seaot 10-09w vs s.ppt topics • asce 7 – simplified wind provisions • asce 7 – seismic...

11/5/2009

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Designing for Wind/Seismic

SEAoT State Conference2009

Austin, Texas


Wind Versus SeismicWhich Controls?

byLarry Griffis P.E.

Walter P. Moore and Associates, Inc.


Seminar Topics

• ASCE 7 – Simplified Wind Provisions• ASCE 7 – Seismic Provisions: ELF Method

– Equivalent Lateral Force Procedure• Controlling Wind and Seismic Torsion• Other Design Tips• Preliminary design example for wind and

seismic loads


The Code


The Challenge East Coast Engineers

• 2006 IBC invokes seismic design all across US – not just western US

• Seismic design impacts many more designs than in previous codes

• Engineers need to know early in design:“Does wind or seismic control the design”


Early knowledge needed….

• Selection of proper structural system• Architectural planning for structural system• Budgeting for structural costs• Fast-track structural delivery

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Wind versus Seismic Behavior

VE

Fully Yielded StrengthVy

Vs

Ds DE

Elastic Response

Design Force Level

Rd

RΩ

ο

First Significant Yield

Cd

Late

ral L

oad

Drift


Seismic Requirements


ASCE 7 Seismic Map


Spectral AccelerationsSS, S1 (SDS, SD1)

• USGS web site:

• Latitude / Longitude

http://earthquake.usgs.gov/research/hazmaps/design/

http://www.travelgis.com/geocode/


Importance Factor I


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Site Soil ConditionsStrong Influence on Seismic Design


Site Coefficients Fa, Fv


Design Spectral AccelerationsSDS, SD1


Fundamental Period T


Fundamental Period T

T ≤ Cu Ta


Base Shear (V)Seismic Design

or Cs = 0.044SDS I

ASCE 7-05 addendum

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Response Modification CoefficientR

Seismic Design Category RestrictionsSystem Category R Ωo Cd A B C D E F

Concrete:1 Shear Wall Frame Interaction SW/Frame Interaction 4 1/2 2 1/2 4 NL NL NP NP NP NP

(Ord SW + Ord MF)2 Ordinary Shear Wall Building Frame System 5 2 1/2 4 1/2 NL NL NL NP NP NP3 Ordinary Shear Wall + IMF Dual System 5 1/2 2 1/2 4 1/2 NL NL NL NP NP NP4 Ordinary Shear Wall + SMF Dual System 6 2 1/2 5 NL NL NL NP NP NP5 Special Shear Wall + Int MF Dual System 6 1/2 2 1/2 5 NL NL NL 160 / 240 100 / 160 1006 Special Shear Wall + SMF Dual System 7 2 1/2 5 1/2 NL NL NL NL NL NL7 Special Moment Frame Moment Frame 8 3 5 1/2 NL NL NL NL NL NL

Concrete Systems


Response Modification CoefficientR

Steel:1 Steel Systems w/o Seismic Steel Sys w/o Seismic 3 3 3 NL NL NL NP NP NP2 Ord Steel Conc Braced Frame Building Frame System 3 1/4 2 3 1/4 NL NL NL 35 / 60 35 / 60 NP / 603 Ord Moment Frame Moment Frame System 3 1/2 3 3 NL NL NL NP / 65 NP / 65 NP / 654 Int Moment Frame Moment Frame System 4 1/2 3 4 NL NL NL 35 / 65 NP / 65 NP / 655 Sp Steel Conc Braced Frame Building Frame System 6 2 5 NL NL NL 160 160 1005 Sp Steel Conc Br Frame + IMF Dual System 6 2 1/2 5 NL NL NL 35 / 65 NP / 65 NP / 656 Sp Steel Plate Shear Wall Building Frame System 7 2 6 NL NL NL 160 160 1006 Buckling Restr Braced Frame Building Frame System 7 2 5 1/2 NL NL NL 160 160 100

(w/o MC)6 Steel Ecc Braced Frame Building Frame System 7 2 4 NL NL NL 160 160 100

(w/o MC)6 Special Truss MF Moment Frame 7 3 5 1/2 NL NL NL 160 100 NP6 Sp Stl Conc Br Frame + SMF Dual System 7 2 1/2 5 1/2 NL NL NL NL NL NL7 Buckling Restr Braced Frame Building Frame System 8 2 1/2 5 NL NL NL 160 160 100

