May 2012DESIGN FOR TWISTING MOMENT IN SLAB PANELS USING WOOD ARMER METHODOLOGY NIMISH PRABHUKHANOLKAR 16 March 2011 AGENDA • Background • Mx, My, Mxy: A Closer Look • The Wood Armer Equations • Sign Convention • Fundamentals of the Approach • Spreadsheet formulation • Case-Study 1: MH3 Inlet Manhole Old Whittington • Case-Study 2: Regular Panel Study • General Conclusions 2 16 March 2011 BACKGROUND • QC Comment from Client on a Project to consider Mxy • Objective of the study was the understand the impact of Mxy on the designs as they stand currently and establish a way forward • Hence it is required to create a platform wherein the design can accommodate Mxy as well, subject to constraints of time and effort. 3 16 March 2011 MXY. MX AND MY: CLOSER LOOK WOOD ARMER BASICS Mxy generates torsion/twist in the element 4 . : WOOD ARMER BASICS 5 .16 March 2011 THE ORIGINS OF MXY • The equilibrium equation written for the foregoing plate element is . 16 March 2011 WOOD ARMER EQUATIONS • Bottom Reinforcement(M is +ve for tension at bottom – or equivalently Face 1) • Mx* = Mx + |Mxy|. no bott. My*=My+|Mxy| WOOD ARMER BASICS • If either Mx* or My* is found to be negative. • For eg if Mx* <0 then • My* = My+|Mxy2/Mx| and Mx* is set to zero. then no bottom reinforcement is required. reinf’t required • If both Mx* and My* are negative. and vice versa • In doing so. 6 . if My* is negative. it is changed to zero and My* or Mx* is adjusted. 7 . it is changed to zero and My* or Mx* is adjusted. if My* is positive.g. • In doing this.|Mxy| • If either Mx* or My* is found to be positive.16 March 2011 WOOD ARMER EQUATIONS(CONT. My*=My . no top reinf’t required • If both Mx* and My* are negative.|Mxy|. WOOD ARMER BASICS • For e. then no bottom reinforcement is required. if Mx* >0 then • My* = My-|Mxy2/Mx| and Mx* is set to zero.) Top Reinforcement(M is -ve for tension at top or equivalently Face 2): • Mx* = Mx . 16 March 2011 SIGN CONVENTION • The same signs as outputted by STAAD can be taken for the whole calculation provided face 1 and face 2 is identified. EXCEL SPREADSHEET 8 . 16 March 2011 THEORETICAL BASIS OF WOOD ARMER APPROACH • Johanssen’s Yield Criterion • The Wood Armer Equations 9 . 16 March 2011 METHODOLOGY FOR SOLVING THE MXY PROBLEM • A Spreadsheet tool was prepared for automating the process of getting Wood Armer moments for all area elements in model • The Spreadsheet calculates and finally gives a graphical output of the calculation. EXCEL SPREADSHEET • The output is in terms of Indices. which are directly useful to the designer (introduced ahead) 10 . 11 . • Note that the Spreadsheet plot may be a mirror of your actual STAAD Plot.16 March 2011 SPREADSHEET WORKFLOW: • The Spreadsheet takes the STAAD Forces Data. in that direction. on that face. Node and Plate Geometry data as input • It calculates the Wood Armer moments for each plate for each load combination input and compares against the maximum NON Wood Armer Moments in each direction per face EXCEL SPREADSHEET • The final output is a graphical display of MAXIMUM Wood Armer moment of a plate divided by the maximum Non Wood Armer Moment for the whole panel. • If X>1. • Hence an index was used which stands for the ratio of the Wood Armer Moment at a plate element. then the actual design moment including Wood Armer is X times the STAAD summary moment corresponding to that face. and also lend themselves to quick interpretation of the effects of Mxy.03. it is displayed in RED in the plot. divided by the maximum NonWood Armer moment encountered ANYWHERE in the panel. EXCEL SPREADSHEET • This enables us to think in the following way – If the index is X at a plate. liable for further corrective action 12 . with constrains of time for quick design and decisions . in X/Y direction .16 March 2011 SPREADSHEET RESULTS: • The results of the spreadsheet should be easily usable to the Design Engineer. Inlet Manhole for Old Whittington Project • Case Study 2: Example analysis was done for many regular panel geometries and also applying it to some complex real project geometries EXAMPLES 13 .16 March 2011 CASE STUDIES: • Case-Study 1: MH3 . 