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

16 March 2011

2

• 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

16 March 2011

3

4

WO

OD

AR

ME

R B

AS

ICS

Mxy generates torsion/twist in the element

MXY, MX AND MY: CLOSER LOOK

16 March 2011

5

WO

OD

AR

ME

R B

AS

ICS

THE ORIGINS OF MXY

16 March 2011

• The equilibrium equation written for the foregoing plate element is - :

WO

OD

AR

ME

R B

AS

ICS

• 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

16 March 2011

6

WO

OD

AR

ME

R B

AS

ICS

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.)

16 March 2011

7

EX

CE

L S

PR

EA

DS

HE

ET

• The same signs as outputted by STAAD can be taken for the whole calculation provided face 1 and face 2 is identified.

SIGN CONVENTION

16 March 2011

8

• Johanssen’s Yield Criterion• The Wood Armer Equations

THEORETICAL BASIS OF WOOD ARMER APPROACH

16 March 2011

9

EX

CE

L S

PR

EA

DS

HE

ET

• 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

16 March 2011

10

EX

CE

L S

PR

EA

DS

HE

ET

• 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:

16 March 2011

11

EX

CE

L S

PR

EA

DS

HE

ET

• 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:

16 March 2011

12

EX

AM

PLE

S

• 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:

16 March 2011

13

The Base slab (highlighted) is taken for analysis

MH3 GEOMETRY

16 March 2011

14

MH3 BASE: SUMMARY SHEET

16 March 2011

15

Fig. Mx moments for the maximum load combination for Mx-moments

16 March 2011

16

Fig. My moments for the maximum load combination for My-moments

16 March 2011

17

16 March 2011

18

D1 index diagram- Exceedences seen at centre:

WA CALCULATION: MX_WA/MXMAX – FACE 1 = D1:

16 March 2011

19

D2 index diagram- Exceedences seen at one edge:

WA CALCULATION: MX_WA/MXMAX – FACE 2 = D2:

16 March 2011

20

D3 index diagram- Exceedences seen at centre:

WA CALCULATION: MY_WA/MYMAX – FACE 1 = D3:

16 March 2011

21

D4index diagram- No Exceedences

WA CALCULATION: MY_WA/MYMAX – FACE 2 = D4:

16 March 2011

22

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

16 March 2011

23

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

16 March 2011

24

• 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

16 March 2011

25

Fig. An example panel

CASE STUDY 2: CONT.

16 March 2011

26

EXAMPLE INDICES OF 3X6 FFF PANEL

16 March 2011

27

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

28

D1 D2

D3 D4

EXAMPLE INDICES OF 7X7 FFF PANEL

16 March 2011

29

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

16 March 2011

30

CO

NC

LUS

ION

S

• 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

31

The end

SAMPLE RUN

QUESTIONS….??

16 March 2011

32