(w/ MC)7 Steel Ecc Braced Frame Building Frame System 8 2 4 NL NL NL 160 160 100

(w/ MC)7 Special Steel Moment Frame Moment Frame System 8 3 5 1/2 NL NL NL NL NL NL7 Buckling Restr Br Frame + SMF Dual System 8 2 1/2 5 NL NL NL NL NL NL7 Steel Ecc Braced Frame + SMF Dual System 8 2 1/2 4 NL NL NL NL NL NL7 Sp Steel Plate Shear Wall + SMF Dual System 8 2 1/2 6 1/2 NL NL NL NL NL NL

Steel Systems


Building WeightW vs No. Floors

Building Density

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80

No. Floors

Bld

g. D

ensi

ty (p

cf)

Concrete

Steel

Building Wt. (pcf)No. Floors Stl Conc

2 6 1210 6.375 1320 7.125 14.2540 9 17.560 12 2280 16 28


Period FormulasWind and Seismic

0

1

2

3

4

5

6

7

8

9

10

0 200 400 600 800 1000 1200 1400

Building Ht. h (ft.)

Per

iod

T (s

ec)T=h/75 h/100 h/150

T=h / 75h < 300 ft.

T=0.232h0.5

h > 300 ft.

T=0.028h0.8

MF Conc.

T=0.016h0.9

MF Steel.

EBF Steel

All other


Distribution of Base ShearFx

Fx


Seismic Force DiagramSeismic Force Fx

0

10

20

30

40

50

60

70

80

90

100

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 1.100 1.200 1.300 1.400

Fx

Hei

ght h

k=1 k=1.25 k=1.5 k=1.75 k=2.0

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Seismic Shear DiagramStory V

0

10

20

30

40

50

60

70

80

90

100

0.00 1.00 2.00 3.00 4.00 5.00

Story Shear

Bui

ldin

g H

eigh

t h

k = 1.0

k = 2.0


Seismic Moment DiagramOverturning Moment

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500

Overturning Moment

Bui

ldin

g H

eigh

t h

k = 1.0k = 2.0


Cvx versus kCvx vs k

0

10

20

30

40

50

60

70

80

90

100

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26

Cvx

% B

uild

ing

Hei

ght h

k=1 k=1.25 k=1.5 k=1.75 k=2

M = V x jhjh

V


Calculation Base M from Vk vs M arm

0.7

0.71

0.72

0.73

0.74

0.75

0.76

0.77

0.78

0.79

0.8

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

k

Eqv

Mom

ent A

rm

- jh

M = V x jhV = Base shear


Wind Requirements


The Wind Pressure Equation

p = I ·½ ρV2·Kd • Kz·Kzt·Cp·Gf

I Importance of Building½ρV2 Velocity PressureKz Terrain ExposureKd Directionality Factor Kzt Topographic Effect (Wind speed up)Cp Shape CoefficientGf Gust Effect Factor

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ASCE 7-05 Wind Speed Map


ASCE 7-05 Wind Pressure Equation

• Involves 48 different variables• Requires solution to 24 equations


Wind Variable Categories (6 categories, 48 variables)

Building Geometry (5 variables):B, L, h, Cpw, Cpw, z

Building Properties (3 variables)I , T, β

Wind Speed (4 variables)V, zV , qz, qh

Wind Climate (18 variables)Kz, Gf, zI , z , gQ, gR, gv, Q, R, zL , RN , Rh , RB , RL, N1, BLh ,, ηηη

Terrain Exposure (8 variables)α, zg, α , b , c, l , ε , zmin

Site Topographic Features (9 variables)Kzt, K1, K2, K3, H, LB, x, μ, γ


Wind Load MethodBuilding Types

Metal Building TypeResidential

Low RiseSimple Diaphragm

-Use Method 2: Low Rise (Figure 6-10)“Envelope Approach” from ASCE 7-05 Commentary C6.5.11

-Use Method 1: Low Rise (Figure 6-2)Simplified “Envelope Approach”from ASCE 7-05 Commentary C6.4


Low Rise Building

• Mean roof height h ≤ 60 feet• Mean roof height h does not exceed

least horizontal dimension


Simple Diaphragm Building

• Building in which both windward and leeward wind loads are transmitted through floor and roof diaphragms to the same MWFRS

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Simple Diaphragm Building

floordiaphragms

Main Wind ForceResisting System

( MWFRS)


The Basis of Simplification


Simplified Wind Design

• Simple diaphragm buildings• h ≤ 160 feet• Generally flat roofs• Based on ASCE 7-05 Figure 6-6 – Method 2

Traditional “Directional Approach” from ASCE 7-05 Commentary C6.5.11


Assumptions

• Rigid diaphragm buildings• h = 15 – 160 ft. • Period T = h/75 seconds (upper bound)• Damping = 1% (lower bound)• L/B = 0.5. 1.0, 2.0 (interpolate between)• I = 1.0• No topographic effects (kzt = 1)