16 March 2011 MH3 GEOMETRY The Base slab (highlighted) is taken for analysis 14 . 16 March 2011 MH3 BASE: SUMMARY SHEET 15 . Mx moments for the maximum load combination for Mx-moments 16 .16 March 2011 Fig. 16 March 2011 Fig. My moments for the maximum load combination for My-moments 17 . 16 March 2011 18 . Exceedences seen at centre: 19 .16 March 2011 WA CALCULATION: MX_WA/MXMAX – FACE 1 = D1: D1 index diagram. Exceedences seen at one edge: 20 .16 March 2011 WA CALCULATION: MX_WA/MXMAX – FACE 2 = D2: D2 index diagram. 16 March 2011 WA CALCULATION: MY_WA/MYMAX – FACE 1 = D3: D3 index diagram.Exceedences seen at centre: 21 . No Exceedences 22 .16 March 2011 WA CALCULATION: MY_WA/MYMAX – FACE 2 = D4: D4index diagram. 404 -106. Comparison of Wood Armer calculations using the summary versus the spreadsheet The values stand for the design values after considering the twisting moment • The above table shows that spreadsheet WA moments can be more than summary Wood Armer moments 23 .8 Face 2 Spreadsheet -99.96kN Spreadsheet 71.607 -107.121 Table.146 STAAD Summary -99.302 89.16 March 2011 WOOD ARMER FROM STAAD SUMMARY VERSUS SPREADSHEET CALCULATIONS Face 1 STAAD Summary Mx* My* 71.197 88. 16 March 2011 CASE STUDY 1: CONCLUSIONS • Mxy effect was considerable along both directions at the mid-span • Summary sheet was not enough to get the maximum design values. the actual maximums exceeded the summary table values by a small margin • Spreadsheet tool can be used to identify problem areas and check those areas for the higher demand. and reinforce accordingly (possibly give additional steel) 24 . Pinned on 2 sides • For the 7X7.7X7.3X6.5X5. 7X12 panels only Fixed on 3 sides considered 25 . Pinned on 3 sides . 9X9.7X12.16 March 2011 CASE STUDY 2: REGULAR PANELS • To get a general idea of twisting behavior. some regular panels of representative sizes were applied a hydrostatic load and evaluated by the spreadsheet • The panel sizes considered were 3X3.9X9. • For the 3X6 and 5X5: 4 boundary conditions were considered for each panel size – Fixed on 3 sides. Fixed on 2 sides. An example panel 26 .16 March 2011 CASE STUDY 2: CONT. Fig. 973 1.018688342kN.m -14.023908684kN.m -14.060368203 1.m -12.421092374 D4 Units -13.966kN.394kN.16 March 2011 EXAMPLE INDICES OF 3X6 FFF PANEL D1 D2 D3 Actions Maximum Moment Mx(Wood Armer) Maximum Moment My(Wood Armer) Maximum Moment Mx( Non-Wood Armer) Maximum Moment My( Non-Wood Armer) Evaluation and Summary Face 1 Face 2 7.276kN.663kN.m 1.m 27 .007 3.646 7.m 1.43 5. 16 March 2011 EXAMPLE INDICES OF 5X5 FFF PANEL D1 D2 D3 D4 28 . 16 March 2011 EXAMPLE INDICES OF 7X7 FFF PANEL D1 D2 D3 D4 29 . the pinned on two sides panels were considerably affected by twisting moments • Generally.16 March 2011 CASE STUDY 2: RESULTS AND CONCLUSIONS • Link to tabular file for results • For a panel of the same size and load. • For larger panel sizes. (D3 direction) 30 . at least one direction was affected by twisting moments. the magnitude of the twisting moment effect would be highest for pinned-pinned condition. even for fixed on 3 sides. and lowest for fixed-fixed-fixed condition • Even for small panel sizes. it is seen that exceedence of moments from maximum non-Wood Armer moment is of the order of 2030%. 3 times higher than the otherwise maximum out of plane bending Mx or My CONCLUSIONS • Engineers should be especially alert for Mxy in case they are thinking of curtailing reinforcement. 31 .16 March 2011 GENERAL CONCLUSIONS • It is found that Mxy moments have a considerable effect atleast in ONE direction for most geometries. Hence it would be prudent to have a brief look at Mxy design in all cases. • Spreadsheet can be used for an accurate assessment of effect of Mxy moments to take design decisions in problem areas. pointing to Wood Armer moment being 1.2-1. • The highest Indices as noticed in the study were of the order of 20-30%. ?? The end 32 .16 March 2011 SAMPLE RUN QUESTIONS….