysis. Response of a RC structure possessing walls of different length – used to highlight issues associated with force-based design. However. Current codes typically require that the behaviour factor for mixed structural systems be set equal to the lower of the two systems. However. B and C) and the total system as it is displaced to a deformation limit required to control damage to non-structural elements. (2007) in detail. identified and discussed in Priestley et al. This can be seen in Figure 1 by considering the elastic shear proportions that have developed when Wall B first yields. The right side of Figure 1 presents the forcedisplacement behaviour for the three walls (A. it is clear that the proportion of shear in Walls A & C has now doubled to be 50% of that in Wall B. because elements within the structure do not all yield at the same level of deformation. The system ductility at this displacement is obtained by dividing the design displacement by the yield displacement of the system. Furthermore. B and C. this does not consider how the ductility demands and forces will develop for the combined structural system. as Walls A & C have considerably larger yield displacements than Wall B. such as frame-wall structures. (2004). since these affect the energy dissipation characteristics of the structure. The first task of the procedure. In reality. given that the cracked section stiffness is best defined using the secant stiffness to first yield as EI=Mn/?y. this version of DBDsoft has been developed for regular RC buildings. As such. The relationship illustrated for the wall system within Figure 1 uses the equal-displacement rule. Sullivan et al. the flexural strength is required. the displacement profile is obtained using first principles. proposing displacement-based approaches for earthquake engineering evaluation and design. however. (2007) and also released in model code format (Calvi and Sullivan 2008). 2005. For some forms of MDOF structure. The most developed DBD method currently available is the Direct DBD approach. I is the second moment of inertia. Mn is the section flexural strength and ?y is the yield curvature) it is clear that the stiffness of a RC element will depend on the strength it is assigned. the relationship between elastic and inelastic displacements should depend on the hysteretic properties of the structure being considered. This is the approximation adopted in Eurocode 8. As such. however. 2008). 2006 and Beyer et al. The main steps in the Direct DBD procedure are illustrated in Figure 2.htm 11/12/2015 . A review and comparison of different displacement-based design methodologies has been provided by Calvi (2003) and Sullivan et al. As these problems with force-based design have emerged and the importance of displacement has come to be better appreciated. Consequently. The force-based design approach estimates the inelastic displacement response based on the elastic displacement response. further verification and development is required for other structural systems and for complex response due to torsion and higher modes. such as RC frames. could be doubled by simply doubling the amount of longitudinal reinforcement in the section.DBDsoft Page 5 of 93 The inter-dependency of strength and stiffness for certain structural types (such as RC structures). As the force-based design procedure relies on the period of vibration in order to determine the required strength. This is achieved through knowledge of the mass distribution and the displacement profile at maximum response. (where E is the section modulus. empirical shape functions which have been calibrated to fit results of multiple nonlinear time-history analyses are used. the initial stiffness of Wall B in Figure 1 for example. several researchers started pointing out the inconsistency associated with the use of force for design. In the 1990s and early this century. The relationships used to relate elastic displacement to inelastic displacement response. It has been shown by Priestley (1998). this point shows that the design procedure cannot be easily implemented for RC structures. described in a text by Priestley et al. whereas for other MDOF structures. with the aim of providing improved reliability in the engineering process by more directly relating computed response and expected structural performance. different relationships are used whereby the inelastic displacement is often approximated as being less than the elastic displacement. attempts to modify and improve existing force-based approaches have been made. such as the approach for RC walls. Priestley and Kowalsky (1998) and Paulay (2002) that the yield curvature of RC sections is principally a function of the section geometry and yield strain of longitudinal reinforcement. is to develop an equivalent SDOF representation of the MDOF structure being designed. shown as Figure 2 (a). the stiffness is not purely a function of the section geometry and therefore in order to know the cracked elastic period of vibration of an RC structure. While the guidelines in the model code have been relatively well tested for RC structures (see Pettinga et al. In the United States. file:///C:/Users/User/AppData/Local/Temp/~hh512C. whereby the inelastic displacement is assumed equal to the elastic displacement. whereas in Japan the opposite occurs and an equal energy approach is used such that the inelastic displacement is estimated to be larger than the elastic displacement. In other words. The effective height is useful for the estimation of the yield displacement and ductility demands expected of a structural system. he. The effective height is also a function of the displaced shape of the masses at maximum response. Overview of the main phases within the Direct DBD approach (adapted from Priestley et al. The use of the secant-stiffness is based on the Substitute Structure approach developed by Gulkan and Sozen (1974) and Shibata and Sozen (1976). which is highlighted in the second step of the procedure. When the displaced shape of the structure at maximum response is known. This maximum or design displacement value is set by the designer to ensure acceptable levels of deformation for a given risk event. shown as Figure 2(b). in addition to the storey height. can be obtained using: (1) where n is the total number of storeys. whereas force-based design uses the initial stiffness characteristics. as shown in Eq. the effective stiffness is used together with an equivalent viscous file:///C:/Users/User/AppData/Local/Temp/~hh512C. Direct DBD characterises the structure to be designed using the effective or secant-stiffness to peak displacement response. The displacement shape at maximum response signals an important difference between Direct DBD and force-based design. and mi are the masses and Δi the displacements (or displacement shape) at level i. Δd. The bilinear envelope of the lateral forcedisplacement response of the SDOF representation (shown in Figure 2(b)) illustrates the secant stiffness Ke at the maximum displacement ?d. then the design displacement. With reference to Figure 2(a). of the structure.DBDsoft Page 6 of 93 Figure 2. 2007). (2).htm 11/12/2015 . this design displacement corresponds to the displacement at the effective height. hi. (2) Since the actual structural behaviour is non-linear. (4). for building structures in which the main lateral resisting system forms plastic hinges over the full height of the structure (e. is consequently given by Eq. To illustrate how this approach would account for different hysteretic characteristics. it is then necessary to consider how the period. say. (6) In order to obtain design strengths for individual members of the MDOF system. k = 1.g.(7): Floors 1 to n-1: (7a) Roof (Floor n): (7b) Where. (4) Within Eq. the design lateral force. Fd.0 is adopted due to the fact that higher mode effects are not expected to be significant for this kind of structures.(7) is k = 0. the design base shear from Eq. Te. which is equivalent to the design base shear force.DBDsoft Page 7 of 93 damping term. For a given level of ductility demand. and the corresponding damping estimated from the expected ductility demands. Ke. With the design displacement of the substitute structure at maximum response established. a RC frame structure with multiple bays.htm 11/12/2015 . The first is to develop a structural model in which the “effective” stiffness of yielding elements is specified rather than initial stiffness values. (4). the effective period. T. The second approach is to apply an equilibrium approach. Priestley et al. as shown in Eq. K. as is shown in Eq. The lateral forces are set to be proportional to the displacements of the seismic masses. it can be seen that a structural steel frame building with compact members is assigned a higher level of equivalent viscous damping than a reinforced concrete frame building designed for the same level of ductility demand. as illustrated in Figure 2(d). To continue with design.(6) is then applied as a set of equivalent lateral forces up the height of the building. representative of the combined elastic damping and hysteretic energy absorbed during seismic response. (3). ensuring that the lateral resistance provided at each level matches the seismic demand (obtained as a storey shear force by summing the equivalent lateral forces above the storey in question). as a consequence of larger amounts of hysteretic energy dissipated during the inelastic cyclic response of steel sections. (3) The effective stiffness. a value of k = 1. at maximum displacement response can be read from a set of displacement spectra for different levels of damping. the value of k to be used in Eq. of a SDOF oscillator can be related to its stiffness. of the equivalent SDOF system at maximum displacement can be found by inverting this equation to arrive at Eq. file:///C:/Users/User/AppData/Local/Temp/~hh512C. RC wall structures). and mass. (5). frame structures). (5) From Figure 2(b).0. For. ξ. Vb.g. M. (2007) explain that there are two options for identifying the design strengths of plastic hinge zones from the equivalent lateral forces of Eq. me is the effective mass of the structure participating in the fundamental mode of vibration at maximum response.9 and for building structures in which the plastic hinges offering the main lateral resistance form at the base of the building (e. This is also established using the design displacement profile in accordance with Eq.(7). For frame-wall systems. consider the curves shown in Figure 2(c). (6). DBDsoft Page 8 of 93 it is clear that different relative beam strengths could provide the same total storey shear resistance. As such (allowing redistribution of initial elastic force proportions) the equilibrium approach gives the designer greatest flexibility in optimising the seismic design solution. See Priestley et al. (2007) for more discussion of the equilibrium approach. See Sullivan and Lago (2012) for details of the equilibrium approach applied for RC frames within DBDsoft. The design concepts are thus relatively simple. Such complexity that exists relates to determination of the “substitute structure” characteristics, the determination of the design displacement, and application of the equilibrium approach to arrive at the final design strengths. All these aspects are undertaken by DBDsoft, with the user assisting in the equilibrium analyses by specifying the desired strength proportions of plastic hinges. Previous Top Next Overview Overview The program is organised into three distinct phases: (i) the Pre-Processor Phase, (ii) the Processor Phase, and (iii) the PostProcessor Phase. An overview of each phase is provided below. The Pre-Processor Phase is where the general information about the structure, necessary for design, is provided. The PreProcessor Phase requires completion of the following modules: 1. 2. 3. 4. 5. 6. 7. 8. Materials Sections Element Classes Nodes Elements Connectivity Restraint/Releases Loads Performance Criteria The purpose of the Processor Phase is to identify the lateral load resisting system and run the design calculations. The Processor Phase requires the user to indicate the load combination that should be considered. In addition, the user should tell the program to identify the lateral stability systems, after which point the user should verify that the lateral stability systems correspond to those envisaged for the structure. Once the lateral load resisting systems have been identified, must indicate the proportions of overturning that they wish the different lateral load resisting systems to resist. This last phase is an important design decision that the user should make as it will influence the distribution and magnitude of the required strengths throughout the structure. The Post-Processor Phase is where the results of the design solution can be obtained. The main results of interest will be the required nominal flexural strengths (Mn) of plastic hinge regions. For a detailed description of the information required in each phase see the relevant sections of this user manual. For information on how the program works see the background section of this user manual and the references listed there. Getting Started Previous Top Next Getting Started To develop a design solution, basic information on the structural geometry and material properties must first be defined following the order (from left to right) of the tabs within the Pre-Processing unit. To move between modules you can either directly click on the module heading or use the drop-down menu by clicking: or Modules>Next Properties Module Modules>Previous Properties Module Example Building Previous Top Next Example Buildings file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm 11/12/2015 DBDsoft Page 9 of 93 Four case study models have already been developed within the program and by opening and reviewing them, users can quickly see how a model should be defined. To access these examples you can select the models from the drop down menu clicking: File>Test Cases>TestB1 This case study structure represents an 8-storey RC wall building in which the lateral load resisting system is formed of three cantilever walls. File>Test Cases>TestB2 This case study structure represents a 6-storey RC frame building in which the lateral load resisting system is formed of three separate frame systems. File>Test Cases>TestB3 This case study structure represents a 6-storey RC frame-wall building in which the lateral load resisting system is formed of one frame, two cantilever walls and one frame-wall system with link beams. File>Test Cases>TestB4 This case study structure represents an 8-storey steel frame building in which the lateral load resisting system is formed of one frame in the X direction. Step-by-step computation of base shear demand and overturning moment at the base are provided for all examples here. Note that information within the tables of the program can be copy-pasted (CTRL+C) into excel spreadsheets. This can be useful for development of larger structures and for exchanging common input information with other programs (such as Seismostruct; see www.seismosoft.com). Pre-Processor Previous Top Next Pre-processor The Pre-Processor Phase is where the general information about the structure, necessary for design, is provided. The PreProcessor Phase requires completion of the modules listed below, that are explained in the sub-sections that follow: 1. 2. 3. 4. 5. 6. 7. 8. Materials Sections Element Classes Nodes Elements Connectivity Restraint/Releases Loads Performance Criteria Materials Previous Top Next Materials To add a new material, first ensure that you have selected the Materials module (see Getting Started). Then either click on the blue plus symbol (see Figure) or double click on the grid of the table. The form Add New Material will then open. After providing the requested information (described in detail below) click on the Add and Close button to confirm the addition of the new material. file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm 11/12/2015 DBDsoft Page 10 of 93 To add a new material enter the material’s name, choose the material type (concrete and Reinforcing_ Steel, for reinforced concrete structures, or Structural_Steel, for steel structures) and fill in the requested fields with the material characteristics, in line with the recommendations in the next pages. Please note that in the current version of DBDsoft it is not possible to combine reinforced concrete and steel sections. Add Concrete Material Previous Top Next Add Concrete Material Add new material>type>Concrete: file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm 11/12/2015 even if well confined. εec or εeo : The strain at peak stress refers to the strain at which the concrete will be expected to have developed its “expected compressive strength”. εeu : The ultimate compressive strain refers to the strain at which the concrete will be expected to crush. Currently.5kN/m3. To account for the weight of reinforced concrete members. Currently. Ultimate compressive strain. The materials that have been added will then be listed in the grid.htm 11/12/2015 . users should specify suitable seismic masses within the Loads module. (2012) recommend that f’ce = 1. spacing and effectiveness of transverse reinforcement. this version of DBDsoft does not use this information in the calculations and therefore users can leave the default value of 24. Note that it is likely to be significantly greater than the concrete compressive strength at 28days due to the tendency for concrete to gain strength with time and the construction practice of specifying characteristic rather than mean or median strength values.5kN/m3. Priestley et al.003. (2007) and Sullivan et al.e. In lieu of more refined information.01. Aff Reinforcing Steel Material Previous Top Next Add Reinforcing Steel Material file:///C:/Users/User/AppData/Local/Temp/~hh512C. Specific weight: The specific weight of concrete should be specified in units of kN/m3 with account for the weight of reinforcement (i.3f’c where f’c is the 28 day cylinder concrete compressive strength. The default value is 24. The value of ultimate strain will depend on the quantity.004 might be specified for unconfined concrete compared to values of 0. this version of DBDsoft does not use this information in the calculations and therefore users can leave the default value of 0.010 for confined concrete. The provision of transverse confining reinforcement will tend to increase the strain at peak stress such that values of 0. Once the material information has been specified. Strain at peak stress. click on Add + Close. this version of DBDsoft does not use this information in the calculations and therefore users can leave the default value of 0. f’ce : The expected concrete compressive strength refers to concrete strength expected at the time of an earthquake. it should correspond to the weight of reinforced concrete). Repeat the operation for as many different material properties as desired.DBDsoft Page 11 of 93 Expected compressive strength. Currently. Priestley et al. Ultimate strength. Add Structural Steel Material Previous Top Next Add Structural Steel Material Add new material>type>Structural_Steel: file:///C:/Users/User/AppData/Local/Temp/~hh512C. click on Add + Close. The materials that have been added will then be listed in the grid. Fy : The expected yield strength refers to the yield strength expected of longitudinal reinforcing bars at the time of an earthquake.c is the characteristic yield strength of the reinforcing bars. In lieu of more refined information. Note that it is likely to be greater than the characteristic yield strength which is typically based on 5 th percentile values of strength. Elastic Modulus.htm 11/12/2015 . one could specify Fu= 1.c is the characteristic ultimate strength of the reinforcing bars. and will tend to be greater than the expected yield strength due to strain hardening. Typical values for the elastic modulus of reinforcing steel are between 200000MPa and 210000MPa. E: The elastic modulus of reinforcing steel should be specified with unit of MPa.c where Fy.1Fu.DBDsoft Page 12 of 93 Add new material>type>Reinforcing_Steel: Expected yield strength.1Fy. Repeat the operation for as many different material properties as desired. Note that it is typically used in DBD to account for strain-hardening effects on the plastic hinge lengths of walls and the like.c where Fy. Once the material information has been specified. Fu : The ultimate strength refers to the ultimate strength expected of longitudinal reinforcing bars at the time of an earthquake. In lieu of more refined information. (2007) recommend that Fy = 1. 