Simplified Method

1. The building shall be a simple diaphragm building as defined in Section 26.2. 2. The building shall have a mean roof height h ≤ 160 ft. 3. The ratio of L/B shall not be less than 0.5 nor more than 2.0. 4. The fundamental frequency (hertz) of the building used to determine the Gust Effect

Factor Gf defined in Section 26.9.2 shall not be less 75/h where h is in feet. 5. The structural damping ratio β of the building used to determine the Gust Effect

Factor Gf defined in Section 26.9.2 shall not be less than one percent (1%) of critical. 6. The arrangement of elements of the MWFRS (walls, braced frames, moment frames)

is symmetric about each principal building axis direction.


Figure 6-6

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Wind Pressure Equation

( )pipf GCqCqGp −=

pf CqGp =

( )plhpwzfz CqCqGp +=

- General Equation (6-23)

- For simple diaphragm buildings

- windward, leeward walls



Wind Pressure Vs HeightASCE 7-05

0

20

40

60

80

100

120

140

160

40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70

Pressure (psf)

Hei

ght (

ft)

h=160 ft.V=120 MPHExposure CT=h/75Damping=1%

ASCE 7-05 ExactSimplified

p15

p = 1.04p160


Story Shear Vs HeightExact vs Simplified

0102030405060708090

100110120130140150160

0 1000 2000 3000 4000 5000 6000 7000 8000

Story Shear (pounds)

Hei

ght (

ft)


Story Moment Vs HeightExact vs Simplified

0102030405060708090

100110120130140150160

0 100000 200000 300000 400000 500000 600000 700000

Moment (foot-pounds)

Hei

ght (

ft)


Wind Load Equations

Pressure (psf):pz = p0 (1 - z / h) + (z / h) ph

Story Shear (pounds):vz = 0.5(h - z) [(p0 (1 - z / h) + ph (1 + z / h)]

Overturning Moment (ft.-pounds):mz = 1/3 (h - z)2 [0.5p0 (1 – z / h) + ph (1 + 0.5 z / h)]

p0

ph

zpz

zvz

zmz

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Why is Building Period Important?• Related to mass and stiffness of building

– Stiffness affects drift and motion perception– Mass affects wind forces – Mass affects seismic forces– Mass affects motion perception

• Period affects Gust Effect Factor, thus p• Buildings with high periods interact more with the wind • Note:

– Higher Period T is conservative (opposite from seismic!)

– Higher T is softer more flexible building


Period Building Period T

T = f ( mass / stiffness )

T = 4 ∑ mikii=1

nmi = wi / g floor iki = story stiffness floor iwi = weight floor i


Proposed Period Formulas


Period FormulasWind Load

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0 200 400 600 800 1000 1200 1400Bldg Ht h (ft)

Perio

d T

(sec

)

h/75 h/100 h/150

0.232h0.5

RecommendedPeriod Equations:

T = h/0.75 h < 300 ftT = 0.232h0.5 h > 300 ft

h/75

300 ft.


Period FormulasWind and Seismic

0

1

2

3

4

5

6

7

8

9

10

0 200 400 600 800 1000 1200 1400

Building Ht. h (ft.)

Perio

d T

(sec

)

T=h/75 h/100 h/150

T=h / 75h < 300

T=0.232h0.5

h > 300 ft.

T=0.028h0.8

MF Conc.T=0.016h0.9

MF Steel.

EBF Steel

All other


T – Service or Ultimate?

• Steel Buildings:T proportional (1/0.8 stiffness)0.5 = 1.12

• Concrete Buildings:T proportional (1/0.7 stiffness)0.5 = 1.20

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Anatomy of Wind

p = I·½ ρV2·Kd * Kz·Kzt·Cp·G

I Importance of Building½ρV2 Velocity PressureKz Terrain ExposureKd Directionality Factor

Kzt Topographic Effect (Wind speed up)Cp Shape CoefficientGf Gust Effect Factor


Velocity Pressure Exposure Cofficient vs Height

0100200300400500600700800900

100011001200130014001500

0 0.5 1 1.5 2 2.5Kz

h (ft

)

Exp B: Kz = 2.01(h/1200)2/7

Exp C: Kz = 2.01(h/900)2/9.5

Exp D: Kz = 2.01(h/700)2/11.5


Normalized Velocity Pressure Exposure Coefficients Normalized Gust Effect Factor x Vel. Pressure Exp. Coef.

