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Metropolitan Tower, New York City
68-story, 716 ft (218m) skyscraper
Reinforced Concrete Design of Tall Buildings by Bungale
- S. Taranath
Observations in Shear Wall Strength in Tall Buildings Presented by - - PowerPoint PPT Presentation
Observations in Shear Wall Strength in Tall Buildings Presented by - - PowerPoint PPT Presentation
Observations in Shear Wall Strength in Tall Buildings Presented by StructurePoint at ACI Spring 2012 Convention in Dallas, Texas 1 Metropolitan Tower, New York City 68-story, 716 ft (218m) skyscraper Reinforced Concrete Design of Tall
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Jin Mao Tower, Shanghai, China
88-story, 1381 ft (421m)
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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
- n 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
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Outline
Observations
P-M Diagram Irregularities
Symmetry/Asymmetry
Strength Reduction Factor
Uniaxial/Biaxial Bending
Moment Magnification Irregularities
Conclusions
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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
Section shape symmetrical
Reinforcement symmetrical
z x y P M
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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+ side
P (kip) Mx (k-ft) 700
- 200
180
- 180
(Pmax) (Pmax) (Pmin) (Pmin) 1 2 3 4 5 6 7 8 9 10
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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
- 40000
(Pmax) (Pmax) (Pmin) (Pmin) 1 2 3 4
x
Mx>0
y
Compression
x
Mx<0 Compression
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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 = const
P ( kN ) Mx ( kNm) 4500
- 1500
450
- 450
(Pmax) (Pmax) (Pmin) (Pmin) 1 2 3
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P-M Diagram – Factor
Strength reduction factor = (t )
t n n
(c ) P usually ( P ) sometimes
Compression controlled fy Es 0.75 or 0.7 0.65 Spiral* Other 0.005 Transition zone Tension Controlled 0.9
c
1 c
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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
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P-M Diagram – Factor
(Pu1 , Mu1 ) OK, (Pu2 , Mu2 ) NG, (Pu3 , Mu3 ) OK Mu1 < Mu2 < Mu3 with Pu = const
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P-M Diagram – Factor
(Pu1 , Mu1 ) OK, (Pu2 , Mu2 ) NG, (Pu3 , Mu3 ) OK |Mu1 | < |Mu2 | < |Mu3 | with Pu = const
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P-M Diagram – Factor
(Pu1 , Mu1 ) OK (Pu2 , Mu2 ) NG (Pu3 , Mu3 ) OK Pu1 < Pu2 < Pu3 with Mu = const
P (kip) 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 1 2 3
fs=0.5fy fs 0 1 2 3
t n n
(c ) M
- r
( M )
- r
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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
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Uniaxial/Biaxial – Asymmetric case
Tips of 3D failure surface may be
- ff the P axis
Uniaxial X means N.A. parallel to X axis but this produces Mx ≠ and My ≠
Uniaxial X may be different than Biaxial P-Mx with My = 0
c
1 c
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Uniaxial/Biaxial – Asymmetric Case
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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
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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
35 r P f A l
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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
M2 M1 M2 M1
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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
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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
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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
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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
- rder analysis
Apply engineering judgment rather than following general code provisions literally
Use reliable software and verify its results
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