observations in shear wall strength in tall buildings · 2012-03-29 · observations in shear wall...
TRANSCRIPT
![Page 1: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/1.jpg)
1
Observations in Shear Wall Strength in Tall Buildings
Presented by StructurePoint at ACI Spring 2012 Convention
in Dallas, Texas
![Page 2: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/2.jpg)
2
Metropolitan Tower, New York City
68-story, 716 ft (218m) skyscraper
Reinforced Concrete Design of Tall Buildings by Bungale
S. Taranath
![Page 3: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/3.jpg)
3
![Page 4: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/4.jpg)
4
![Page 5: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/5.jpg)
5
Jin Mao Tower, Shanghai, China
88-story, 1381 ft (421m)
![Page 6: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/6.jpg)
6
![Page 7: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/7.jpg)
7
![Page 8: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/8.jpg)
8
Motivation
Sharing insight from detailed analysis and implementation of code provisions
Sharing insight from members of ACI committees
Sharing insight from wide base of spColumn users
Raising awareness of irregularities and their impact on design
Conclusions apply to all sections, but especially those of irregular shape and loaded with large number of load cases and combinations, e.g. Shear Walls
![Page 9: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/9.jpg)
9
Outline
Observations
P-M Diagram Irregularities
Symmetry/Asymmetry
Strength Reduction Factor
Uniaxial/Biaxial Bending
Moment Magnification Irregularities
Conclusions
![Page 10: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/10.jpg)
10
P-M Diagram
Design
(Pu1
, Mu1
) NG
(Pu2
, Mu2
) OK
(Pu3
, Mu3
) NG
Notice Pu1 < Pu2 < Pu3
with Mu
=const
One Quadrant OK if
Pu
0 and Mu
0
Section shape symmetrical
Reinforcement symmetrical
z
x
y
PM
![Page 11: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/11.jpg)
11
P-M Diagram –
Pos./Neg. Load Signs
All four quadrants are needed if loads change sign
If section shape and reinforcement are symmetrical then M-
side is a mirror of M+ sideP (kip)
Mx (k-ft)
700
-200
180-18 0
(Pmax)(Pmax)
(Pmin)(Pmin)
1
2
3
4
5
6
7
8
9
10
![Page 12: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/12.jpg)
12
P-M Diagram –
Asymmetric Section
Each quadrant different
(Pu1
, Mu1
) NG
(Pu2
, Mu2
) OK
(Pu3
, Mu3
) OK
(Pu4
, Mu4
) NG
Notice:
Absolute value of moments same on both sides
Larger axial force favorable on M+ side but unfavorable on M-
side
P (kip)
Mx (k-ft)
40000
-10000
60000-400 00
(Pmax)(Pmax)
(Pmin)(Pmin)
12
34
x
Mx>0
y
Compressionx
Mx<0Compression
![Page 13: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/13.jpg)
13
P-M Diagram –
Asymmetric Steel
Skewed Diagram
Plastic Centroid ≠
Geometrical Centroid
(Concrete Centroid ≠
Steel Centroid)
(Pu1
, Mu1
) NG, (Pu2
, Mu2
) OK, (Pu3
, Mu3
) NG
|Mu1
| < |Mu2
| < |Mu3
| with Pu
= constP ( kN )
Mx ( kNm)
4500
-1500
450-45 0
(Pmax)(Pmax)
(Pmin)(Pmin)123
![Page 14: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/14.jpg)
14
P-M Diagram –
Factor
Strength reduction factor = (t
)
t
n
n
(c ) Pusually
( P )sometimes
Compression controlled
fy
Es
0.75 or 0.70.65
Spiral*
Other
0.005
Transition zone Tension Controlled
0.9
c
1 c
![Page 15: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/15.jpg)
15
P-M Diagram –
Factor
Usually
Sometimes
n(c ) ( P ) n(c ) ( P )
Sections with a narrow portion along height, e.g.: I, L, T, U, C-
shaped or irregular sections
![Page 16: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/16.jpg)
16
P-M Diagram –
Factor
(Pu1
, Mu1
) OK, (Pu2
, Mu2
) NG, (Pu3
, Mu3
) OK Mu1
< Mu2
< Mu3
with Pu
= const
![Page 17: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/17.jpg)
17
P-M Diagram –
Factor
(Pu1
, Mu1
) OK, (Pu2
, Mu2
) NG, (Pu3
, Mu3
) OK |Mu1
| < |Mu2
| < |Mu3
| with Pu
= const
![Page 18: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/18.jpg)