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1.000 1.100 1.200 1.300 1.400 1.500 1.600 1.700 1.800

Rato (Kz Exp C,D/ Kz Exp B), Ratio [(Gf x Kz) Exp C,D/ (Gf x Kz) Exp B]

Hei

ght h

(ft)

Kz: Exp D/B

Kz: Exp C/B

Gf x Kz: Exp D/B

Gf x Kz: Exp C/B

150 ft.

150 ft.

WindV = 90 mphβ = 1%T = 0.232 h0.5 h > 300 ft.T = h/75 h ≤ 300 ft.


Gust Effect Factor• Amplification Factor - Gustiness of the wind• Accounts for the loading effects in the along-wind

direction (parallel to the direction of the wind) due towind turbulence-structure interaction.

• Accounts for along-wind loading effects due to dynamicamplification for flexible structures.

• Complex equation:

( )⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

+++

=zbarv

.RQzbar

f Ig.RgQgI.

.G711

7119250

502222


Gust Effect Factor

• Seven key parameters– Wind velocity (V)– Building geometry (B, L, h)– Building properties (T,β)– Terrain exposure parameters (Table 6-2 ASCE 7- 05)

( )β= ,T,h,L,B,osureexpterrain,VfGf

Exposure α zg ft.

α b c l ft.

ε zmin ft.

B 7.0 1200 1/4 0.45 0.30 320 1/3 30 C 9.5 900 1/6.5 0.65 0.20 500 1/5 15 D 11.5 700 1/9 0.80 0.15 650 1/8 7


Gust Factor Simplification

• Use L/B ratio instead B, L separately (reduces one variable)

• Relate T to building height (reduces one variable)• Use lower bound damping ratio (β = 1%)

– β = 1% for typical steel buildings– β = 2% for typical concrete buildings

• Thus, Gf = f (V, exposure, h)

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Gust Effect Factor Vs HeightL/B=1 T=h/75 1% Damping

30

40

50

60

70

80

90

100

110

120

130

140

150

160

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

Gust Effect Factor

Hei

ght (

ft)

Exp B; V = 90 mphExp B; V = 120 mphExp B; V = 150 mph

Exp C; V = 90 mphExp C; V = 120 mphExp C; V = 150 mph

Exp D; V = 90 mphExp D; V = 120 mphExp D; V = 150 mph

β = 1%T = h/75 sec.L/B = 1.0


Gust Effect Factor vs Height

0100200300400500600700800900

100011001200130014001500

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

Gust Effect Factor Gf

Hei

ght h

(ft.)

V = 90 mph V = 120 mph V = 150 mph

Exp C

Exp D

Exp B

Wind

L = 150 ft.

B =150 ft.

L/B = 1T = h/75 h < 75 ft.T = 0.232h0.5 h ≥ 75 ft.β = 2%



0100200300400500600700800900

100011001200130014001500

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2


Hei

ght h

(ft.)

L = 100 ft.

B = 200 ft.Wind

L/B = 0.5T = h/75 ft. h ≤ 75 ft.T = 0.236 h0.5 h > 75 ft.β = 2%

Exp C

Exp D

Exp B

V = 90 mph V = 120 mph V = 150 mph



0100200300400500600700800900

100011001200130014001500

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2


Hei

ght (

ft.)

L = 200 ft.

B = 100 ft.Wind

Exp C

Exp D

Exp BL/B = 2.0T = h/75 h ≤ 75 ftT = 0.232h0.5 h > 75 ft.β = 2%


Solve Wind Pressure Equationat Height h and z = 15 ft.

( )plhpwzfz CqCqGp +=

Pressure (psf):

pz = p0 (1 - z / h) + (z / h) ptop

ptop = Cxph

p0 = p15

h

C varies: 1.00 at h=15 ft to1.04 at h=160 ft

pz


Wind Pressure MWFRS (psf) Exposure C

V(mph) 85 90 100 110 120 130 140 150h(ft.), L/B 0.5 1 2 0.5 1 2 0.5 1 2 0.5 1 2 0.5 1 2 0.5 1 2 0.5 1 2 0.5 1 2

160 29.0 28.7 25.9 32.8 32.4 29.3 41.7 41.2 37.3 52.0 51.3 46.6 63.9 62.8 57.2 77.2 75.8 69.1 92.3 90.6 82.5 109.1 106.6 97.421.1 21.0 17.7 24.1 23.8 20.1 30.6 30.2 25.7 38.2 37.6 32.0 46.9 46.1 39.3 56.7 55.6 47.5 67.7 66.3 56.7 80.1 78.2 66.9