2Fu. first ensure that you have selected the Sections module (see Getting Started).c for S355 and S450.c for S235. F u = 1. The materials that have been added will then be listed in the grid. F y = 1. Fy : The expected yield strength refers to the yield strength expected of the structural steel at the time of an earthquake. and F u = 1.1Fy. Elastic Modulus. Typical values for the elastic modulus of reinforcing steel are between 200000MPa and 210000MPa.c for S275.where Fu.15Fu. Ultimate strength. Note that it is typically used in DBD to account for strain-hardening effects on the plastic hinge lengths of walls and the like. Repeat the operation for as many different material properties as desired.c is the characteristic ultimate strength of the reinforcing bars.c is the characteristic yield strength of the reinforcing bars. In lieu of more refined information.2Fy.c for S355 and S450. Then either click on the blue plus symbol (see Figure) or double click on the grid of the table. Sections Previous Top Next Sections After defining the material characteristics. one could specify Fu = 1. Priestley et al. After providing the requested information (described in detail below) click on the Add and Close button to confirm the addition of the new section. where Fy. and will tend to be greater than the expected yield strength due to strain hardening.15Fy. and F y = 1. To add a new section. (2007) recommend that Fy = 1.1Fu. The form Add New Section will then open. Fu : The ultimate strength refers to the ultimate strength expected of the structural steel at the time of an earthquake. E: The elastic modulus of reinforcing steel should be specified with unit of MPa.c for S275.c for S235.DBDsoft Page 13 of 93 Expected yield strength. file:///C:/Users/User/AppData/Local/Temp/~hh512C. click on Add + Close. the geometry of the structural cross sections must be defined. In lieu of more refined information. Once the material information has been specified. Note that it is likely to be greater than the characteristic yield strength which is typically based on 5 th percentile values of strength.htm 11/12/2015 . and they will extend the possibility of use of currently existing sections. as well as IPE and HE steel profiles. Please note that. Future versions will include other section shapes. in the current version of DBDsoft.htm 11/12/2015 . S1) for the section and selecting the section type. For example. After assigning a name (e. Rectangular Sections Previous Top Next Rectangular Sections file:///C:/Users/User/AppData/Local/Temp/~hh512C.and Lshaped sections. such as C.DBDsoft Page 14 of 93 The current version of DBDsoft has been developed for rectangular. and circular RC sections can only be used as columns. Section Curvature performance criteria assume that wall and beam sections are defined so that they bend around local axis 2. T-shaped RC sections can only be used as beams. Please note the orientation of the sections’ local axes with respect to the definition of sections’ parameters such as width and depth. for some features of the software assume a standardised engineering approach is to be followed by the user.g. circular and T-shaped RC sections. a series of parameters must be defined. as described below. Section Width: The section width should be input (typically in units of metres). Material: By clicking on the drop-down box a list of the materials that have been defined will appear. Fill in the section properties and click on the Add and Close button. the section depth typically refers to the wall length. For a rectangular wall section. Select the appropriate type of concrete for the section. whether the section bends about its strong or weak axis for a given loading direction) will be controlled by defining the direction of axis-3 using a non-structural node (see the Section on Nodes). Note. Repeat the procedure for as many other sections as required. that orientation of the section (i. circular sections can only be used for the definition of columns. Rebars Material: By clicking on the drop-down box a list of the materials that have been defined will appear.DBDsoft Page 15 of 93 Name: Define a non-existing name for the new section. The new section is listed in the Sections’ grid. For a rectangular wall section. Select the appropriate type of reinforcing steel for the section.e. Section Depth: The section width should be input (typically in units of metres). Circular Sections Previous Top Next Circular Sections Note: in the current version of DBDsoft. file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm 11/12/2015 . the section width typically refers to the wall thickness. htm 11/12/2015 . Select the appropriate type of concrete for the section. T-Shape Sections Previous Top Next T-Shape Sections Note: in the current version of DBDsoft. Rebars Material: By clicking on the drop-down box a list of the materials that have been defined will appear. Repeat the procedure for as many other sections as required. The new section is listed in the Sections’ grid. Select the appropriate type of reinforcing steel for the section. Fill in the section properties and click on the Add and Close button. Section Diameter: Specify the section’s diameter (typically in units of metres).DBDsoft Page 16 of 93 Name: Define a non-existing name for the new section. file:///C:/Users/User/AppData/Local/Temp/~hh512C. T-shaped sections can only be used for the definition of beams. Material: By clicking on the drop-down box a list of the materials that have been defined will appear. The new section is listed in the Sections’ grid. Rebars Material: By clicking on the drop-down box a list of the materials that have been defined will appear. Material: By clicking on the drop-down box a list of the materials that have been defined will appear. Section Width: Specify the section’s width (typically in units of metres).htm 11/12/2015 . the beam’s horizontal dimension. i.e. Select the appropriate type of concrete for the section. the distance from the bottom of the beam to the top of the slab. IPE Steel Section Previous Top Next IPE Steel Section file:///C:/Users/User/AppData/Local/Temp/~hh512C. Section Depth: Specify the section’s depth (typically in units of metres). Slab Thickness: Specify the slab’s thickness (typically in units of metres). i. Slab Width: Specify the width (typically in units of metres) of slab that will contribute with the beam to resist the seismic actions.e. Select the appropriate type of reinforcing steel for the section. Repeat the procedure for as many other sections as required.DBDsoft Page 17 of 93 Name: Define a non-existing name for the new section. Fill in the section properties and click on the Add and Close button. HE Steel Section Previous Top Next HE Steel Section Name: file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm 11/12/2015 . Repeat the procedure for as many other sections as required. Fill in the section properties and click on the Add and Close button. Select the appropriate type of structural steel for the section. The new section is listed in the Sections’ grid. Material: By clicking on the drop-down box a list of the materials that have been defined will appear.DBDsoft Page 18 of 93 Name: Define a non-existing name for the new section. Section Type: Select the type of IPE profile from the drop-down menu. first ensure that you have selected the Element Classes module (see Getting Started). file:///C:/Users/User/AppData/Local/Temp/~hh512C. The form Add new element class will then open. To assign the element class you should then: § Give a name to the element class you are creating. Section Type: Select the type of HE profile from the drop-down menu. Future versions of DBDsoft will support the use of T-shape as well as other sections for columns and walls as well. only rectangular sections will be listed. column elements or wall elements. Material: By clicking on the drop-down box a list of the materials that have been defined will appear. all sections except circular ones and. The new section is listed in the Sections’ grid. Repeat the procedure for as many other sections as required. shown below. while for a beam class.DBDsoft Page 19 of 93 Define a non-existing name for the new section. Fill in the section properties and click on the Add and Close button. Note that floor diaphragm elements do not need to be specified and DBDsoft automatically assumes rigid in-plane behaviour of floor diaphragms by constraining all nodes at the same level to move horizontally together. To add a new element class. Please note that for a wall element class. Select the appropriate type of structural steel for the section. Then either click on the blue plus symbol or double click on the grid of the table (as for the Materials and Sections modules). This will be important for the plastic mechanism and deformed shape that the program will assume during the design process.htm 11/12/2015 . for columns. a set of element classes must be defined. Then § Select the section Type from the drop-down list. all sections except T-shape ones will be available. The purpose of this module is to tell the program whether the sections defined should be considered as beam elements. and then § Select the type of section that is being given this element classification. Previous Top Next Element Classes Element Classes After defining the material characteristics and section properties. and then § Enter the X. Then either click on the blue plus symbol or double click on the grid of the table (as for the Materials and Sections modules). To assign the node you should then: § Give a name to the node you are creating. file:///C:/Users/User/AppData/Local/Temp/~hh512C. The form Add new node will then open. shown below. To add a node.htm 11/12/2015 . Then § Select the node Type from the drop-down list (either structural or non-structural). Note that non-structural nodes can be provided anywhere on the plane of the local z-axis (see Figures above). first ensure that you have selected the Nodes module (see Getting Started).DBDsoft Page 20 of 93 After providing the requested information click on the Add and Close button to confirm the addition of the new element class. After providing the requested information click on the Add and Close button to confirm the addition of the new node. Nodes Previous Top Next Nodes Every structural element will be defined by a pair of nodes that set the ends of the element and a non-structural node that is used to define the orientation (rotation) of the section (see the figures below). Y and Z coordinates of the nodes. and this update should thus be done manually by the user. The user can modify node properties at any time.”. and the number of new nodes to generate. this effect is considered. as shown in the figure below. Note as well that at roof level all nodes should be at the same elevation or the program will classify the structure as being vertically irregular. Given the fact that the nodes’ coordinates are given all together in the same column. first ensure that you have selected the Element Connectivity module (see Getting Started). it is possible to use the Automatic Incrementation tool.htm 11/12/2015 . the end nodes of the element and a non-structural node that will define the orientation (rotation) of the section. In the case of frame-wall systems with link beams. beams and columns are defined by nodes lying at their centrelines. the design displaced shape. Then either click on the blue plus symbol or double click on the grid of the table (as for the Materials and Sections modules). Note that in the current version of DBDsoft. separated from one another by three spaces. the current version of the software does not update it within the elements that have already been defined using the previous name. and no corrections are made to account for the fact that the bending moments at the faces of the elements are different than those at their centrelines. Y and Z coordinates in the spreadsheet. Element Connectivity Previous Top Next Element Connectivity Structural elements can be defined by indicating the element class. file:///C:/Users/User/AppData/Local/Temp/~hh512C. The form Add new element will then open. a window pops up asking the user to specify the increment to be used for the new nodes’ names. Additionally. with the aim of automatically generating more complex series of nodes. shown below. it is possible to paste tables generated with external spreadsheet applications. When doing so. To add an element. it is important to bear in mind that if the field to modify is the node’s name. However. the increments in each coordinate. however. given its importance in the determination of the walls’ contraflexure height and. available when clicking on the button labelled “Inc.DBDsoft Page 21 of 93 In order to speed up the process of node generation. hence. it is recommended to use functions to concatenate the X. the axis will be pointing at its projection over the plane of the section at Node i.htm 11/12/2015 . If the geometrical definition of the element does not allow for local axis 3 to be directly pointing at the non-structural node. Then ? Select the element Type from the drop-down list (either beam. and then ? Select the non-structural node that defines the orientation (rotation) of the section. column. as shown in the following example: Top view file:///C:/Users/User/AppData/Local/Temp/~hh512C. wall or rigid-link). Node i and Node j.DBDsoft Page 22 of 93 To define the element you should then: ? Give a name to the element you are creating. Then ? Select the structural nodes that define the ends of the member. Then ? Select the Element Class from the drop-down list (the list will include all element classes specified in the Element Classes Module). Local axis 3 of the element’s section will be pointing at the non structural node selected. Non-structural node lies in the X-Y plane Perspective . please refer here. this effect tends to be more significant due to the larger dimensions of walls. In the case of frame-wall systems with link beams. Future versions of the software will allow for steel sections to be defined with any desired orientation.Non-structural node does not lie in the X-Y plane. For this reason. users should use rigid links in order to define the connectivity between walls and beams. initial node. final node and non-structural node that define the element within the spreadsheet. and no corrections are made to account for the fact that the bending moments at the faces of the elements are different than those at their centrelines. As mentioned here.htm 11/12/2015 . beams and columns are defined by nodes lying at their centrelines.DBDsoft Page 23 of 93 Perspective . For further information. Restraints/Releases Previous Top Next Restraints/Releases file:///C:/Users/User/AppData/Local/Temp/~hh512C. it should be noted that in the current version of DBDsoft. Given the fact that the elements’ properties are given all together in the same column. however. it is recommended to use functions to concatenate the element class. separated from one another by three spaces. Defining steel beams and columns with other angles will lead to the bending strength capacity of the sections to be estimated as zero. In order to speed up the definition of structural members. it is possible to paste tables generated with external spreadsheet applications. Please note as well that the current version of DBDsoft only allows for steel beams and columns to be defined with their local axes oriented parallel and perpendicular to the global axes. but section maintains its orientation with respect to its projection over the X-Y plane After providing the requested information click on the Add and Close button to confirm the addition of the new element. The form Add new restraints/releases will then open. To add a restraint or release. To define a restraint or release you should then: § Give a name to the restraint or release that you are creating. whether the DOF is retrained (yes) or not (no). from the drop-down list. Then § Indicate whether you would like to specify a restraint or release by using the drop-down menu. Then For Node Restraints § Select. Nodal releases can be defined to indicate pin releases within members. shown below. for each degree of freedom (DOF). the number of the node to be restrained and then § Indicate. Then either click on the blue plus symbol or double click on the grid of the table (as for the Materials and Sections modules). file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm 11/12/2015 . first ensure that you have selected the Restraints/Releases module (see Getting Started).DBDsoft Page 24 of 93 Nodal restraints should be defined at the base of the building. for axial releases) only a yes/no selection is required. After providing the requested information. select the release situation that is desired using the options provided in the drop down list (no release.htm 11/12/2015 . file:///C:/Users/User/AppData/Local/Temp/~hh512C. (i) Load Cases. For each Load Case a series of applied loads (masses or earthquakes) can be defined (within the Applied Loading sub-module) and then in the Load Combinations sub-module. Then either click on the blue plus symbol or double click on the grid of the table (as for the Materials and Sections modules). shown below. from the drop-down list. The form Add new load case will then open. note that the current version of DBDsoft does not take account of axial releases and therefore they should not yet be used. released at both ends or released at one end only. click on the Add and Close button to confirm the addition of the new restraint or release. Then § For releases in the axis 1 direction (i. first ensure that you have selected the Loads module (see Getting Started) and the Load Cases sub-module. The inputs required for each sub-module are described