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Describes ways of accouting for twisiting moment in designinig a slab
Citation preview
May
201
2
NIMISH PRABHUKHANOLKAR
DESIGN FOR TWISTING MOMENT IN SLAB PANELS USING WOOD ARMER METHODOLOGY
• 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
AGENDA
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• 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.
BACKGROUND
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Mxy generates torsion/twist in the element
MXY, MX AND MY: CLOSER LOOK
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THE ORIGINS OF MXY
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• The equilibrium equation written for the foregoing plate element is - :
WO
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• Bottom Reinforcement(M is +ve for tension at bottom – or equivalently Face 1)
• Mx* = Mx + |Mxy|; My*=My+|Mxy|• If either Mx* or My* is found to be negative, it is changed to
zero and My* or Mx* is adjusted.• For eg if Mx* <0 then• My* = My+|Mxy2/Mx| and Mx* is set to zero. and vice versa• In doing so, if My* is negative, no bott. reinf’t required
• If both Mx* and My* are negative, then no bottom reinforcement is required.
WOOD ARMER EQUATIONS
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Top Reinforcement(M is -ve for tension at top or equivalently Face 2):
• Mx* = Mx - |Mxy|; My*=My - |Mxy|• If either Mx* or My* is found to be positive, it is changed to
zero and My* or Mx* is adjusted.• For e.g. if Mx* >0 then• My* = My-|Mxy2/Mx| and Mx* is set to zero.• In doing this, if My* is positive, no top reinf’t required
• If both Mx* and My* are negative, then no bottom reinforcement is required.
WOOD ARMER EQUATIONS(CONT.)
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• The same signs as outputted by STAAD can be taken for the whole calculation provided face 1 and face 2 is identified.
SIGN CONVENTION
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• Johanssen’s Yield Criterion• The Wood Armer Equations
THEORETICAL BASIS OF WOOD ARMER APPROACH
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• 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.
• The output is in terms of Indices, which are directly useful to the designer (introduced ahead)
METHODOLOGY FOR SOLVING THE MXY PROBLEM
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• The Spreadsheet takes the STAAD Forces Data, 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
• 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, in that direction, on that face.
• Note that the Spreadsheet plot may be a mirror of your actual STAAD Plot.
SPREADSHEET WORKFLOW:
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• The results of the spreadsheet should be easily usable to the Design Engineer, with constrains of time for quick design and decisions , and also lend themselves to quick interpretation of the effects of Mxy.
• Hence an index was used which stands for the ratio of the Wood Armer Moment at a plate element, in X/Y direction , divided by the maximum Non-Wood Armer moment encountered ANYWHERE in the panel.
• This enables us to think in the following way – If the index is X at a plate, then the actual design moment including Wood Armer is X times the STAAD summary moment corresponding to that face.
• If X>1.03, it is displayed in RED in the plot, liable for further corrective action
SPREADSHEET RESULTS:
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• Case-Study 1: MH3 - 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
CASE STUDIES:
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The Base slab (highlighted) is taken for analysis
MH3 GEOMETRY
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MH3 BASE: SUMMARY SHEET
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Fig. Mx moments for the maximum load combination for Mx-moments
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Fig. My moments for the maximum load combination for My-moments
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D1 index diagram- Exceedences seen at centre:
WA CALCULATION: MX_WA/MXMAX – FACE 1 = D1:
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D2 index diagram- Exceedences seen at one edge:
WA CALCULATION: MX_WA/MXMAX – FACE 2 = D2:
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D3 index diagram- Exceedences seen at centre:
WA CALCULATION: MY_WA/MYMAX – FACE 1 = D3:
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D4index diagram- No Exceedences
WA CALCULATION: MY_WA/MYMAX – FACE 2 = D4:
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Table. 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
WOOD ARMER FROM STAAD SUMMARY VERSUS SPREADSHEET CALCULATIONS
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Face 1 Face 2
STAAD Summary
Spreadsheet STAAD Summary
Spreadsheet
Mx* 71.197 71.302 -99.404 -99.607
My* 88.96kN 89.146 -106.8 -107.121
• 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)
CASE STUDY 1: CONCLUSIONS
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• 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 3X3,3X6,5X5,7X7,9X9,7X12.
• For the 3X6 and 5X5: 4 boundary conditions were considered for each panel size – Fixed on 3 sides, Fixed on 2 sides, Pinned on 3 sides , Pinned on 2 sides
• For the 7X7, 9X9, 7X12 panels only Fixed on 3 sides considered
CASE STUDY 2: REGULAR PANELS
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Fig. An example panel
CASE STUDY 2: CONT.
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EXAMPLE INDICES OF 3X6 FFF PANEL
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D1 D2
D3 D4
Evaluation and SummaryActions Face 1 Face 2 UnitsMaximum Moment Mx(Wood Armer) 7.43 -13.276kN.mMaximum Moment My(Wood Armer) 5.646 -14.663kN.mMaximum Moment Mx( Non-Wood Armer) 7.007 -12.966kN.m Maximum Moment My( Non-Wood Armer) 3.973 -14.394kN.m 1.060368203 1.023908684kN.m 1.421092374 1.018688342kN.m
EXAMPLE INDICES OF 5X5 FFF PANEL16 March 2011
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D1 D2
D3 D4
EXAMPLE INDICES OF 7X7 FFF PANEL
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D1 D2
D3 D4
• Link to tabular file for results • For a panel of the same size and load, the magnitude of the
twisting moment effect would be highest for pinned-pinned condition, and lowest for fixed-fixed-fixed condition
• Even for small panel sizes, the pinned on two sides panels were considerably affected by twisting moments
• Generally, it is seen that exceedence of moments from maximum non-Wood Armer moment is of the order of 20-30%.
• For larger panel sizes, even for fixed on 3 sides, at least one direction was affected by twisting moments. (D3 direction)
CASE STUDY 2: RESULTS AND CONCLUSIONS
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• 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.
• The highest Indices as noticed in the study were of the order of 20-30%, pointing to Wood Armer moment being 1.2-1.3 times higher than the otherwise maximum out of plane bending Mx or My
• Engineers should be especially alert for Mxy in case they are thinking of curtailing reinforcement.
• Spreadsheet can be used for an accurate assessment of effect of Mxy moments to take design decisions in problem areas.
GENERAL CONCLUSIONS16 March 2011
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The end
SAMPLE RUN
QUESTIONS….??
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