2 1 0 2 y a M
DESIGN FOR TWISTING MOMENT IN SLAB PANELS USING WOOD ARMER METHODOLOGY NIMISH PRABHUKHANOLKAR
16 March 2011
AGENDA •
Background
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Mx, My, Mxy: A Closer Look
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The Wood Armer Equations
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Sign Convention
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Fundamentals of the Approach
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Spreadsheet formulation
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Case-Study 1: MH3 Inlet Manhole Old Whittington
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Case-Study 2: Regular Panel Study
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General Conclusions
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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
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16 March 2011
BACKGROUND •
QC Comment from Client on a Project to consider Mxy
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Objective of the study was the understand the impact of Mxy on the designs as they stand currently and establish a way forward
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Hence it is required to create a platform wherein the design can accommodate Mxy as well, subject to constraints of time and effort.
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MXY, MX AND MY: CLOSER LOOK
S C I S A B R E M R A D O O W
Mxy generates torsion/twist in the element
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THE ORIGINS OF MXY •
The equilibrium equation written for the foregoing plate element is - :
S C I S A B R E M R A D O O W
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WOOD ARMER EQUATIONS
S C I S A B R E M R A D O O W
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Bottom Reinforcement(M is +ve for tension at bottom – or equivalently Face 1)
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Mx* = Mx + |Mxy|; My*=My+|Mxy|
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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
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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
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If both Mx* and My* are negative, then no bottom reinforcement is required. 6
16 March 2011
WOOD ARMER EQUATIONS(CONT.) Top Reinforcement(M is -ve for tension at top or equivalently Face 2):
S C I S A B R E M R A D O O W
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Mx* = Mx - |Mxy|; My*=My - |Mxy|
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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
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My* = My-|Mxy2/Mx| and Mx* is set to zero. In doing this, if My* is positive, no top reinf’t required
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If both Mx* and My* are negative, then no bottom reinforcement is required. 7
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.
T E E H S D A E R P S L E C X E
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THEORETICAL BASIS OF WOOD ARMER APPROACH • Johanssen’s Yield •
Criterion
The Wood Armer Equations
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16 March 2011
METHODOLOGY FOR SOLVING THE MXY PROBLEM
T E E H S D A E R P S L E C X E
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A Spreadsheet tool was prepared for automating the process of getting Wood Armer moments for all area elements in model
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The Spreadsheet calculates and finally gives a graphical output of the calculation.
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The output is in terms of Indices, which are directly useful to the designer (introduced ahead)
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16 March 2011
SPREADSHEET WORKFLOW:
T E E H S D A E R P S L E C X E
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The Spreadsheet takes the STAAD Forces Data, Node and Plate Geometry data as input
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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
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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.
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Note that the Spreadsheet plot may be a mirror of your actual STAAD Plot. 11
16 March 2011
SPREADSHEET RESULTS:
T E E H S D A E R P S L E C X E
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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.
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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 NonWood Armer moment encountered ANYWHERE in the panel.
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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.
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If X>1.03, it is displayed in RED in the plot, liable for further corrective action 12
16 March 2011
CASE STUDIES: •
Case-Study 1: MH3 - Inlet Manhole for Old Whittington Project
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Case Study 2: Example analysis was done for many regular panel geometries and also applying it to some complex real project geometries
S E L P M A X E
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MH3 GEOMETRY
The Base slab (highlighted) is taken for analysis
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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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WA CALCULATION: MX_WA/MXMAX – FACE 1 = D1:
D1 index diagram- Exceedences seen at centre:
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WA CALCULATION: MX_WA/MXMAX – FACE 2 = D2:
D2 index diagram- Exceedences seen at one edge:
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16 March 2011
WA CALCULATION: MY_WA/MYMAX – FACE 1 = D3:
D3 index diagram- Exceedences seen at centre:
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WA CALCULATION: MY_WA/MYMAX – FACE 2 = D4:
D4index diagram- No Exceedences 22
16 March 2011
WOOD ARMER FROM STAAD SUMMARY VERSUS SPREADSHEET CALCULATIONS
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
Table. Comparison of Wood Armer calculations using the summary versus the spreadsheet The values stand for the design values after considering the twisting moment
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The above table shows that spreadsheet WA moments can be more than summary Wood Armer moments
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16 March 2011
CASE STUDY 1: CONCLUSIONS •
Mxy effect was considerable along both directions at the mid-span
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Summary sheet was not enough to get the maximum design values, the actual maximums exceeded the summary table values by a small margin
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Spreadsheet tool can be used to identify problem areas and check those areas for the higher demand, and reinforce accordingly (possibly give additional steel)
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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
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The panel sizes considered were 3X3,3X6,5X5,7X7,9X9,7X12.
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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
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For the 7X7, 9X9, 7X12 panels only Fixed on 3 sides considered
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CASE STUDY 2: CONT.
Fig. An example panel 26
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EXAMPLE INDICES OF 3X6 FFF PANEL
D1
D2
D3
D4
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 7.43 5.646 7.007 3.973
Units -13.276 kN.m -14.663 kN.m -12.966 kN.m -14.394 kN.m kN.m
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EXAMPLE INDICES OF 5X5 FFF PANEL
D1
D2
D3
D4
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EXAMPLE INDICES OF 7X7 FFF PANEL
D1
D2
D3
D4
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CASE STUDY 2: RESULTS AND CONCLUSIONS •
Link to tabular file for results
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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
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Even for small panel sizes, the pinned on two sides panels were considerably affected by twisting moments
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Generally, it is seen that exceedence of moments from maximum non-Wood Armer moment is of the order of 2030%.
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For larger panel sizes, even for fixed on 3 sides, at least one direction was affected by twisting moments. (D3 direction) 30
16 March 2011
GENERAL CONCLUSIONS
S N O I S U L C N O C
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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.
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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
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Engineers should be especially alert for Mxy in case they are thinking of curtailing reinforcement.
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Spreadsheet can be used for an accurate assessment of effect of Mxy moments to take design decisions in problem areas
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SAMPLE RUN
QUESTIONS….??
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