in the following pages. However. Loads Previous Top Next Loads Three different sub-modules must be completed within the Loads module.DBDsoft Page 25 of 93 For Element Releases § Select. The Load Cases sub-module is used to specify different load case scenarios that could be considered. the number of the element in which to insert the release and then § For releases about the section axis 2 or 3. (ii) Applied Loading. Load Cases Previous Top Next Load Cases To add a new load case. one or more Load Cases can be combined by specifying different load combination factors. (iii) Load Combinations.e. Note that in the current version only earthquake load cases can be defined. Then § Select the Type of loadcase from the drop-down list. click on the Add and Close button to confirm the addition of the load case.DBDsoft Page 26 of 93 To add the load case you should then simply: § Give a name to the load case that you are creating.htm 11/12/2015 . The form Add new applied loading will then open. To define the applied loading you should then: file:///C:/Users/User/AppData/Local/Temp/~hh512C. Then either click on the blue plus symbol or double click on the grid of the table (as for the Materials and Sections modules). After providing the requested information. Applied Loads Previous Top Next Applied Loads To add a new applied load. as shown below. first ensure that you have selected the Applied Loads sub-module. This value should correspond to the elastic spectral displacement demand (shown as ∆D. but more than one Load Case can be selected to run simultaneously under the same Load Combination. it should already be amplified to account for local soil conditions). For EC8 users. According to EC8 the value of TD is typically 2s for the type 1 spectrum. the load case for which the lumped mass will be considered. § Insert the value of the corner period. Then § Select the applied loading Type from the drop-down list (either lumped mass or seismic action in this version of DBDsoft). Then § Select. For EC8 users.htm 11/12/2015 . (i. whether the design response spectrum should be considered dominated by far-field events or near-field events.e. For this reason. respectively. corresponding to the value of period at which spectral displacement demands stop increasing (shown as T D in the Figure below). given that the software does not allow for a separate specification of this parameter. users must ensure that they only file:///C:/Users/User/AppData/Local/Temp/~hh512C.5% in the Figure below) associated with the period TD. § Select. The peak ground acceleration value is used in the short period range to ensure that the simplified shape adopted for the design displacement spectrum is not overly conservative. § Insert the value of the corner displacement. For Seismic Actions: § Select. but values should be obtained in line with national seismicity information. the number of the node at which the lumped mass is to be located. Then § Indicate the value of the lumped mass. from the drop-down list. from the drop-down list.DBDsoft Page 27 of 93 § Give a name to the applied load you are creating. Please note that the current version of DBDsoft assumes that the input spectrum will correspond to 5% and 3% elastic damping for reinforced concrete and steel structures. from the drop-down list. § Indicate the direction of the earthquake loading (either X or Y direction). the load case in which the seismic action will be considered. from the drop-down list. Note that the current version of DBDsoft does not yet modify the design procedure for near-field events and therefore the (more common) far-field option should be selected.ag. this value should already include the effect of the soil factor S. § Insert the value of the peak ground acceleration (in units of m/s2 or similar). this value should correspond to PGA = S. Then For Lumped Masses: § Select. Note that only one seismic input can be introduced for each direction per each Load Case. After providing the requested information. click on the Add and Close button to confirm the addition of the new load combination. in the current version of DBDsoft users should only specify one load case and subsequently only one load combination. After providing the requested information click on the Add and Close button to confirm the addition of the new applied loading. Load Combinations Previous Top Next Load Combinations To add a new load combination. shown below.0 is placed beside the load combination name. Note.DBDsoft Page 28 of 93 specify realistic loading scenarios. first ensure that you have selected the Load Combinations sub-module.htm 11/12/2015 . Then § Click within the table alongside each loadcase name (that you specified in the Load Cases sub-module) and type the factor to be used to combine the different load cases. in which no more than one earthquake at a time is considered for each response direction. in which a 1. The form Add new load combination will then open. To define the load combination you should then: § Give a name to the load combination you are creating. Then either click on the blue plus symbol or double click on the grid of the table (as for the Materials and Sections modules). Performance Criteria Previous Top Next Performance Criteria file:///C:/Users/User/AppData/Local/Temp/~hh512C. To specify a performance criterion. note that the current version of DBDsoft only permits the specification of storey drift limits. The form Add new performance criteria will then open. Maximum-Storey-Drift Limit Previous Top Next Maximum-Storey-Drift Limit file:///C:/Users/User/AppData/Local/Temp/~hh512C. and (iii) chord rotation limits. the type of performance criterion: maximum storey drift limit.htm 11/12/2015 . Then either click on the blue plus symbol or double click on the grid of the table (as for the Materials and Sections modules).DBDsoft Page 29 of 93 Performance Criteria should be specified for the limit state under consideration. To define a performance criterion you should then: • Give a name to the performance criterion that you are creating. However. or chord rotation limit. storey drift limit. Then • Select. shown below. first ensure that you have selected the Performance Criteria module (see Getting Started). Note that at least one of the above performance criteria must be specified in order for the program to run. (ii) section curvature. The program will then establish the design strengths required to satisfy the performance criteria. section curvature limit. from the drop-down menu. Three different types of performance criteria can be specified in DBDsoft: (i) storey drift. • Provide the parameters required for each case. htm Previous Top Next 11/12/2015 . Note that the program will check this storey drift limit in both the X and Y directions.DBDsoft Page 30 of 93 Enter the value of the storey drift limit. if this option is used.After providing the requested information. Note as well that. at all levels. This limit should be expressed as a percentage of the storey height (i.e. If the user only intends to introduce a certain limit at a specific level.e. Note that the program will check this storey drift limit in both the X and Y directions. After providing the requested information. then he/she should fill in the values corresponding to all the other storeys with a hyphen (“-“). the distance between adjacent levels). click on the Add and Close button to confirm the addition of the new performance criterion. Storey-by-Storey Drift Limit Previous Top Next Storey-by-Storey Drift Limit Enter the value of the storey drift limit. the distance between adjacent levels). Section Curvature Limit file:///C:/Users/User/AppData/Local/Temp/~hh512C. for each storey. click on the Add and Close button to confirm the addition of the new performance criterion. values need to be introduced at all levels. This limit should be expressed as a percentage of the storey height (i. or both. After providing the requested information. and enter a value for the section curvature limit. the following approximation is assumed (illustrated for the case of a wall): file:///C:/Users/User/AppData/Local/Temp/~hh512C. For the definition of the orientation of the local axes. If the criterion is to be applied to several elements. which must be selected from the corresponding drop-down menu. In order to transform plastic curvature demands into equivalent plastic hinge rotations. General Considerations on Elements’ Yield Curvature Whether the specified limit state curvature is greater or smaller than the element’s yield curvature is an important factor for all element class types. This is done in a very similar fashion for all element class types. or to allow the software to compute it automatically based on empirical formulas. Finally.DBDsoft Page 31 of 93 Section Curvature Limit Choose the element class type for which the criterion will apply. it is also possible for the user to specify a plastic hinge length. given the fact that the software assumes that the definition of the section’s dimensions will be carried out so that the section works in bending around this axis. The software gives the possibility of either applying the criterion to all elements that are defined using that class type. In order to determine this parameter. as described in the following sections. or to a specific element. If more than one element generates different equivalent interstorey drift limits at the same storey. the software calculates the equivalent interstorey drift limit corresponding to each element and applies it to the storey in which the element is located. DBDsoft verifies the section curvature limits by calculating equivalent interstorey drift limits that correspond to the attainment of the specified curvature for the element/s under consideration. click on the Add and Close button to confirm the addition of the new performance criterion. for which an estimated reinforcement bar diameter needs to be provided. specify whether the criterion should be applied for bending about local axis 2 or local axis 3. please refer here. Currently. DBDsoft makes use of the approximate formulas derived by several authors and compiled as Annex 1 of the DBD12 Model Code shown here. for beams and walls it is only possible to specify curvature limits for bending about axis 2. the smaller is used for that specific storey. Given that no guidance can be found in literature regarding how to estimate the yield curvature of RC sections for axes other than the principal ones.htm 11/12/2015 . but each of them presents its own peculiarities. based on the estimated reinforcement bar diameter specified by the user when determining the parameters for the performance criterion: Specification of Several Section Curvature Criteria for the Same Element Class If more than one section curvature criterion is specified for the same element class or particular element. the software will verify each criterion separately. the yield curvature is: For bending around global axis Y (seismic excitation in direction X): For bending around global axis X (seismic excitation in direction Y): Strain Penetration Length If the user specifies the use of an automatically computed plastic hinge length. the yield curvature is: For bending around local axis 3. Y). For the case of walls. it is assumed that no curvature limit is applied for bending around local axis 3. and thus the out-of-plane deformation is ignored and assumed admissible. The situation is illustrated in the figure below: For the case of columns. users must be aware that the plastic hinge length and estimated reinforcement bar diameter of the last specified criterion will be used for all criteria related to that element / element class.htm 11/12/2015 . the penetration length is calculated using the expression of Priestley et al (2007). the user needs to verify the deformation capacity of the elements in all directions. In order to complete the design process. Equivalent Interstorey Drift Limits in Local and Global Axes The equivalent interstorey drift limits are first calculated for bending around the elements’ local axes (2. 3) and then projected onto the global axes (X. if curvature limits are specified for bending around only one of the local axes. However. then curvatures file:///C:/Users/User/AppData/Local/Temp/~hh512C.DBDsoft Page 32 of 93 For bending around local axis 2. the user specifies curvature limits for bending around both local axes. and ) to yield ( ) strength of the reinforcement of the section: is the wall’s section height. instead.DBDsoft Page 33 of 93 around the other axis are also assumed admissible and need to be verified by the user. can be directly defined by the user while setting up the section curvatures performance criteria. the interstorey drift limit at a level having a height equal to or greater than the contraflexure height ( ) is determined as: Section Curvature Limits for Beams If the specified limit curvature ( ) is greater than the yield curvature ( the beam) at the beam’s level is calculated as: ). is the plastic hinge length which. the specified limit curvature ( ) is smaller than the yield curvature ( ). the interstorey drift limit (in the direction of is the plastic hinge length where is the storey drift at frame yield. and is calculated as explained here. or can be automatically computed by the software as: where depends on the ratio of the expected ultimate ( . and which. as shown in the following figure: Section Curvature Limits for Walls If the specified limit curvature ( ) is greater than the yield curvature ( ). as said before. as said before.htm 11/12/2015 . or can be automatically computed by the software as: file:///C:/Users/User/AppData/Local/Temp/~hh512C. If. the software will use the smallest resulting projection of the equivalent interstorey drift. instead. can be directly defined by the user while setting up the section curvatures performance criteria. If. the interstorey drift limit (in the direction of the wall) at a level having a height equal to or greater than the contraflexure height ( ) is determined as: In the previous equation. the equivalent interstorey drift limit (in the direction of local axis 2 or 3. Note that for bi-directional elements. and the specified limit curvature ( ) is greater than 75% of the yield curvature ( software assumes that this performance criterion will not be critical. the interstorey drift limit at the level of the column is determined as: if if where is the column’s contraflexure height. the specified limit curvature ( beam’s level is calculated as: ) is smaller than the yield curvature ( ). can be directly defined by the user while setting up the section curvatures performance criteria. instead. the interstorey drift limit at the level of the column is determined as: if if Chord Rotation Limit Previous Top Next Chord Rotation Limit Enter the value of the chord rotation limit. and is calculated as explained here.DBDsoft where Page 34 of 93 is the beam’s length. the specified limit curvature ( smaller than 75% of the yield curvature ( specified) for that storey is calculated as: where ). If the column is located in the ground floor and the specified limit curvature ( ) is greater than the yield curvature ( ). the element for which the chord rotation limit will be applied. given that the latter should be protected from yielding through capacity design principles. This limit should be expressed as a rotation value with units of radians. such as columns. as is the storey drift at frame yield. if the column is not located in the ground floor. from the drop-down list. instead. the ) is ). the interstorey drift limit at the Section Curvature Limits for Columns The software treats section curvature limits differently for columns located at the ground floor or in the upper storeys. is the column’s height. Select. If. and is the plastic hinge length for the column which. In this way. as said before. the user is further prompted to indicate whether the curvature limit acts about the section’s file:///C:/Users/User/AppData/Local/Temp/~hh512C. If.htm 11/12/2015 . or can be automatically computed by the software as: If the column is located in the ground floor but the specified limit curvature ( ) is smaller than the yield curvature ( ). the user is also required to specify an overstrength factor to be used to estimate the capacity design forces that should be withstood by members that need to remain elastic during seismic action. This phase is an important design decision that the user should make as it will influence the distribution and magnitude of the required strengths throughout the structure. To specify this information. After providing the requested information. after which point the user should verify that the lateral stability systems correspond to those envisaged for the structure. this overstrength factor should normally be established based on a moment-curvature analysis of members. the user should tell the program to identify the lateral stability systems.htm 11/12/2015 . As described here. Processor Previous Top Next Processor The purpose of the Processor Phase is to identify the lateral load resisting system and run the design calculations. Once the lateral load resisting systems have been identified. § Then click on the second drop-down list and select the performance criterion that should be considered for the design.DBDsoft Page 35 of 93 strong or weak axis. Finally. click on the Add and Close button to confirm the addition of the new performance criterion. The default value is 1. The module is used to firstly identify and classify the lateral load resisting systems (e. specify a value for the overstrength factor to be used to estimate the capacity design forces that should be withstood by members that need to remain elastic during seismic action. the user must indicate the proportions of overturning moment that they wish the different lateral load resisting systems to resist.30. Finally. The Processor Phase requires the user to indicate the load combination that should be considered. first ensure that you have selected the Design Case module (see Getting Started) within the Processor phase of the program. frames or walls) and then ask the designer to indicate what fraction of the lateral load (i. Design Case Previous Top Next Design Case The Design Case module within the Processor Phase is used to select the load combination that will be considered in the design and to identify the relevant performance criteria for the selected load combination. The list of loadcombinations will include all those specified in the Pre-Processor phase. In addition. These strength proportions will then be used by the program when evaluating the required design strength of the whole system. file:///C:/Users/User/AppData/Local/Temp/~hh512C.g.e. Design Strength Proportions Previous Top Next Design Strength Proportions The Set Design Strength Proportions module within the Processor Phase is an important design phase. To provide the necessary information simply do the following: § Click on the first drop-down list and select the load combination that should be considered. Please note that this option is not yet available in the current version of DBDsoft. what strength proportions) should be carried by each sub-system. htm 11/12/2015 . each identified by a