18
P-M Diagram –
Factor
(Pu1
, Mu1
) OK
(Pu2
, Mu2
) NG (Pu3
, Mu3
) OK Pu1
< Pu2
< Pu3
with Mu
= const
P (k ip)
Mx (k -ft)
60000
-10000
70000-70000
fs=0.5fy
fs=0
fs=0.5fy
fs=0
(Pmax)(Pmax)
(Pmin)(Pmin)
fs=0.5fy
fs=0
fs=0.5fy
fs=0
123
fs=0.5fy
fs 0
123
t
nn
(c )M or( M ) or
![Page 19: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/19.jpg)
19
Uniaxial/Biaxial –
Symmetric Case
3D failure surface with tips directly on the P axis
Uniaxial X = Biaxial P-Mx
with My = 0
Uniaxial Y = Biaxial P-My
with Mx
= 0
![Page 20: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/20.jpg)
20
Uniaxial/Biaxial –
Asymmetric case
Tips of 3D failure surface may be off the P axis
Uniaxial X means N.A. parallel to X axis but this produces Mx
≠
0 and My
≠
0
Uniaxial X may be different than Biaxial P-Mx
with My
= 0
c
1 c
![Page 21: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/21.jpg)
21
Uniaxial/Biaxial –
Asymmetric Case
![Page 22: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/22.jpg)
22
Moment Magnification –
Sway Frames
Magnification at column ends (Sway frames)
M2
= M2ns
+ s
M2s
If sign(M2ns
) = -sign(M2s
) then the magnified moment, M2
, is smaller than first order moment (M2ns
+M2s
) or it can even change sign, e.g.:
M2ns
= 16 k-ft, M2s
= -10.0 k-ft,
= 1.2
M2
= 16 + 1.2 (-10.0) = 4.0 k-ft (M2ns
+M2s
) = 6.0 k-ft
M2ns
= 16 k-ft, M2s
= -14.4 k-ft,
= 1.2
M2
= 16 + 1.2 (-14.4) = -1.28 k-ft
(M2ns
+M2s
) = 1.6 k-ft
First-order moment may govern the design rather than second order-moment
![Page 23: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/23.jpg)
23
Moment Magnification –
Sway Frames
Since ACI 318-08 moments in compression members in sway frames are magnified both at ends and along length
Prior to ACI 318-08 magnification along length applied only if
u
u'c g
35r P
f A
l
![Page 24: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/24.jpg)
24
Moment Magnification –
M1
M1
may govern the design rather than M2
even though |M2
| > |M1
| and ACI 318, 10.10.6 provision stipulates that compression members shall be designed for Mc
= M2
. Consider:
Double curvature bending (M1
/M2
< 0)
Asymmetric Section
M2
OK but M1 NG
M
P
M2M1 M2M1
![Page 25: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/25.jpg)
25
Moment Magnification –
M2nd/M1st
ACI 318-11, 10.10.2.1 limits ratio of second-order moment to first-order moments
M2nd/M1st < 1.4
What if ratio is negative, e.g.:
M1st
= Mns
+ Ms
= 10.0 + (-9.0) = 1.0 k-ft
M2nd = (Mns
+ s
Ms
) = 1.05 (10.0+1.3(-9.0)) = -1.78 k-ft
M2nd/M1st
= -1.78 OK or NG ?
Check |M2nd/M1st|= 1.78 > 1.4 NG
![Page 26: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/26.jpg)
26
Moment Magnification –
M2nd/M1st
What if M1st
is very small, i.e. M1st < Mmin
, e.g.:
M1st
= M2
= 0.1 k-ft (Nonsway frame)
Mmin
= Pu
(0.6 +0.03h) = 5 k-ft
M2nd = Mc
= Mmin
= 1.1*5 = 5.5 k-ft
M2nd/M1st
= 5.5/0.1 = 55 OK or NG ?
Check M2nd/Mmin
= 1.1 OK
![Page 27: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/27.jpg)
27
Conclusions
Summary
Irregular shapes of sections and reinforcement patterns lead to irregular and distorted interaction diagrams
Large number of load cases and load combinations lead to large number of load points potentially covering entire (P, Mx
, My
) space
Intuition may overlook unusual conditions in tall structures
![Page 28: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/28.jpg)
28
Conclusions
Recommendations
Do not eliminate load cases and combinations based on intuition
Run biaxial rather than uniaxial analysis for asymmetric sections
Run both 1st order and 2nd
order analysis
Apply engineering judgment rather than following general code provisions literally
Use reliable software and verify its results
![Page 29: Observations in Shear Wall Strength in Tall Buildings · 2012-03-29 · Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint ... Observations P-M Diagram](https://reader034.vdocuments.mx/reader034/viewer/2022042118/5e97a0083ea705614431fbc0/html5/thumbnails/29.jpg)
29