observation sins hear wall strength in tall buildings

8/13/2019 Observation Sins Hear Wall Strength in Tall Buildings

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Observations in Shear Wall

Strength in Tall Buildings

Presented by StructurePoint

at ACI Spring 2012 Convention in Dallas, Texas


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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


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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 impacton design

Conclusions apply to all sections, but especially

those of irregular shape and loaded with largenumber 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

0

Section shapesymmetrical

Reinforcementsymmetrical

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

18018 0

(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 ofmoments same onboth sides

Larger axial forcefavorable on M+ sidebut unfavorable onM-

side

P (kip)

Mx (k-ft)

40000

-10000

6000040000

(Pmax)(Pmax)

(Pmin)(Pmin)

12

34

x

Mx>0

y

Compressionx

Mx


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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

= constP ( kN)

Mx ( kNm)

4500

-1500

45045 0

(Pmax)(Pmax)

(Pmin)(Pmin)

123


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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 0.70.65

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 portionalong 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

) OKMu1

< 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

7000070000

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

123

t

n

n

(c )M or

( M ) or


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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 beoff the P axis

Uniaxial X means N.A. parallel toX axis but this produces Mx

0

and My

0

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 thansecond order-moment


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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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M

1

M1

may govern thedesign rather than M2

even though |M2

| > |M1

|

and ACI 318, 10.10.6provision stipulates thatcompression membersshall be designed forMc

= M2

. Consider:

Double curvature

bending (M1

/M2

< 0)

Asymmetric Section

M2

OK but

M1 NG

M

P

M2M1 M2M1


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M2nd/M1st

ACI 318-11, 10.10.2.1 limits ratio of second-ordermoment 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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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 reinforcementpatterns lead to irregular and distortedinteraction diagrams

Large number of load cases and loadcombinations lead to large number of load pointspotentially covering entire (P, Mx

, My

) space

Intuition may overlook unusual conditions in tallstructures


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Conclusions

Recommendations

Do not eliminate load cases and combinationsbased 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


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observation sins hear wall strength in tall buildings

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