different colour. within the frame example case study. a warning message will pop up. For example. as well as any node restraints (in green here) or member releases (in blue here) if present. plastic hinges are assumed to develop at all wall bases.DBDsoft Page 36 of 93 To complete this module. unless a release is provided at the column base. The figure below shows how the program identifies three separate frame systems. In the current version. End releases can be specified by the user to indicate that a certain assumed plastic hinge is not such. Since the current version of the software cannot file:///C:/Users/User/AppData/Local/Temp/~hh512C. In addition. and the designer should account for this if the intention is actually not to form plastic hinges in the locations assumed by the program. the software will simply interpret this as rigid link connections and the beams will not be considered to be acting as link beams. the location of plastic hinges cannot be shifted. if a frame and a wall are connected by beam elements released on both ends. The program then groups together all lateral load resisting elements that will be considered to work together. the designer should check that the systems were as intended. When selected for the first time. Similarly. the following image should be visible: As indicated in the figure above. the first task is to click on the “Identify Lateral Stability Systems” button. Note that for frame structures the program assumes that a beam-sway mechanism will be desired and therefore all beam ends that are connected (without a release) into a column will be assumed as potential plastic hinge regions. Having told the program to identify the lateral load resisting systems. all column bases will be assumed as plastic hinge locations. first ensure that you have selected the Set Design Strength Proportions module within the Processor phase of the program. If a column is linked to the rest of the structural system only by beams that are released on both ends. explaining the user that an isolated column has been found. Also note that the program indicates (in yellow here) where the plastic hinges will be assumed to form. local strength proportions are required and upon clicking the local strength proportion buttons. the user needs to either eliminate the conflictive member or re-define it as a wall member (using a Wall Element Class). the software allows for a 5° tolerance.0. local strength proportions need not be specified for walls when these are not part of frame-wall systems (the βxx and βyy values for walls are simply 100%).e. This means that.htm 11/12/2015 . The next task within the Set Design Strength Proportions module is to indicate the local or global strength proportions. For frame and frame-wall structures. To specify the local strength proportions. As a cantilever wall should only form a single plastic hinge at the base of the wall. Local Strength Proportions Previous Top Next Local Strength Proportions Local strength proportions refer to the ratio of the bending moment of a single plastic hinge to the sum of the bending moments of all plastic hinges in the local sub-system for a given excitation direction. the software will assume that the frame works only in the X direction. In other words.DBDsoft Page 37 of 93 yet treat isolated columns as if they were cantilever structures. They can be set by the designer to optimise. they are the ratio of the overturning moment carried by a single plastic hinge to the one carried by all plastic hinges in the local sub-system. It is noted that the approximate method for determining the design profile of walls and frame-walls systems suggested in DBD12 is valid for walls with aspect ratios (i. for example. ratio of total height to length) greater than or equal to 3. click on one of the buttons as shown in the figure below. the required beam strengths within a frame structure by specifying that all beams at the same level within a frame will be provided the same strength (and therefore same beta value). These buttons become available after selecting a sub-model from the sub-models list below. the following form will open: file:///C:/Users/User/AppData/Local/Temp/~hh512C. if a frame is contained in a plane inclined at 5° or less with respect to the X global axis. Local strength proportions are denoted by the βxx or βyy symbols for the X and Y directions respectively. for example. For the definition of the direction in which each sub-system works. by inserting the strength proportions they desire. an additional line is added to the grid showing the additional contribution to the general overturning moment resistance provided by them. Only when the values introduced have passed all the relevant checks. if no value has been manually modified before performing this operation. Auto-Betas Function file:///C:/Users/User/AppData/Local/Temp/~hh512C. If the structure is a frame-wall with linked beams. if the file is closed. However. If the sum of the strength proportions lies between 99% and 101%. When link beams (i. thus. the OK button is enabled. generated them using a spreadsheet). that the summation of strength proportions at each level is different from zero and that the summation of strength proportions at each level is smaller than that of the levels below (except with respect to the ground floor). the strength proportion allocated to the walls’ base is kept constant and all the other values are scaled. which automatically accounts for the possibility of having releases specified at either end of the link beam.e. it can occur that the user needs to press ENTER in order for the “Update Values” button to become available.DBDsoft Page 38 of 93 Within the table the user should then complete the fields shown in green. it will be necessary to introduce them again. and the software automatically computes this additional contribution as shown in the equation below. beams with one or two of their ends rigidly connected to walls and transmitting bending moments to them) are specified. The user should note as well that the current version of DBDsoft does not save the local strength proportion values and. It is noted that users can paste values from the clipboard into the form (if they. the software will automatically check that the sum of the strength proportions adds to 100%.htm 11/12/2015 . for example. The user simply needs to specify the strength proportion corresponding to the plastic hinge at the face of the wall. When clicking on “Update Values”. the software presents the user the option of scaling all the values by the ratio between 100% and the actual sum. where the beam strength should be reduced by half. the program offers users the option for beta values to be computed automatically. 11/12/2015 . as shown in the figure above.25 and 0. The general expression for the computation of the Auto-Betas for a pure frame structure is: If the structure in a specific direction consists. assuming a reinforcement ratio of 3% for beams and columns and 1. is the expected yield strength of the reinforcing steel bars. and is the axial load ratio. Whether this assumption is correct or not depends on the geometry of the building and the way it has been modelled. When the structure in a specific direction consists only of frames. Interaction with axial forces is incorporated using the approach of Eurocode 8. the Auto-Betas are calculated based only on the estimation of the strength of the sections specified by the users. For the estimation of the base columns’ flexural strength. The estimation of the strength of reinforced concrete members is carried out automatically by the software. and are the section’s height and base.DBDsoft Page 39 of 93 In order to speed up the assignment of local strength proportions in frames and frame-walls. the program automatically assigns a series of beta values whose calculation depends on the structural type. and the user only needs to click on “Update Values” and “OK” to close the form. as defined by the user in the Sections module. and by allocating that same strength proportion of the roof beams to the plastic hinges at the base of the columns. but not with shear. and thus their resistance only differs from that of a rectangular section in the fact that the gross area accounts for the whole real section.10 for shear walls. The approximate flexural strength is estimated as: where is the section’s gross area. it includes reinforcement both in tension and compression). It is noted that the characterization of a column as being external or internal is carried out based on it being the extreme of the submodel under consideration. if desired. respectively. The values thus obtained are distributed within each floor using the proportions of approximate strength of the sections defined by the user in the Sections module. Circular columns’ height and base are simply taken as times the diameter of the section. and 0. and and is the flange thickness. of frames and walls simultaneously. It is noted that the estimation of flexural strength of steel columns is carried out accounting only for interaction with axial forces (with the same axial load ratios defined for reinforced concrete sections). the user needs to account for this difference and manually adjust the strength proportions. It should be noted that these reinforcement ratios correspond to the total reinforcement of the member (i.e. Note that these values are not necessarily the optimum. file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm is the gross sectional area. reducing the plastic moment ( ) capacity as shown in the following equation: where is the axial load ratio. instead.40 for external and internal columns. the software assumes (gravity) axial load ratios of 0. In cases like this. respectively. It is possible to obtain a constant shear profile in the frames at all levels by designing all beams for equal strength except at the roof. but should lead to reasonable results. the Auto-Betas are computed based on the design shear profile expected for a frame determined from the provisions for design displaced shape and distribution of base shear in height specified in DBD12. thus. that is. The estimation of the strength of steel sections is carried out assuming that the sections can fully develop their plastic moment ( ) and. The use of constant beam strengths along the height comes up as an appealing option that certainly eases the construction process. lateral supports and section stiffeners will be designed and provided to prevent lateral and lateral-torsional buckling problems. By clicking on it. is the flange width. is the concrete expected compressive strength.2% for walls. The button for this option is located on the lower left corner of the input form. T-shaped beams’ base corresponds to the beam’s width. for the wall will then be designed to carry the design shear not carried by the frames. . Global strength proportions Previous Top Next Global strength proportions Global strength proportions refer to the ratio of the overturning resistance provided by a specific sub-model as a whole and the total design overturning moment. click on the button indicated in the figure below. with the number of rows equal to the number of sub-systems (GMs) identified by the program. To specify the global strength proportions. In the X direction. and the remaining 25% will be carried by system GM2 (sub-system 2-0) instead. its sub-system 1-0). 40% of the overturning moment will be carried by GM0. Actual reinforcement contents.htm 11/12/2015 . with the only requirement being that the sum of the beta values adds to 100% in each direction. it will be necessary to introduce them again. respectively. even if their lengths are different (see Priestley et al. a form such as that shown below will open. and serve the sole purpose of assisting in calculating reasonable strength proportions to be assigned automatically by the program.DBDsoft Page 40 of 93 Note that the flexural strengths computed as explained above are only approximations based on a series of assumptions. Different proportions could be specified by the designer as desired. for example. steel profiles and final strength proportions should be computed by the designer. They are denoted by the βx or βy symbols for the X and Y directions. For the example shown below. and can be set by the designer to reduce torsion. Upon clicking the global strength proportion button. The user should note as well that the current version of the software does not save the global strength proportion values and. if the file is closed. Each green cell within the table indicates a field that the user must complete. thus. while the remaining 60% will be equally split between systems GM1 (sub-system 1-1) and GM2 (sub-system 21) . or to ensure that walls possess similar reinforcement ratios. 2007 for further clarification). the user is specifying that 75% of the total overturning demand in the Y direction will be resisted by system GM1 (more specifically. file:///C:/Users/User/AppData/Local/Temp/~hh512C. DBDsoft Page 41 of 93 With the strength assignments made, the designer can proceed to the Run Design module. Final Strength Proportions Previous Top Next Final strength proportions The final proportion of the total design overturning moment that each individual plastic hinge will resist is finally calculated by the software as: In the former equation, proportions. can make reference either to the user-defined or the automatically calculated strength With the strength assignments made, the designer can proceed to the Run Design module. Role of Strength Proportions in Structural Response Previous Top Next Role of strength proportions in structural response The first of the following figures illustrates the relationship between the assigned strength proportions and the storey shear profile for the case of a simple frame. From the point of view of the statics of the problem, it can be observed that the overturning moment caused by seismic forces is resisted by the plastic hinges at the columns’ base and the couple generated by the axial forces in the columns. The latter are the consequence of the shear forces developed in the beams, which are directly associated to the moment capacity of the plastic hinges. Contraflexure points are assumed at the columns’ mid-height for all columns, except at the ground floor, in which the contraflexure height ratio ( ) is dictated by the assumed strength distribution. If is the summation of beta values at ground floor, is the summation at the first level of beams, and so on, the contraflexure height of the ground columns can be determined from the following equation: Understanding the relationship between the assigned strength proportions and the storey shear profile is particularly important for frame-wall systems, due to the fact that the strength proportions and distribution in height assigned to the frames determines those of the shear walls, which define the contraflexure height and, thus, the displacement profile. As opposed to the case of the simple frames, the distribution is not carried out assuming a specific contraflexure height but splitting the summation of the beams’ moments at a certain node in equal halves, each of which is carried by the bottom file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm 11/12/2015 DBDsoft Page 42 of 93 of the column above and the top of the column below the beam level. The second of the following figures illustrates this situation. In this case, the contraflexure height ratio at the ground floor ( ) can be simply determined as: If the user encounters seemingly incoherent results after running an analysis for a frame-wall system, revision of the assigned strength proportions is highly recommended. Simple Frame System Frame-Wall System (without link beams) Run Design file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm Previous Top Next 11/12/2015 DBDsoft Page 43 of 93 Run Design The Run Design module within the Processor Phase is simply used to instruct the program to perform the Direct displacement-based design calculations. To do this, ensure that you have completed the Design Case and set the design strength proportions within the Processor phase of the program. Then select the Run Design module and click on the button “Run”. A message box will then appear, such as that shown below, in which the design base shear obtained for the global X and Y directions is reported. The design base shear values may be useful for designers who wish to quickly gauge the impact of different member dimensions, design strength proportions, or other input data on the required system strength. For more detailed design results, users should proceed to the Post-Processor phase of the program. Structural Solvers Previous Top Next Structural Solvers The algorithms within the software follow the equations and procedures developed by numerous researchers for the different structural types. However, the DDBD method is still under development, and thus the software relies as well on reasonable assumptions that have not been fully tested yet. The purpose of this chapter is to present the main points the user needs to bear in mind when interpreting the results obtained. General Previous Top Next General The current version of the software does not account for higher mode effects. It does not take into consideration either the amplification of displacements due to three-dimensional torsion. Future versions of DBDsoft will address these issues. Iteration Process to Satisfy Performance Criteria Previous Top Next Iteration Process to Satisfy Performance Criteria The verification of performance criteria is carried out by means of an iterative process. The design drift used to start the iteration process in each direction is defined as follows: § If only one criterion of the type “Maximum-Storey-Drift” is specified, the software will take the corresponding drift limit as the design drift and no further iteration will be required. § If only one criterion of the type “Storey-Drift-Limit” (i.e. a storey-by-storey limit) is specified, and the structure consists only of walls in the direction under analysis, the drift limit specified for the top floor will be considered to file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm 11/12/2015 for it will be typical that some contribution from the slab can be accounted for. and is the section’s diameter. § If only one criterion of the type “Storey-Drift-Limit” (i. and thus the same expression provided for Tshaped concrete sections is assumed.e. respectively. iteration will be necessary.e. the maximum drift limit at any storey will be considered to be the design drift. the software will need to compute the yield curvature of the elements defined in the model. perpendicular to the axis around which the yield curvature is being calculated. § If more than one criterion is specified. and will then take the minimum among all criteria as the value to start the design process.htm 11/12/2015 . the drift limit specified for the bottom floor will be considered to be the design drift. column’s and beam’s dimension. and that these are not satisfied when using the one specified at the bottom as the starting value and. it might occur that other values of drift limit are specified at other storeys. it might occur that other values of drift limit are specified at other storeys. § If only one criterion of the type “Storey-Drift-Limit” (i. Response Spectrum Modification Factor Previous Top Next Response Spectrum Modification Factor The response spectrum modification factor is computed as a function of the equivalent viscous damping of the structural system. the file:///C:/Users/User/AppData/Local/Temp/~hh512C. The maximum is chosen to guarantee that the verification of the criteria does not yield a positive result for storey drifts much lower than those specified by the user. a storey-by-storey limit) is specified. a storey-by-storey limit) is specified. as shown: Note that the previous equation is applicable for sites where near-field effects are not expected. Note as well that no expression is provided in DBD12 for rectangular concrete beams. and are the wall’s. and that these are not satisfied when using the one specified at the top floor as the starting value and. However. Empirical expressions developed by several authors have been compiled and presented as Annex 1 of the DBD12 Model Code. However. Element Classes’ Yield Curvature Previous Top Next Element Classes' Yield Curvature If Section Curvature performance criteria are defined. As mentioned here. given the fact that the location of the critical drift is unknown until after the determination of the contraflexure height of the system. Iteration will most probably be required. and the structure consists only of frames in the direction under analysis. in these cases. . and the structure consists of a frame-wall system in the direction under analysis. for the critical drift of pure cantilever wall systems occurs at the top of the wall. for the critical drift of a pure frame system occurs at its bottom. iteration will be necessary. Note that the expression used for T-shaped concrete beams assumes the occurrence of strain-hardening. Those currently used by DBDsoft are: Rectangular concrete walls: Rectangular concrete columns: Circular concrete columns: Rectangular concrete beams: T-shaped concrete beams: IPE and HE steel sections: in which is the yield strain of the reinforcement. the software will determine a design drift from each criterion as described before. in these cases.DBDsoft Page 44 of 93 be the design drift. according to the equation suggested by the DBD12 Model Code for use with the expressions for the calculation of the equivalent viscous damping specified in the Code as well. DBDsoft Page 45 of 93 current version of DBDsoft does not yet account for near-field effects. for the latter case. and the corresponding values of the output are highlighted: file:///C:/Users/User/AppData/Local/Temp/~hh512C.30 is imposed to the P-Delta stability coefficient. the summation of Pj from j=i to j=n implies that the total axial load at level i is being calculated. The final design base shear is.htm 11/12/2015 . DBDsoft automatically assumes that the input spectrum will correspond to a 5% elastic damping in the case of reinforced concrete structures. is the spectral displacement at the corner period for the structure’s level of equivalent viscous damping (i.30. the additional base shear is directly proportional to the summation of second-order moments generated by the displacement of the application points of all vertical loads due to the lateral deformation of the structure. If the stability coefficient is greater than 0. a warning message is shown to the users. and 1. which is confronted with pre-established limits.5 for concrete structures and structures characterized by relatively thinner hysteretic loops (e. Ramber-Osgood. thus: (5) An upper limit of 0. etc). which is a function of the elastic damping ( = 3%) and the ductility demand of the system ( ): Note that. reduced by the response spectrum modification factor). is the corner period. The largest storey P-Delta stability coefficient is taken as the coefficient for the whole structure.0 for steel structures and structures characterized by relatively thicker hysteretic loops (such as bi-linear. and is the structure’s design characteristic displacement. P j is the vertical load applied at each level. the response spectrum modification factor reported in the Post-Processor module corresponds to the final product of and . the spectral displacement at the corner period for 5% damping introduced by the user. a P-Delta stability coefficient is calculated for each storey.e. simply as the product of the design displacement ( effective stiffness ( ). in the case of steel frames. etc). elasto-plastic. for steel frames. by multiplying by a correction factor proposed by Pennucci et al. with the aim of reducing the probability of dynamic instability. When the stability coefficient is larger than 0. [2011]. as: (1) In the previous equation. the design base shear is increased in a quantity given by: (4) In the formula above. the response spectrum modification factor is modified. As specified in DBD12. For this reason. Takeda. the software sets an upper limit to the effective stiffness. and Vdi is the design shear force at level i. as recommended in the DBD12 Model Code.05 (for steel structures) or 0. according to DBD12: (2) The base shear is computed as described here.g. Determination of the Structure’s Effective Period and Base Shear Previous Top Next Determination of the Structure's Effective Period and Base Shear The structure’s effective period is determined from the values introduced for the corner period and the spectral displacement at the corner period defined by the user in the Applied Loads section. ) and the required After this first design base shear has been calculated and distributed up the height of the building. If the effective period is larger than . constant C is 0. and 3% elastic damping.10 (for concrete structures). using the following formula: (3) In the formula above. Flag-Shape. Nominal strength values are calculated taking into account each element’s ductility demand. carried out as explained in Background. transcribed below: (1) Equivalent Viscous Damping Each storey’s yield drift ( ) is calculated as a weighted average of each individual beam end with respect to its relative contribution to the overturning resistance of that storey. and its associated yield drift. even though a stability coefficient larger than 0. file:///C:/Users/User/AppData/Local/Temp/~hh512C. is the beta value of plastic hinge j in storey i. Determination of Elements’ Flexural and Shear Design Strength Previous Top Next Determination of Elements' Flexural and Shear Design Strength Internal forces distribution is carried out by multiplying the strength proportion ( ) values and the overturning moment caused by the distribution in height of the base shear force. Frame Systems Previous Top Next Frame Systems Overview DBDsoft carries out the design of frame systems according to DBD12. with no special considerations except those concerning the calculation of the system’s equivalent viscous damping. It is noted that current version of DBD soft does not implement capacity design principles and. thus. as described next. as explained in Beams Details and Columns Details.2 of the code. as shown in the following equation.30 implies that an adjustment in design is required. this should be applied separately by the designer. the software still computes all the design parameters as usual.DBDsoft Page 46 of 93 Please note that.htm 11/12/2015 . The design displacement profile is assumed to follow Equation 6. due to the development of a plastic hinge.0. Wall Systems Previous Top Next Wall Systems Design Displacement Profile DBDsoft carries out the design of cantilever wall systems according to DBD12.DBDsoft Page 47 of 93 (2) The individual beam’s yield drift is estimated from the expressions developed by Priestley [1998]: Reinforced concrete frames: (3) Steel frames: (4) Each storey’s ductility demand ( ) is then calculated as the ratio of that storey’s design drift ( ) and its yield drift calculated as per Equation 2. is the yield curvature of the longest wall. using the approximate method of Priestley et al (2007). 20 mm diameter ( ) reinforcement bars are assumed if no bar diameter has been specified as a part of a section curvature file:///C:/Users/User/AppData/Local/Temp/~hh512C. in which the design displacement profile is assumed to result from the summation of an elastic deformation profile and a rigid-body rotation about the base. ratio of total height to length) greater than or equal to 3. (4) The plastic hinge length is computed from Equations 5 to 7. Defining steel beams and columns with other angles will lead to the bending strength capacity of the sections to be estimated as zero. Future versions of the software will allow for steel sections to be defined with any desired orientation. for it ignores the contribution of shear deformations to the shape of the displacement profile. from Equation 4.htm 11/12/2015 . since the strain in it will be determinant for the whole system.e. The system’s equivalent ductility demand ( ) is calculated by weighting each storey’s ductility demand with respect to the design storey shear and storey drift. For the calculation of the penetration depth ( ). For rectangular concrete walls it can be estimated. It is noted that this method is valid for walls with aspect ratios (i. The elastic curvature profile is assumed to vary linearly from the yield curvature at the base to zero at the roof level. as: (5) The equivalent viscous damping of the frame system is finally calculated as: Reinforced concrete frames: Steel frames: (6) (7) Note regarding Steel Frames Please note that the current version of DBDsoft only allows for steel beams and columns to be defined with their local axes oriented parallel and perpendicular to the global axes. (1) (2) (3) In the previous equations. as a function of the reinforcement’s yield strain ( ) and the wall’s length ( ). unless a section curvature criterion has been specified for the longest wall with a user-defined plastic hinge length. as recommended by Priestley et al (2007). Furthermore. and that the value calculated as per the above equation should be considered only as indicative. and do not account for the expected design shear profile. and the system’s equivalent viscous damping is finally obtained as the weighted average of all walls acting in the same direction with respect to their strength proportions. Frame-Wall Systems Previous Top Next Frame-Wall Systems As opposed to the case of pure frame systems. (5) (6) (7) Equivalent Viscous Damping The yield displacement of each wall is calculated by replacing in Equation 3 with the equivalent SDOF system’s equivalent height . (8) (9) Nominal Moment Demand at Base The nominal moment demand at the base of the walls is calculated as a function of the design displacement ( . Even though this option is recommended. the automatic betas proposed by the software are only based on the estimation of members’ strength based on the dimensions and materials of the sections defined by the user. Each wall’s equivalent damping is then calculated by means of Equation 9. the use of constant beam strengths along the height comes up as an appealing option that certainly eases the construction process.DBDsoft Page 48 of 93 criterion. resulting from the product of the total overturning moment and the strength proportion assigned to the wall’s base). Three cases can be found when rigid links are not used to connect the beam and the wall. the user has effective freedom to choose the desired shear profile in the frames. the user has the possibility of specifying any desired strength distribution. Given the fact that any difference between the design shear profile and the actual distribution of strength specified by the users will be carried by the walls. each wall’s ductility demand is computed as the ratio between the system’s characteristic displacement and its yield displacement. it is possible to obtain a constant shear profile in the frames at all levels by designing beams at all levels for equal strength except at roof level. 5% assumed). If the angle lies between file:///C:/Users/User/AppData/Local/Temp/~hh512C. the displacement ductility demand ( ) and the post-yield stiffness ratio ( . the wall is considered to be perpendicular to the beam and thus there is no frame-wall system in the direction of the beam. Link Beams Frames and walls may or may not be connected by moment-transferring beams. rigid links are needed. and by allocating that same strength proportion of the roof beams to the plastic hinges at the base of the columns.htm 11/12/2015 . For this reason. If the smallest angle between them is less than 15°. If the angle is between 75° and 90°. if the Auto-Betas function is used for a Frame-Wall system (either with or without link beams). as described here. Afterwards. as: (for ) (10) It should be noted that a precise definition of the required nominal strength of the walls at their base should stem from the corresponding moment-curvature analyses of the sections. DBDsoft recognizes a series of ways of connecting beams to a wall. which account for different possible geometries. where the beam strength should be reduced by half. strength proportions play a very significant role in the displacement-based design of structures. The proportion of moment transmitted from the beam’s plastic hinge to each connected wall is determined from the relative estimated strengths of the walls. as explained here. as exemplified in the figure below: When link beams are specified. For file:///C:/Users/User/AppData/Local/Temp/~hh512C. the software automatically computes their additional contribution to resisting the overturning moment. Strength Proportions As described here. The software allows for each end of a link beam to be connected to more than one shear wall. The following figures illustrate these three cases: If the beam and the wall are connected by a rigid link. as shown in the figures below: The software recognizes up to two aligned rigid links connecting a beam and a wall.DBDsoft Page 49 of 93 15° and 75°. the software considers that the two elements define a frame-wall system and the beam is a link beam (unless released at both ends). the software considers the existence of a frame-wall system only if the smallest relative angle between them is less than 75°.htm 11/12/2015 . with the equations transcribed herein. Nievas and Sullivan (2014) carried out a preliminary evaluation of a proposal to combine the displacement profiles developed earlier by Sullivan et al. in a given direction. (4) is the number of storeys. (2006) with that of a pure frame. This proposal is currently implemented in DBDsoft.8 of DBD12. Structural systems in which the walls carry very little of the total overturning moment seem to deform almost as pure frames. therefore. Note that. (2006) have proposed expressions to describe the displacement profile of frame-wall systems in which the walls carry a greater proportion of the total overturning moment than the walls. even though the user is warned that it has not been sufficiently tested yet to guarantee its performance. transcribed below as Equations 3 and 4. depends on the profile of the storey shear to be carried by the walls and thus the system’s shear profile as a whole. Design Displacement Profile As the design displacement profile of frame-wall systems depends on the contraflexure height (Sullivan et al. A “hybrid” displaced shape is used for design: for file:///C:/Users/User/AppData/Local/Temp/~hh512C.htm 11/12/2015 . (5) (6) • for (7) for (8) : The frames are stronger than the walls. if link beams exist. Sullivan et al. It is recommended that the designer pays special attention to this and verifies extensively the walls’ ductility capacity with a well-detailed moment-curvature analysis. it is relevant to recall the way the software handles this information and summarizes the whole distribution of strength into fewer parameters: • : the proportion of overturning moment taken by the plastic hinges at the base of the walls. but is used for all cases as a starting point. 2006) and this. the displacement profile is mostly determined by the walls according to article 6. which should actually be applied only for the case of constant frame shear along the frame’s height. the plastic hinge length and the strain penetration length described for the case of cantilever walls systems are applicable. and thus impose very high rotational demands to the bases of the walls. the design displacement profile is determined in different ways: • : the “traditional” profile proposed by Sullivan et al. In order to be able to cover all the possible strength proportions. The walls can be either isolated or connected by link beams to a frame: (1) • : the proportion of overturning moment taken by the plastic hinges at the base of the columns and at the (non-link) beams. The software starts by estimating the contraflexure height ( ) by means of equation 6. All considerations regarding walls’ yield curvatures. while . (2) • : the proportion of overturning moment taken by the plastic hinges at the link beams. if (3) If In the above equations. in turn.4 of DBD12. The influence of the walls is significant and.DBDsoft Page 50 of 93 this reason. (2006) is used. the plastic hinge connected to a frame’s column counts as contributing to the plastic hinge connected to a wall contributes to . an iterative approach needs to be followed. Depending on the contraflexure height ratio. in a given direction. in a given direction. The iterative process followed is described in the following figure. The longest (assumed to be the stiffest) wall is used to determine the yield curvature at the wall base to be used for the calculation of the displaced shape. as shown in Equation 9.10%. Given the fact that small errors in the determination of the contraflexure height do not affect results significantly. and the calculation of the members’ required strengths. in the extreme case in which the frames take 100% of the overturning moment and the walls take 0%. and these turn out to be the longest walls. and the displacement profile reduces to that of a pure frame. the tolerance is currently set to 0. and FCL and FCQ are their corresponding weighting factors. If the model contains more than one wall with the same length in a certain direction. the software calculates the contraflexure height of the system as the weighted average of the contraflexure heights of these individual walls with respect to the proportion of overturning moment each of them is expected to carry. and the final overall viscous damping of the frame system is obtained as a weighted average (Equation 13). The iteration process is controlled by a convergence check based on the ratio of the contraflexure height calculated at a certain step and the contraflexure height obtained in the previous step.htm 11/12/2015 . the contraflexure height is equal to zero. • : The walls become less influential as the frames take a greater percentage of the overturning moment. but still participate enough for the behaviour to be different from the case above. This procedure is relevant in the case that some of the walls are connected to link beams while others are not. the yield drift of the end of the link beam connected to the wall is calculated as suggested by Sullivan et al.DBDsoft Page 51 of 93 heights below the inflexion point. while for the rest of the building the displacements are calculated as for the case of a pure frame. the walls’ profile is used (Equation 7 above). (13) It is noted that for the case of frame-wall systems in which link beams are present. as well as the contraflexure height.ls CQ are the profiles corresponding to and . as well as a limit set to the maximum number of iteration steps to be carried out. starting from the inflexion point. (9) It is clear that. [2006] as: (14) Design Flow Chart file:///C:/Users/User/AppData/Local/Temp/~hh512C. The software then proceeds with the calculation of the base shear and overturning moment demands. The yield profile shown in the Post-Processor module corresponds to the walls (calculated as per Equations 7 and 8 above). A combined profile is used: (10) (11) (12) where Δi. a situation that leads to walls of the same length having different contraflexure heights. ductility demands and equivalent viscous damping are computed independently for frames and walls (as described earlier in the respective sections). The first storey height is taken as the average storey height of the storeys above the inflexion height.ls CL and Δi. respectively. Once the convergence criterion has been met. appropriate capacity design principles need to be file:///C:/Users/User/AppData/Local/Temp/~hh512C. Coupled Walls Systems Previous Top Next Coupled-Walls Systems The current version of DBDsoft does not support coupled-wall systems.htm 11/12/2015 . Corresponding solvers will be developed for future versions. Capacity Design Previous Top Next Capacity Design In order for the plastic hinges to develop at the intended locations.DBDsoft Page 52 of 93 Nominal Moment Demand at Base The nominal moment demand at the base of the walls is calculated as shown here. but DBD12 suggests that one single approximate value may be used. the effective modal superposition method or using a simplified approximate method. The moment at mid-height is calculated as: (1) (2) In the last equation. DBDsoft determines the capacity design moments and shears in columns and walls following the approximate method described in DBD12. as described here. as the design actions in members are determined from a first mode deformed shape. taking into account the possibility of increased material strength in the plastic hinges and higher mode amplification of actions. The default value is 1.htm 11/12/2015 . n order for the plastic hinges to develop at the intended locations. Previous Top Next General Capacity Design: General Conceptually. Further. including the effects of cracking. Clearly.30. capacity design moments and shears are determined by amplifying the design actions by means of an overstrength factor and a dynamic amplification factor. appropriate capacity design principles need to be applied in order to ensure that elements meant to remain elastic during seismic excitation are able to sustain the forces induced in them. this increase in forces needs to be accounted for separately. It should normally be established based on a moment-curvature analysis of members using their maximum feasible strength levels. Alternative methods will be included in upcoming versions. The overstrength factor takes into account the possibility that plastic hinges possess strength higher than calculated due to many factors. The dynamic amplification factor represents the increase in the expected storey shear forces due to the effect of higher modes. Currently. The current version of DBDsoft allows the user to specify this value in the Design Case tab of the Processor area. this means that different overstrength factors could be specified for the capacity design of different members in the structure. The DBD12 Model Code suggests that capacity design moments and shears can be obtained by means of non-linear time history analyses. The first is simply the product of the overstrength factor ( ) defined by the user in the Processor area and the design moment at the base of the wall (resulting from the product of the total overturning moment and the strength proportion assigned to the wall’s base). such as a higher strength of the materials or strain hardening.DBDsoft Page 53 of 93 applied in order to ensure that elements meant to remain elastic during seismic excitation are able to sustain the forces induced in them. as more is understood with respect to the effect of higher modes on structures that behave inelastically. Ti is the initial elastic period. taking into account the possibility of increased material strength in the plastic hinges and higher mode amplification of actions. It is relevant here to recall that higher modes tend to have a bigger influence on the forces generated within a structure than on its displacements and that. and is estimated from the effective period and displacement ductility demand of the structure (determined from the DDBD process) as: (3) The profile of capacity moments along the height of the wall is similar to: file:///C:/Users/User/AppData/Local/Temp/~hh512C. several authors have published alternative approaches in the recent years. defined by the moment at the base (M o base) and the moment at mid-height (M o MH). Capacity Design of RC Walls Previous Top Next Capacity Design of RC Walls The envelope of capacity moments for walls is approximated by a bilinear curve. and the largest of the two should be taken as the final value.htm 11/12/2015 . or exceptionally equal. It is relevant to notice that the moment at the base (Mo base) used herein to define the envelope of capacity moments along the height of the walls is larger than the nominal moment demand at the base calculated as described here. the dynamic amplification factor for shear forces at the base is calculated as: (7) (8) If the seismic resistant system in the direction under study only consists on walls. or if the wall is part of a frame-wall system in which the frames carry less than 20% of the total overturning moment. the dynamic amplification factor for shear forces at the base is calculated as: (5) (6) If the wall is part of a frame-wall system in which the frames carry more than 20% of the total overturning moment. It is therefore relevant that the designer analyses the (approximate) nominal required strength and the envelope of capacity moments critically.2 times the mid-height moment due to first mode response. As shown by Priestley and Amaris (2002). when the walls are subject to non-linear time-history analyses for intensities up to double of the design one. the required shear strength at the top of the wall is calculated as: file:///C:/Users/User/AppData/Local/Temp/~hh512C. The latter is the nominal yield capacity of the wall’s base. so as to make a conscious decision with respect to the reinforcement to provide. the capacity moment at mid-height should be confronted against 1.DBDsoft Page 54 of 93 If the wall is part of a frame wall system in which the frames carry more than 20% of the total overturning moment. which can actually end up being higher during seismic excitations that induce inelastic behaviour. The plot shown in the “Walls Capacity Moments” tab of the Post-Processor can be particularly useful for this purpose. or if the wall is part of a frame-wall system in which the frames carry less than 20% of the total overturning moment. the maximum moments developed along the height of the walls are usually smaller than the plastic hinge at the base. due to strain hardening and other sources of overstrength. The capacity design shear strength of the wall shall conform to the following envelope: The required shear strength at the base (Vo base) is calculated as: (4) If the seismic resistant system in the direction under study only consists on walls. DBDsoft Page 55 of 93 (9) If the wall is part of a frame-wall system in which the frames carry more than 20% of the total overturning moment. associated with the overstrength of adjoining beams (i. The user should take this into consideration when defining the overstrength factor (see here). is the seismic design shear force at the base of the columns (ground/foundation level) associated with 1 st mode response. or part of a frame-wall system in which the frames carry more than 60% of the total overturning moment. is the seismic design shear force associated with 1 mode response. as this should be taken into account in the definition of the dependable required strength. respectively. the dynamic amplification factor ( ) is simply taken as 1. moments determined as per equation (1)). moment strength at the base of the columns should not be increased as for the rest of the columns’ height). the storey drift that causes the columns to yield is estimated as: (4) file:///C:/Users/User/AppData/Local/Temp/~hh512C.e. resulting from the product of the total overturning moment and the corresponding strength proportion ). the displacement ductility demand ( ) and the storey force-displacement post-yield stiffness ratio ( . and and are the design moment at the top and bottom of the column. 5% assumed).e. If the columns are part of a pure frame system. the required shear strength at the top of the wall is calculated as: (10) Capacity Design of Columns Previous Top Next Capacity Design of Columns The capacity moments of columns ( ) are calculated from their design ones ( ) as: (1) If the columns are part of a frame-wall system in which the frames carry less than 60% of the total overturning moment. is the characteristic shear resistance of the structural st element. In order to determine the displacement ductility demand. It should be noted that the current version of DBDsoft does not carry out the verification/design of the sections proposed by the users. This is particularly relevant for the capacity design of columns if the provided sectional strength is actually larger than the required one. the dynamic amplification factor ( ) varies with height according to the following figure and equation: (2) The required dependable shear strength of columns is determined as: (3) where is the material strength reduction factor for shear.htm 11/12/2015 .30. The strength provided at the base of the columns should be such that the plastic hinges form at the intended moment demand (i. The nominal moment demand at the base of the columns is approximately calculated as a function of the design moment ( . While viewing the results through the “Sheets and Graphs” option. DBDsoft does not yet provide capacity design shear actions for beams.htm 11/12/2015 . which copies the whole active tab. the user can manually select parts of the output tables and copy (Ctrl + “C”) and paste (Ctrl + “V”) them in any external application. The DBD12 Model Code provides some guidance with respect to the capacity design of columns whose response is biaxial. It is also possible to use the “Copy Sheet To Clipboard” button. and that the value calculated as per the above equation should be considered only as indicative. as well as bending moments and shear plots for all the structural members. However. the user can observe the structure in its deformed shape at development of the critical performance criterion. and combination of actions in these two directions shall be carried out by the designer. just by selecting the corresponding option. To view the tabulated results and graphs. select the option “Sheets and Graphs”. The nominal moment demand at the base of the columns is estimated as: (for ) (6) It should be noted that a precise definition of the required nominal strength of the columns at their base should stem from the corresponding moment-curvature analyses of the sections. To view results graphically select the option named “3D View”. file:///C:/Users/User/AppData/Local/Temp/~hh512C. Capacity Design of Beams Previous Top Next Capacity Design of Beams Currently. but future versions will. The displacement ductility demand for the column’s base is. Selecting the 3D View. as shown in the figure below. Note that the “Save To Excel” option is not yet available in the current version of the software. thus: (5) where is the interstorey drift at the ground level. Post-Processor Previous Top Next Post_Processor The Post-Processor phase includes options to view results graphically or in table format.DBDsoft where Page 56 of 93 is the column’s yield curvature (around the relevant axis) and is the column’s contraflexure height. the current version of DBDsoft treats design in the two perpendicular directions X and Y independently. and.htm 11/12/2015 . Some of them are available only for certain structural types. and are thus lost upon closing of the file. as specified: The results within each of this output forms is described in the sub-sections that follow. the yield displacements of the wall file:///C:/Users/User/AppData/Local/Temp/~hh512C.DBDsoft Page 57 of 93 The following table shows all the different kinds of output that are shown in the different tabs of the Post-Processor module when the “Sheets and Graphs” option is selected. if walls are present. Displacements Previous Top Next Displacements The Displacements tab shows the design displacements that controls the design. It is noted that the output of a certain design run are not saved by the software. It is noted that if two vertical systems are carrying exactly the same proportion of the total storey shear in each storey. as shown on the plot on the right of the following example. the global storey shear is shown as well. as shown on the plot on the left of the following example.DBDsoft Storey Shear Graph Page 58 of 93 Previous Top Next Storey Shear Graph The format of the plots shown in the Storey Shear tab varies depending on the type of structure in each direction. the plot shows the storey shear carried by the frames (i. the columns that make up the frames) and that carried by the walls. the lines corresponding to both systems will overlap and the user will only be able to see one of them. file:///C:/Users/User/AppData/Local/Temp/~hh512C. In both cases. The labels contain the user-defined name of the base element of the vertical system. When the structure is a frame-wall system.e.htm 11/12/2015 . When the system consists of only frames or only walls. the plot shows the storey shear carried by each vertical system (column or wall). DBDsoft Storey Moments Graph Page 59 of 93 Previous Top Next Storey Moments Graph Just as for the case of the Storey Shear Graph. the format of the plots shown in the Storey Moments tab varies depending on the type of structure in each direction.htm 11/12/2015 . the lines corresponding to both systems will overlap and the user will only be able to see one of them. When the structure is a frame-wall system. Walls Capacity Moments Graph Previous Top Next Walls Capacity Moments Graph These plots show the capacity moments profiles (calculated as indicated here) and the nominal base moment (calculated as indicated here) for each wall in the structure. the plot illustrates the moment carried by each wall and by the frames (as a whole). besides showing the global moment. When the system consists of only frames or only walls. Each wall is identified by the user-defined name of its base element. the plot simply shows the global moment. file:///C:/Users/User/AppData/Local/Temp/~hh512C. It is noted that if two different walls are carrying exactly the same proportion of the total storey shear in each storey. Each wall is identified by the user-defined name of its base element. file:///C:/Users/User/AppData/Local/Temp/~hh512C. in each direction. Columns Capacity Moments Graph Previous Top Next Columns Capacity Moments Graph These plots show the sum of the capacity moments profiles of all the columns (calculated as indicated here) along the height of the structure.DBDsoft Walls Capacity Shear Graph Page 60 of 93 Previous Top Next Walls Capacity Shear Graph These plots show the capacity shear profiles (calculated as indicated here) for each wall in the structure.htm 11/12/2015 . DBDsoft Results Tab Page 61 of 93 Previous Top Next Results Tab The Results module within the Post-Processor Phase presents the results of the DDBD calculations made by the program. A screenshot of a typical results table is annotated below: By scrolling down the table using the arrows on the right. file:///C:/Users/User/AppData/Local/Temp/~hh512C. one can see the total system design base shear and overturning moment (see figure below).htm 11/12/2015 . Note that these values already include the additional base shear due to P-Delta considerations. file:///C:/Users/User/AppData/Local/Temp/~hh512C. It is calculated as: for for Clearly. The nominal moment results from combining the design moment with the effects of the displacement ductility demand ( ) and post-yield stiffness ratio (r factor). the Results module shows each storey’s displacement ductility demand as well. However. Results for each The design moment is the moment required for the system to be in equilibrium when subjected to its design deformation limit state. ) moments and shear forces for the beams. the displacement ductility demand ( ) is calculated as the ratio between the design storey drift (shown in the column in the table) and the yield storey drift corresponding to each beam. in order to provide the storey shear stiffness required by design.30. If the structural system in a certain direction is made only of frames. as shown below. the total design base shear and overturning moment are still calculated. Results for the perpendicular (Y) design direction are shown further down the table as well. a warning message appears. and it is the value with which sizing of the longitudinal reinforcement needs to be carried out.htm 11/12/2015 .DBDsoft Page 62 of 93 If the maximum P-Delta stability coefficient is larger than 0. . Beams Details Previous Top Next Beams Details This table contains the design ( . ) and nominal ( direction (X and Y) are shown in independent tabs. DBDsoft Columns Details Page 63 of 93 Previous Top Next Columns Details This table contains the columns’ design moments that equilibrate the design moments ( ) of the beams. calculated as described here. as shown in the figure below: Walls Details file:///C:/Users/User/AppData/Local/Temp/~hh512C. It is noted that the current version of the software does not calculate the demands in columns working out of the plane of the frame. Results for each direction (X and Y) are shown in independent tabs.htm Previous Top Next 11/12/2015 . as well as their corresponding design shear ( ) and seismic axial force demands. for each column. It also contains the columns’ nominal and capacity moments ( ) and shear ( ). The table also shows the ratio of the contraflexure height with respect to the total height of the column. the contraflexure point is located at 0. as well as their corresponding design shear demands. The nominal strengths are calculated as indicated here. In the example below.DBDsoft Page 64 of 93 Walls Results This table contains the walls’ moments ( ) at the design deformation limit state. file:///C:/Users/User/AppData/Local/Temp/~hh512C. as shown in the figure below: Wall Base Details Previous Top Next Wall Base Details This tab shows a summary of the required moments and main properties of all the walls present in the model. while walls that are part of frame-wall systems present one contraflexure point along their height. the table shows the axial force demands in the walls as well. calculated as described here. The required strengths shown are simply the product of the final strength proportion and the total overturning moment in each direction. Yield curvatures (calculated as indicated here) and displacement ductility demands in both directions ( ) are shown as well. Results for each direction (X and Y) are shown in independent tabs. It also shows the nominal moment demand ( ) at the base. Final strength proportions ( ) are shown for each direction ( and and ). and the capacity moments and shear forces along the height.htm 11/12/2015 . For the case of frame-wall systems in which the walls are connected to the frames by means of link beams. The table also shows the ratio of the contraflexure height with respect to the total height of the wall. Each wall is identified by the user-defined name of its base element. It is noted that the current version of the software does not calculate the demands in walls working out of plane. Note that structural systems made up only of cantilever walls do not present a contraflexure point.86 times the height of elements W4/W14. for each element that makes up the wall. respectively). so their values represent the secant slope of the displaced shape instead of the tangent slope. The user can check if this is the case by taking a look at the tab “Other”. in some cases. as shown here. The table shows the criteria defined by the user. Results for each direction (X and Y) are shown in independent tabs. It is noted that the maximum drifts obtained by the software might.htm 11/12/2015 . please refer to Iteration Process to Satisfy Performance Criteria. For details regarding the iteration process. One reason for this is the fact that interstorey drifts are a discrete and not a continuous function of the building’s height. be smaller than the limits specified by the user. Design Process Previous Top Next Design Process These tabs show how the iteration process to satisfy performance criteria has been carried out. as well as the values obtained by the software at each iteration step.DBDsoft Page 65 of 93 Final Betas Previous Top Next Final Betas This tab shows a summary of the local ( ) and final ( ) strength proportions of each element in the model. Values marked in red do not satisfy the specified criterion. Another possible reason is the dominance of the walls’ material strain limits over user-specified drift limits (please refer here and here for details on the calculation of the design plastic rotation ( ) for wall and frame-wall systems. file:///C:/Users/User/AppData/Local/Temp/~hh512C. file:///C:/Users/User/AppData/Local/Temp/~hh512C.DBDsoft Other Results Page 66 of 93 Previous Top Next Other Results The tab “Other” shows other various results of interest. To view these options. show node or element names. and summarize some information regarding the design of the structure in both directions. and states whether this value is governed by the walls’ material strain limits or the user-defined maximum interstorey drift (indicated as “Code Drift” in the table). click on any one of the three square buttons located on the right of the screen (see below). The plot menus that are revealed (see figure below) include options that permit the user to change the view. show the base grid. Note that the 3D plotting options can also be accessed from the main drop-down menu of the program. among others.htm 11/12/2015 . For the case of cantilever walls or frame-wall systems. as shown in the figure below. change the colour scheme. select between solid. and scale the deformed shape. Using the 3D plotting tools Previous Top Next Using the 3D plotting tools The software has been developed with a number of 3D plotting options. wireframe or shaded elements. the table presents the design plastic rotation ( ). This chapter provides step-by-step hand calculations for those example buildings that the user can easily compare to the results obtained with the software.htm 11/12/2015 .DBDsoft Page 67 of 93 The user can also select to plot the bending moment or shear diagrams over the structure. Note that the perspective view of the structural model can be changed with a left-click drag of the mouse. columns or walls. The example files can be opened by clicking on File --> Test Cases and selecting the corresponding example file. Y or both directions simultaneously. The view can also be moved in a translation motion with a right-click drag. as shown below: Test B1 Previous Top Next Example Test B1 file:///C:/Users/User/AppData/Local/Temp/~hh512C. Examples Previous Top Next Examples As mentioned here. and for them to be shown for all elements or only for beams. four example files are provided. in X. The scale of the bending moment and shear diagrams can be changed with the corresponding control as well. the projected length along each global axis (X and Y) is used: Element Yield Curvature Limit Curvature file:///C:/Users/User/AppData/Local/Temp/~hh512C.DBDsoft Page 68 of 93 Description Value Units Mass per storey 600 ton/storey Number of storeys 8 [-] Interstorey height 3.03 m Corner Period 6.0 [m] f'ce 30 [Mpa] fye 500 [Mpa] fue 600 [Mpa] Es 205000 [Mpa] Limit Drift 2.htm Section height [m] 11/12/2015 .0 % PGA 0.4 g Step-by-step calculations Walls' yield curvature and limit state curvature: For the case of Wall 3.0 sec Elastic Damping 5.0 [%] The design displacement spectrum is characterized by the following parameters: Parameter Value Units Corner Displacement 1. i (m) mi.i (m) mi.22 600 0.i (m) Δd.8 9.6 58.00113 0.22 600 0.9 21.076 0.6 19.22 600 0.056 0.003 0.00143 0.8 18.7 2707.5 18068.195 116.Δi mi·Δi2 mi ·Δi·hi 600 0.000 0.011 0.7 5313.6 3 9 9.181 108.3 102.1 33.3 21.1 3182.4 18.3 Storey hi (m) 8 Total 4800 In Y: H + Lsp Mass (m) (T) 24 24.22 600 0.4 3895.033 19.5 57.0 0.3 Plastic hinge length: Plastic component of the design displacement profile: Due to the maximum drift limit: Due to limit state curvatures: Hence.DBDsoft Page 69 of 93 X Y X Y Ltot Lx Ly Wall 1 0.023 0.2 15 15.4 75.8 0 0 0.01800 4 - 4 Wall 3 0.7 1303.9 15 15.8 22. the final design plastic rotation is controlled by the maximum code drift of 2% in both directions: In X: H + Lsp Mass (m) (T) 24 24.02118 0.6 297.22 7 21 6 18 5 4 Δy.0 2 6 6.8 691.22 600 0.128 76.104 0.354 212.8 4 12 12.4 81.8 52.6 0.0 3.251 150.038 0.22 600 0.8 Storey hi (m) 8 file:///C:/Users/User/AppData/Local/Temp/~hh512C.22 7 21 6 18 5 Δy.i (m) Δd.01674 5 3.7 281.369 221.4 4.0 0.0 12 12.070 0.8 1 3 3.5 12.7 5958.000 0.309 185.141 0.2 4459.22 600 0.142 85.222 0.295 176.22 600 0.22 600 0.22 600 0.078 47.22 0 0.181 0.097 0.htm 11/12/2015 .Δi mi·Δi2 mi·Δi·hi 600 0.22 600 0.7 2131.7 1752.414 248.237 142.00900 - 8 8 - Wall 2 - 0.119 0.0 1031.00061 - 0.00122 - 0.2 1025.4 37. 000 0 Total 4800 0.8 0.0 0.254 m Effective height: Hex = 17.1 t and mey = 3392.006 0.000 0.22 600 0.3 0 0.020 0.22 600 0.8 196.3 38.2 15443.8 2 6 6.288 m and Δdy = 0.22 600 0.0 862.2 5.3 219.095 57.4 Characteristic displacement: Δdx = 0.021 12.2 t Each wall's yield displacement is calculated as: Wall 1 (X): Wall 2 (Y): Wall 3 (X): Wall 3 (Y): Each wall's ductility demand: Wall 1 (X): Wall 2 (Y): Wall 3 (X): Wall 3 (Y): Each wall's equivalent viscous damping: Wall 1 (X): Wall 2 (Y): file:///C:/Users/User/AppData/Local/Temp/~hh512C.2 1 3 3.0 0.DBDsoft Page 70 of 93 3 9 9.5 514.91 m Effective mass: mex = 3577.042 0.52 m and Hey = 17.055 32.htm 11/12/2015 .22 0 0.7 1. 50% for Wall 3 In this way.104) exceeds the 0. The additional base shear in direction X is 289 kN. and thus the design base shear is increased by the following quantity: For concrete. the maximum P-Delta stability coefficient (0. as shown in the table below. In X.htm 11/12/2015 .10 limit for concrete structures.50. file:///C:/Users/User/AppData/Local/Temp/~hh512C. and thus the final design base shear is the same as calculated before.064) is smaller than the 0. 25% for Wall 3 Direction Y: 50% for Wall 2.DBDsoft Page 71 of 93 Wall 3 (X): Wall 3 (Y): We make the decision of distributing the base shear (and overturning moment) in each direction in the following way: Direction X: 75% for Wall 1. In Y. we calculate the equivalent viscous damping of the system as: In X: In Y: The design spectrum reduction factors are calculated as In X: In Y: Effective period: In X: In Y: Required effective stiffness: In X: In Y: Design base shear (no P-Delta amplification verified or accounted for yet): In X: In Y: Calculation of the P-Delta stability coefficient for each storey: The vertical load at each storey is the product of the cumulative mass and the acceleration of gravity.10 limit for concrete structures. the maximum P-Delta stability coefficient (0. C = 0. The design storey shear is equal to the proportion of storey shear with respect to the base shear (Vi/Vb) and the base shear calculated above. 104 13 3 0.020 7 21 0.881 7227 0.099 30 9 0.5 0.056 600 1200 0.142 0.020 7 21 0.011 600 4200 0.056 3 0.447 2735 0. for example).195 4 12 3 2 1 Cum.095 0.618 3785 0.033 0.000 8204 0.DBDsoft Page 72 of 93 The following tables contain the corresponding calculations.947 7771 0.646 5303 0.981 6009 0.018 600 3000 0.021 0.181 0.i 600 600 0.i θi Mass (t) 8 24 0.078 0. Mass (t) Vi.861 5274 0.055 0.257 2106 0.5 84262 0 28087 Mwall Y EQ (kNm) 0 73470 73470 NOTE: The result of each step of the procedure has been presented in a rounded format.782 6414 0.015 600 4200 0.369 0.019 600 1800 0.020 6 18 0.064 9 0.414 0.041 The final design base shear is: In X: In Y (as before): Overturning moment at the base: In X: In Y: For each wall: Element's Name Wall 1 Wall 2 Wall 3 βx βy Mwall X EQ (kNm) 0.062 0.251 5 15 0.011 600 4800 1.x/Vb Vdi θP-Δ VP-Δ.25 0. Mass (t) Vi. Direction X: Level hi (m) Δd.x/Vb Vdi θP-Δ 600 600 0.295 5 15 0.084 5 VP-Δ --> 289 Direction Y: Level hi (m) Δd.241 1474 0.020 6 18 0.007 600 4800 1.064 0.000 6125 0.128 0.019 600 1800 0.102 22 6 0. but all decimal places have been carried throughout the calculations.i θi Mass (t) 8 24 0.090 50 0.309 0.htm 11/12/2015 .017 600 3600 0.017 600 2400 0.472 3872 0.062 6 0.095 40 0.935 5730 0. Test B2 Previous Top Next Example Test B2 file:///C:/Users/User/AppData/Local/Temp/~hh512C.756 4629 0.059 0.354 0.75 0 0 0.016 600 3000 0.014 600 3600 0.237 4 12 3 2 1 Cum.085 59 0.080 70 600 1200 0. if not all decimal places are used (with the aid of a spreadsheet.019 600 2400 0.985 8083 0. This explains small differences that the user can obtain when following the numbers by hand. DBDsoft Page 73 of 93 Description Value Units Mass per stroey 600 ton/storey Number of storeys 6 [-] Interstorey height 3.0 % PGA 0. and is determined from: Higher mode reduction factor (1.0 [m] f'ce 30 [Mpa] fye 500 [Mpa] fue 600 [Mpa] Es 205000 [Mpa] Drift Limite 2.03 m Corner Period 6.htm 11/12/2015 .0 [%] The design displacement spectrum is characterized by the following parameters: Parameter Value Units Corner Displacement 1.00.4 g Step-by-step calculations The displacement profile is identical in both directions. for this case): Distribution of equivalent lateral force in height: file:///C:/Users/User/AppData/Local/Temp/~hh512C.0 sec Elastic Damping 5. 000 0 0.000 1.50 0.x (7) (8) 3043 0.000 0.000 Tot.00 1.i Massa mi.164 600 99 16 887 0. and that frames GM0.174 0.00813 0.335 0.50 0.y (9) (10) (11) - 0.00976 0.Δi mi.y Vi.00 4.685 2 6 0.60 0. Yield drift values for different frames are combined taking into account the proportion of overturning moment that each frame is designed to carry.107 0.DBDsoft Page 74 of 93 Fi. we assume that frames GM1 and GM2 carry 70% and 30% respectively of the overturning moment in direction X.Δi. As all beams are defined with the same height.00244 0.282 600 169 48 Fi.Δi2 mi.060 600 36 2 108 0.542 0. GM1.00366 0. In this example.153 0.115 600 69 8 413 0.000 1.50 2. 20% and 40% respectively of the overturning moment in direction Y.hi (1) (2) (3) (4) (5) (6) 6 18 0. in each direction: Frame GM0 Frame GM1 Frame GM2 X Y X Y X Y Lb (m) - 2.207 0.854 0.00488 The dimensions of beams are the same within each frame.00244 0. 0 0 0 646 137 8185 Characteristic design displacement: Effective height: Effective mass: The interstorey yield drift ratio is calculated as: For each frame. and thus the storey yield drift of each frame directly coincides with the storey yield drift of its beams.335 i Hi (m) Δd. the yield drift of all storeys is the same in each direction.00 4.00244 0.50 0.00488 0.050 0.htm 11/12/2015 .717 0.248 600 149 37 2230 0.950 0.838 1 3 0.x Vi.194 0. and it can be calculated as: Direction X: file:///C:/Users/User/AppData/Local/Temp/~hh512C.230 0.209 600 125 26 1503 0.096 0.00 hb (m) - 0.50 ey - 0. and GM2 carry 40%.492 3 9 0.00244 0.00244 Qy (rad) - 0.262 4 12 0.944 0 0 0.056 0.137 0.262 - 5 15 0. 03982 0.00976 0.y / Vb i Frame GM1 Frame GM2 (rad) Vi.00585 3.7 0.00976 0.00813 0.82 0.y / Vb (rad) (rad) · · 6 0.3 0.0136 0.00488 0.00366 0.011 0.0343 0.921 0.00813 0.011 0.4 0.7 0.00366 0.3 0.00707 4 0.2 0.2 0.0200 0.02677 0.4 0.717 0.0038 5 0.4 0.0063 0.4 0.00976 0.013 0.665 0.00813 0.2121 0.00731 0.4 0.12 0.y / Vb · · 6 0.00366 0. in each direction.178 0.00379 5 0.00366 0.0106 3 0.020 1.00679 2.00585 3.0071 4 0.y / Vb Frame GM0 (rad) Frame GM1 Frame GM2 (rad) (rad) (rad) Vi.020 1.00813 0.690 0.00488 0.53 0.018 0.01575 0.0729 Total Equivalent viscous damping: In X: In Y: The design spectrum reduction factors are calculated as: In X: file:///C:/Users/User/AppData/Local/Temp/~hh512C.434 0.00679 1.542 0.00976 0.93 0.00488 0.017 0.00488 0.00679 1.00488 0.3 0.00585 1.3 0.0729 Total Direction Y: i (rad) Vi.DBDsoft Page 75 of 93 Direction Y: Each storey’s displacement ductility demand is calculated as: The ductility demand of the whole system.4 0.2 0.00488 0.717 0.7 0.00366 0.2 0.015 0.00679 2.00813 0.00585 2.4 0.00488 0.017 0.4 0.2 0.013 0.4 0.0231 0.7 0.htm 11/12/2015 .0467 0.0141 2 0.00585 2.00679 2.4 0.00488 0.7 0.4 0.1829 0.335 0. is computed as: Direction X: Direction Y: Direction X: (rad) Vi.00488 0.y / Vb · Vi.02000 0.854 0.00585 2.3 0.00488 0.42 0.335 0.06833 0.00813 0.950 0.0589 0.854 0.00488 0.950 0.000 0.0173 1 0.00976 0.23 0.00366 0.018 0.05412 0.2 0.00976 0.015 0.00488 0.01060 3 0.01735 1 0.946 0.000 0.542 0.3 0.4 0.01411 2 0.y / Vb · Vi.00679 2.7 0. 282 0.069 38 2 6 0.000 6591 0. Direction X: Level hi (m) Δd.015 600 1800 0.107 14 VP-Δ --> 250.436 Direction Y: file:///C:/Users/User/AppData/Local/Temp/~hh512C.DBDsoft Page 76 of 93 In Y: Effective period: In X: In Y: Required effective stiffness: In X: In Y: Design base shear (no P-Delta amplification accounted for yet): In X: In Y: Calculation of the P-Delta stability coefficient for each storey: The vertical load at each storey is the product of the cumulative mass and the acceleration of gravity.717 4726 0.018 600 3000 0.950 6261 0.x/Vb Vdi θP-Δ VP-Δ.248 0.164 0. The following tables contain the corresponding calculations. C = 0.013 600 1200 0.10 limit for concrete structures. the maximum P-Delta stability coefficient exceeds the 0.i θi Mass (t) Cum.542 3572 0.043 58 4 12 0.i 6 18 0.335 2208 0.020 600 3600 1.209 0.086 27 1 3 0.011 600 600 0.htm 11/12/2015 . Mass (t) Vi. The design storey shear is equal to the proportion of storey shear with respect to the base shear (Vi/Vb) and the base shear calculated above.50.055 49 3 9 0. and thus the design base shear is increased by the following quantity: For concrete.017 600 2400 0.854 5629 0. In both directions.115 0.060 0.030 65 5 15 0. 045 58 4 12 0.060 0.i θi Mass (t) Cum.DBDsoft Page 77 of 93 Level hi (m) Δd.282 0.335 2092 0.032 65 5 15 0. Mass (t) Vi.115 0.091 27 1 3 0.013 600 1200 0.015 600 1800 0.020 600 3600 1.854 5333 0.htm 11/12/2015 .209 0.017 600 2400 0.058 49 3 9 0.113 14 VP-Δ --> 250.542 3385 0.000 6245 0.717 4477 0.164 0.018 600 3000 0.950 5932 0.073 38 2 6 0.011 600 600 0. Test B3 Previous Top Next Example Test B3 file:///C:/Users/User/AppData/Local/Temp/~hh512C.i 6 18 0.x/Vb Vdi θP-Δ VP-Δ.248 0.436 The final design base shear is: In X: In Y: Overturning moment at the base: In X: In Y: NOTE: Small numerical differences with respect to the output of the software are due to rounding of decimal places along calculations carried out by hand. (10% for Wall 1. the contraflexure height is estimated from: if file:///C:/Users/User/AppData/Local/Temp/~hh512C.0 % PGA 0.4 g Step-by-step calculations in X: Frame-Wall System without Link Beams .htm 11/12/2015 .0 [%] The design displacement spectrum is characterized by the following parameters: Parameter Value Units Corner Displacement 1. assuming 25 mm rebars: Plastic hinge length : Design plastic rotation (with As and ): depend on the contraflexure height.DBDsoft Page 78 of 93 Description Value Units Mass per storey 300 ton/storey Number of storeys 6 [-] Interstorey height 3. with: Strain penetration length.03 m Corner Period 6. they will vary at each iteration step.0 sec Elastic Damping 5. Iteration process: To start.5 [m] f'ce 30 [Mpa] fye 500 [Mpa] fue 600 [Mpa] Es 205000 [Mpa] Limit Drift 2. 20% for Wall 2) Dominant wall is Wall 2. 05 831.01 9.089 0. Step Lp (m) Ratio H /H H (m) Q (rad) CF n CF p 1 0.387 0.275 150.01755 16.01916 26.82 115.00 0.00 0. and the corresponding equations for the displacement profile are updated.5140 1. The following table shows the values for some of the parameters obtained at each iteration step. together with the ratio of the newly calculated contraflexure height. the "traditional" profile is used: for for At each iteration step.275 150.88 2 7.6435 13.35 25.115 0.02000 47.180 0.01327 1.112 0.4490 1.1877 2 0.50 1 3.29 0.01327 1.51 file:///C:/Users/User/AppData/Local/Temp/~hh512C.13 518. the following process is followed (shown here for the last iteration step): 1.0001 4 0.5392 11.00 0.00 7.01991 37.44 1218.50 3.775 150.317 0.5160 1.01388 7.065 0.006 0.110 0.50 17.0048 3 0.02000 58.56 4.01 22.3232 1.775 150.htm 11/12/2015 .00 0. the contraflexure height ratio is confronted to the pre-established limits.180 0.01434 1.15 3 10.44 4 14.177 0.775 150.00 0.275 150.516 m in this case).23 5 17.021 0. Computation of the yield displacement and the total design displacement as a function of the contraflexure height obtained in the previous iteration step (13.6404 13.00 21.0000 At each iteration step.00 14.049 0.042 0.178 0.51 15.50 10. and the auxiliary columns that allow for the final computation of: i hi (m) hi+Lsp (m) mi (tn) Dyi (m) Ddi (m) Qi (rad) mi*Di mi*Di^2 mi*Di*hi 6 21.70 278.00 0.DBDsoft Page 79 of 93 if As .50 1.01331 1.6436 13.247 0. 1919 0. 3.1434 0.00 0.7000 i hi (m) S 4.1028 -0. and their corresponding moment profile . .49 2987.1234 4.7390 0.000 0.00 0.4443 1.665 0. Computation of the strength distribution of the frame in height.000 5 17.4324 0.00 0.1004 0.4443 0.8766 7.5179 2. As this is the last step of the iteration process.0717 0.1435 0.502 4 14.50 0. The whole frame’s ductility demand and equivalent viscous damping are computed as: file:///C:/Users/User/AppData/Local/Temp/~hh512C.000 0. based on an approximate estimation of the elements’ capacity.1434 0.50 0.110 0. With the aim of later comparing the results with those of DBD soft. Note that the frame’s moment at the base is equal to . Computation of the frame’s ductility demand and equivalent viscous damping.50 0.1004 0. At roof level: Intermediate levels: Ground level: 4.402 1 3.2113 0. this value is constant for all beams and all storeys: rad 7.0000 1.96 0.1004 0.00 0.9622 0.000 S 0.0000 0.1377 0.4443 6.843 0. for which is the corresponding moment profile.1434 0.0855 0.00 0. As all beams’ height and length is the same.88 53. Computation of the system’s distribution of base shear in height. from which the contraflexure height can be determined.215 0 0.775 0.5471 0.889 2 7.555 0.0378 1.DBDsoft 0 Page 80 of 93 0. Computation of the frame’s storey yield drift. Computation of the walls’ storey shear as .0502 0. for a global base shear equal to unity ( ).4443 3. bloc i bglob i Vbfr i (kN) Mbfr i (kN) Fi sys (kN) Vi sys (kN) Vw i (kN) Mw i (kNm) 6 21. the contraflexure height determined from the walls’ moment profile matches the value used for starting this iteration step.2463 0.1434 0. where .8767 0.142 3 10.647 6.3008 -0.4443 4.2947 -0. For each storey. based on the displaced shape and the mass distribution: 5.220 0.1479 10.00 192.000 0.275 0.htm 11/12/2015 .72 2.00 0.00 0. the strength proportions used here are those resulting from the Auto Betas function of the program.1004 0. Computation of the storey shear profile of the frame .1004 0.1434 0.3008 0. effective stiffness and base shear: file:///C:/Users/User/AppData/Local/Temp/~hh512C. Hcf (for ) 9. Computation of the system’s equivalent viscous damping for excitation in the X direction: 10.htm 11/12/2015 . Determination of the system’s effective period. ductility demand and equivalent viscous damping.DBDsoft Page 81 of 93 8. Determination of the system’s spectral reduction factor and the reduced spectral corner displacement: 11. Computation of each wall’s yield displacement. 13. the maximum P-Delta stability coefficient is smaller than the 0.htm 11/12/2015 .10 limit for concrete structures and. the design base shear calculated in the previous step is the final design base shear). no increase in the design base shear is necessary (i. therefore. Determination of design overturning moment: Step-by-step calculations in Y: Frame-Wall System with Link Beams file:///C:/Users/User/AppData/Local/Temp/~hh512C. The design storey shear is equal to the proportion of storey shear with respect to the base shear (Vi/Vb) and the base shear calculated above.e. The following table contains the corresponding calculations: As it can be observed. Verification of P-Delta Stability and calculation of final base shear: Calculation of the P-Delta stability coefficient for each storey: The vertical load at each storey is the product of the cumulative mass and the acceleration of gravity.DBDsoft Page 82 of 93 12. they will vary at each iteration step. Wall 3: Strain penetration length. Iteration process: To start. assuming 25 mm rebars: Plastic hinge length : Design plastic rotation: As and depend on the contraflexure height. the contraflexure height is estimated from: if if file:///C:/Users/User/AppData/Local/Temp/~hh512C.DBDsoft Page 83 of 93 .htm 11/12/2015 . 970 0.00 14.00895 0.DBDsoft Page 84 of 93 As .9996 4 0.971 0.02000 55. and the auxiliary columns that allow for the final computation of: i hi (m) hi+Lsp (m) mi (tn) Dyi (m) Ddi (m) Qi (rad) mi*Di mi*Di^2 mi*Di*hi 6 21. and the corresponding equations for the displacement profile are updated.179 in this case). separately.96 0.9537 1.88 4 14.000 0. The following table shows the values for some of the parameters obtained at each iteration step.00906 0.50 3.00906 0.9999 At each iteration step.6276 13.00 0.00 0.302 0. Computation of the yield displacement and the total design displacement as a function of the contraflexure height obtained in the previous iteration step (13.7597 15.31 13.95 5 17.035 0.01875 24.275 0. without counting the ends of the link beams connected to the wall ( ) and. Computation of the strength distribution of the frame in height.16 0 0. In this example.50 17.069 0.040 0.30 3 10.372 0.24 21.974 0.00 0. the contribution of the link beams ( ).78 S 2. the "traditional" profile is used: for for At each iteration step.84 2 7.00 0.htm 11/12/2015 .1790 0.02000 45.69 792. the following process is followed (shown here for the last iteration step): 1. Step HCF / Hn HCF (m) Lp (m) Qp (rad) Ratio 1 0.41 101.275 150.64 1 3.00 0.00 180.00681 0.775 150.275 150.107 0.162 0.13 2830.00 0.81 20.96 255.52 1.184 0.01152 6.011 0.6339 13.00 0.37 3.00 0.00 21. the contraflexure height ratio is confronted to the pre-established limits.6278 13.08 487. local file:///C:/Users/User/AppData/Local/Temp/~hh512C.00 0.00 7.50 10.275 150.232 0.054 0.85 48.1840 0.76 1171.097 0.3110 0.8344 2 0.81 8.775 150.01614 14. together with the ratio of the newly calculated contraflexure height.05 0.000 0.775 150.01989 34.9905 3 0.145 0. 3423 2. This moment profile needs to be adjusted due to the effect of the link beams over the wall’s moments. As both ends of the link beams are assigned the same capacity. As this is the last step of the iteration process. as shown below.2505 0.990 2.0125 0.419 0.0250 0.0765 0.1051 S 7.DBDsoft Page 85 of 93 strength distributions are global distributions as well.1374 6.000 0. 5.3423 1.0250 0.0765 0. for which is the corresponding moment profile.118 4 14.5260 0.0000 0 0.641 3 10. Computation of the storey shear profile of the frame .3423 0.00 0.0803 0.0383 0.14997 0.7516 0. and thus it is necessary to compute the final moment just above and just below each beam level.2168 -0.6411 5.9666 0.00 0.97726 0.5440 2.0250 0. and their corresponding moment profile . the strength proportions used here are those resulting from the Auto Betas function of the program.14997 0. based on the displaced shape and the mass distribution: i hi (m) bfr i bLB i Vbfr i (kN) Mbfr i (kN) MLB i (kNm) Fi sys (kN) Vi sys (kN) Vw i (kN) Mw i (kNm) 6 21. From the final moment profile of the wall. the contribution from their connected end at any intermediate storey is computed as: 3.0337 0. for a global base shear equal to unity ( ). Note that the frame’s moment at the base is equal to .htm 11/12/2015 .163 8. the contraflexure height can be determined.1925 0. With the aim of later comparing the results with those of DBD soft.4093 0. based on an approximate estimation of the elements’ capacity.073 2 7.58635 0. since the frame-wall is the only subsystem working in the Y direction.0334 1.0765 0.0000 0.1347 0.75906 0.233 2.50 0.594 1.6243 3.792 1.0765 0.00 0. Computation of the walls’ storey shear as .0250 0. and so the final moment profile of the wall is calculated as . Computation of the link beam’s moment profile in height as the cumulative product of the link beams’ strength proportion and the overturning moment corresponding to a unitary base shear. It is noted that the link beams introduce “jumps” in the wall’s moment profile.00 0. At roof level: Intermediate levels: Ground level: 4.19545 0. Computation of the system’s distribution of base shear in height.0250 0.3086 -0.8863 0.3423 3.3423 4. file:///C:/Users/User/AppData/Local/Temp/~hh512C.000 5 17.198 0.5591 0.3589 6.396 0.3086 0.50 0. the contraflexure height determined from the walls’ moment profile matches the value used for starting this iteration step.978 1 3.0765 0.36816 0.50 0. DBDsoft 7. For each storey. the storey shear to be used to compute the ductility demand of the system is that resulting not only from but also from . Page 86 of 93 Computation of the frame’s storey yield drifts.htm 11/12/2015 . Computation of the frame’s ductility demand and equivalent viscous damping. as shown below: file:///C:/Users/User/AppData/Local/Temp/~hh512C. as the weighted average of the yield drift corresponding to each plastic hinge with respect to their strength proportions: Individual yield drifts are calculated as follows: “Standard” beam ends: rad Link-beam unconnected ends: rad Link-beam connected ends: rad 8. The whole frame’s ductility demand and equivalent viscous damping are computed as: It is noted that the ductility demand and equivalent viscous damping of the frame includes the contribution of the ends of the link beams that are connected to the wall and. . thus. Determination of the system’s spectral reduction factor and the reduced spectral corner displacement: 12. Computation of the wall’s yield displacement.htm 11/12/2015 .DBDsoft Page 87 of 93 9. ductility demand and equivalent viscous damping. Computation of the system’s equivalent viscous damping for excitation in the Y direction: 11. effective stiffness and base shear: file:///C:/Users/User/AppData/Local/Temp/~hh512C. (for ) 10. Determination of the system’s effective period. the design base shear calculated in the previous step is the final design base shear). Verification of P-Delta Stability and calculation of final base shear: Calculation of the P-Delta stability coefficient for each storey: The vertical load at each storey is the product of the cumulative mass and the acceleration of gravity. if not all decimal places are used (with the aid of a spreadsheet. The design storey shear is equal to the proportion of storey shear with respect to the base shear (Vi/Vb) and the base shear calculated above. the maximum P-Delta stability coefficient is smaller than the 0.DBDsoft Page 88 of 93 14. therefore. Determination of design overturning moment: NOTE: The result of each step of the procedure has been presented in a rounded format.e. but all decimal places have been carried throughout the calculations. The following table contains the corresponding calculations: As it can be observed. for example). This explains small differences that the user can obtain when following the numbers by hand.htm 11/12/2015 .10 limit for concrete structures and. 15. no increase in the design base shear is necessary (i. Test B4 Previous Top Next Example Test B4 file:///C:/Users/User/AppData/Local/Temp/~hh512C. 5=2. Drift Limit 0.0 [%] f'ce 30 [Mpa] fye 484 [Mpa] fue 581 [Mpa] Es 210000 [Mpa] eye 0.DBDsoft Page 89 of 93 Description Value Units Number of storeys 9 - Interstorey height 3.889 m Corner Period 8.0 sec file:///C:/Users/User/AppData/Local/Temp/~hh512C.955·2.5 m External columns HE300M - Internal columns HE320M - Beams Storeys 1-2 IPE550 - Beams Storeys 3-4-5 IPE500 - Beams Storeys 6-7 IPE450 - Beams Storey 8 IPE 400 - Beams Storey 9 IPE330 - Number of Bays 6 - Bay length 6.002305 [-] Max.0 m Description Value Units Mass per storey 736 ton/storey Elastic Damping 3.5 m Building height 31.38 [%] The design displacement spectrum is characterized by the following parameters: Parameter Value Units Corner Displacement 0.htm 11/12/2015 . 552 6 21.5 736 0.306 225 69 3149 0.024 1.778 4 14.485 357 173 8739 0.864 3 10.137 0.DBDsoft Page 90 of 93 Elastic Damping 3.hi Fi Vi/Vb 9 31.0 736 0.535 394 211 11021 0. The design storey shear (Vi/Vb) is computed by simply summing the equivalent lateral forces down the building height.264 0.046 0.5 736 0.Δi mi.000 0 0 0 0.370 272 101 4766 0.931 2 7.955.976 1 3.1 of the DBD12 Model Code.0 % PGA 0.i mi.Δi2 mi.5%.000 0 0. Storey Hi (m) Mass Δd.0 736 0.86 1002.Δi. The resulting displacement profile and the auxiliary calculations needed to compute the equivalent SDOF substitute structure are shown in the following table.104 0.264 8 28.580 427 248 13450 0.000 2345.htm 11/12/2015 .90 Total Characteristic design displacement: m tn m The proportion of base shear that is applied at each storey as an equivalent force is calculated as shown below.0 736 0. from Figure 5. Results are shown in the table above. = 2.5 736 0.121 0.084 62 5 215 0.415 7 24.5 736 0.430 316 136 6642 0.151 0.162 119 19 836 0.4 g Step-by-step calculations The displacement profile of a steel frame is calculated from: Higher mode reduction factor Code drift limit = 0.0 0 0.236 174 41 1827 0. Floors 1 to n-1: Roof (floor n): Yield drift: IPE550: rad IPE500: rad IPE450: rad IPE400: rad IPE330: rad file:///C:/Users/User/AppData/Local/Temp/~hh512C.5 736 0.673 5 17.067 0.23 50646.086 0.0 736 0. 0272 0.5 0.5 0.02388 1.176 0.03488 0.01880 0. the design drift and ductility demand are computed.00866 0.00342 0.415 0.931 0.00594 0.864 0. a value of 1.00594 0.476 0.0200 6 21.860 3 10.958 1 3.0180 1. thus. In this way.01432 0.264 0.0 0.0143 0. as the product of factor and (Pennucci et al.0200 0.552 0.000 0.03027 0.02198 0.0184 0.0163 1.0157 0.0225 0.12644 Storey Hi (m) · ·Vi/Vb 9 31.0130 0.673 0. as the purpose of this calculation is the determination of the equivalent viscous damping of the system.01148 0.777 14. Note that the upper storeys are not expected to yield and.0163 1.0225 0.5 0.554 0. In these cases.0180 1.0180 1.htm 11/12/2015 .0171 5 17.0198 0.02315 0.01709 0.DBDsoft Page 91 of 93 For each storey.025 0.461 0.0 0.5 0. which is equal to the elastic damping for all values of ductility demand equal to or smaller than 1. The whole frame’s ductility demand is computed as a weighted average of each storey’s ductility demand.0239 0.0 0.0 0.i/Vb 0. as shown in the following table. the ratio of the storey’s design drift to its yield drift is less than unity. The design storey file:///C:/Users/User/AppData/Local/Temp/~hh512C.15127 0.0.01148 0. it is appropriate to assume a 3% elastic damping. the response spectrum modification factor is computed in two steps.854 0.377 0. Equivalent viscous damping: Vi/Vb Vy.976 0.5 4 Total ·Vi/Vb For a steel frame.0211 0.702 0.00866 0.637 7 24.01968 0.785 0.0 0.0 is assigned to the ductility demand.977 0 0.778 0.01467 0.788 0.100 0.00342 8 28.922 2 7.651 0. [2011]): Modification factor for 5% elastic damping: Elastic damping correction factor: Modification factor for 5% elastic damping: Reduced spectral corner displacement: m System’s effective period: System’s required effective stiffness: kN/m Maximum base shear: kN Base shear (no P-Delta amplification accounted for yet): kN Calculation of the P-Delta stability coefficient for each storey: The vertical load at each storey is the product of the cumulative mass and the acceleration of gravity. 673 2798 0.. T. paper No.30 limit and.M.017 736 2944 0. Italy. F. Calvi G.5 0.i 9 31. Lausanne. Second European Conference on Earthquake Engineering and Seismology. 25 th-29th file:///C:/Users/User/AppData/Local/Temp/~hh512C. Calvi G. Como.013 736 736 0.206 124 4 14 0. Sullivan.370 0.911 As it can be observed. DBD09 – Draft Issued for Public Enquiry”. Istanbul Aug.5 0.239 102 3 10.J. Dazio A.J. therefore... P. the maximum P-Delta stability coefficient exceeds the 0. (2014) “Developing the Direct Displacement-Based Design Method for RC Strong Frame – Weak Wall Structures”.x/Vb Vdi θP-Δ VP-Δ. the software is set up to carry out the subsequent calculations anyway (and the process to obtain the additional base shear due to P-Delta considerations is actually the same).024 736 6624 1. but all decimal places have been carried throughout the calculations. References Previous Top References Beyer K. and Sullivan. T. 25.DBDsoft Page 92 of 93 shear is equal to the proportion of storey shear with respect to the base shear (Vi/Vb) and the base shear calculated above. Pinho R. T.276 79 2 7 0. editor (2003) “Displacement-Based Seismic Design of Reinforced Concrete Buildings” fib Bulletin No.014 736 1472 0.I. Mass (t) Vi. 71(12). for example).373 28 VP-Δ --> 1065.535 0. Pavia.415 1725 0. 80pages. From the table.J...023 736 5888 0. (1974) “Inelastic Response of Reinforced Concrete Structures to Earthquake Motions” ACI Journal. M.htm 11/12/2015 . the additional base shear is 1066 kN.778 3233 0.306 0. Research Report No.020 736 4416 0. if not all decimal places are used (with the aid of a spreadsheet. M. This explains small differences that the user can obtain when following the numbers by hand. Priestley.00. the structure might be at risk of suffering dynamic instability.976 4060 0. The design base shear is increased by the following quantity: For steel.264 1097 0.021 736 5152 0.. (2008) “Seismic Design of Torsionally Eccentric Buildings with RC U-shaped walls”.. (2011) “Development of computer software for Direct Displacement Based Design” Proceedings of Structural Engineering World Conference 2011.30 limit. and Sullivan.552 2294 0.084 0. C. Calvi G.120 179 7 24.148 162 6 21 0.162 0. 604-610.320 54 1 3. Gulkan. C = 1. IUSS Press.018 736 3680 0. Magni.5 0. It is recommended that the design maximum drift be reduced so that the maximum P-Delta stability coefficient does not exceed the 0.580 0. fib. ROSE 2008/03.864 3591 0.5 0. and Sozen. 192pp.N.430 0.J.176 144 5 17.236 0.73. The following table contains the corresponding calculations: Level hi (m) Δd. Nievas. Italy. Editors (2009) “A model code for the Displacement-Based Seismic Design of Structures. The final design base shear is: kN The final design overturning moment is : kNm NOTE: The result of each step of the procedure has been presented in a rounded format. However. IUSS Press..085 194 8 28 0.M.931 3869 0.000 4158 0.M.5 0.485 0.i θi Mass (t) Cum.016 736 2208 0. it. Silverstream. Pavia... Kowalsky. Amaris A. "Aspects of Drift and Ductility Capacity of Cantilever Structural Walls. A.. Editors (2012) “A model code for the Displacement-Based Seismic Design of Structures..N. No. T. Vol. G.M.. and Priestley.. M. 140-148.24. D.J. Priestley M. Priestley.J... 1-29 Pettinga.J. Sullivan. Paulay. J. Supplement 1. Sullivan. ASCE. Pennucci.N. (2012) “Towards a simplified Direct DBD procedure for the seismic design of moment resisting frames with viscous dampers” Engineering Structures. Priestley. Italy. file:///C:/Users/User/AppData/Local/Temp/~hh512C.J. Calvi. Vol.. J.” Bulletin of the New Zealand National Society for Earthquake Engineering.M. Pavia. No. pp1165-1171. Vol. G. and Lago. 154 pages. IUSS Press. Silverstream. Priestley. (2006) “Seismic design of frame-wall structures” Research Report ROSE2006/02. (1993). and Significance to Seismic Design” Bulletin of the New Zealand National Society for Earthquake Engineering.. n..J.3.J. A. M. T.N. M. Italy. IUSS Press.N. M. T.N.DBDsoft Page 93 of 93 2014. G. and Sozen. 31.D. M.J. and Calvi. IUSS press: www. Shibata.M. Engineering Structures..iusspress. “Myths and Fallacies in Earthquake Engineering – Conflicts Between Design and Reality” Bulletin NZ National Society for Earthquake Engineering. New Zealand National Society for Earthquake Engineering. N. (2005) “Dynamic Behaviour of Reinforced Concrete Frames Designed with Direct Displacement-Based Design” Report No. 328-341. Priestley M. 26. Calvi. M. Pavia. 720pages. ROSE 2005/02.M. "Brief Comments on Elastic Flexibility of Reinforced Concrete Frames. (1998).2. 105 pages. Sullivan.J. Vol.J.. IUSS Press. “The Displacement Capacity of Reinforced Concrete Coupled Walls”. 35 pp. 333pp Sullivan. (1998). Journal of Earthquake Engineering. Vol.J. 31. Italy.4. 95 pages. Kowalsky M.. Priestley. (1976) “Substitute Structure Method for Seismic Design in Reinforced Concrete” Journal Structural Division. DBD12”. Italy. ROSE Research Report 2002/01. [2011] “Displacement reduction factors for the design of medium and long-period structures”. Pavia.. 15.D. (2002) “Dynamic Amplification of Seismic Moments and Shear Forces in Cantilever Walls”. (2007) “Direct Displacement-Based Seismic Design” IUSS Press. M. G. Vol. J.htm 11/12/2015 . T. Priestley M. 102(12).N.J. pp. 3548-3566. (2002). New Zealand National Society for Earthquake Engineering. Calvi. T.N.J.