150 28.2 28.0 25.2 31.9 31.6 28.5 40.6 40.1 36.3 50.5 49.9 45.3 61.9 61.0 55.5 74.8 73.6 67.1 89.3 87.7 80.0 105.5 103.3 94.420.8 20.6 17.4 23.6 23.4 19.8 30.0 29.7 25.2 37.4 37.0 31.5 45.9 45.2 38.6 55.4 54.5 46.6 66.2 64.9 55.6 78.2 76.5 65.6

140 27.4 27.2 24.5 31.0 30.8 27.7 39.3 39.0 35.2 49.0 48.4 43.9 60.0 59.1 53.8 72.4 71.2 65.0 86.3 84.8 77.5 101.8 99.8 91.320.4 20.3 17.2 23.2 23.1 19.5 29.4 29.2 24.8 36.6 36.2 30.9 44.9 44.2 37.9 54.1 53.3 45.8 64.5 63.4 54.5 76.1 74.7 64.3

130 26.1 26.5 23.7 30.2 29.9 26.9 38.2 37.9 34.2 47.4 46.9 42.5 57.9 57.2 52.1 69.8 68.8 62.8 83.2 81.9 74.8 98.1 96.3 88.220.1 20.0 16.9 22.8 22.6 19.2 28.9 28.6 24.4 35.8 35.5 30.3 43.8 43.3 37.1 52.8 52.0 44.8 62.9 61.9 53.4 74.2 72.8 62.9

120 25.8 25.7 22.9 29.2 29.1 26.1 37.0 36.7 33.0 45.8 45.4 41.1 55.9 55.3 50.2 67.3 66.4 60.6 80.0 78.9 72.1 94.2 92.7 84.919.7 19.6 16.6 22.4 22.2 18.8 28.3 28.1 23.9 35.0 34.7 29.7 42.8 42.3 36.3 51.5 50.8 43.8 61.2 60.4 52.1 72.0 70.9 61.4

110 25.0 24.9 22.2 28.3 28.2 25.2 35.7 36.5 31.9 44.2 43.8 39.6 53.8 53.3 48.4 64.6 63.9 58.3 76.8 75.8 69.3 90.3 89.1 81.619.4 19.3 16.3 21.9 21.8 18.5 27.7 27.5 23.4 34.2 34.0 29.1 41.7 41.3 35.6 50.1 49.5 42.8 59.5 58.8 50.9 70.0 69.0 59.9

100 24.5 24.4 21.8 27.8 27.7 24.8 35.1 34.9 31.4 43.4 43.1 39.0 52.9 52.5 47.7 63.7 63.0 57.5 75.7 74.8 68.4 89.1 87.8 80.619.3 19.2 16.3 21.8 21.7 18.5 27.6 27.4 23.5 34.1 33.9 29.2 41.6 41.2 35.7 50.0 49.5 43.0 59.5 58.7 51.2 70.0 69.0 60.2

90 23.3 23.2 20.6 26.4 26.3 23.3 33.1 32.9 29.4 40.8 40.5 36.4 49.4 49.1 44.4 59.1 58.7 53.3 70.0 69.4 63.2 82.1 81.2 74.218.6 18.6 15.7 21.0 21.0 17.8 26.4 26.3 22.4 32.5 32.4 27.8 39.4 39.2 33.8 47.2 46.9 40.6 55.9 55.4 48.2 65.5 64.8 56.6

80 22.4 22.4 19.7 25.3 25.3 22.4 31.7 31.6 28.2 39.0 38.9 34.7 47.2 46.9 42.2 56.4 56.0 50.6 66.6 66.1 60.0 77.8 77.2 70.418.3 18.2 15.4 20.6 20.6 17.4 25.8 25.7 21.9 31.7 31.6 27.1 38.3 38.1 32.9 45.8 45.5 39.4 54.1 53.7 46.7 63.2 62.7 54.8

70 21.5 21.4 18.8 24.3 24.2 21.3 30.3 30.2 26.8 37.1 37.1 33.0 44.8 44.7 40.0 53.4 53.2 47.8 62.9 62.6 56.6 73.4 72.9 66.217.9 17.8 15.1 20.1 20.1 17.0 25.1 25.1 21.4 30.8 30.7 26.3 37.2 37.1 31.9 44.3 44.1 38.2 52.2 51.9 45.2 60.9 60.5 52.9

60 20.5 20.4 17.8 23.1 23.1 20.2 28.8 28.8 25.3 35.2 35.1 31.1 42.4 42.3 37.7 50.4 50.2 44.9 59.3 59.0 53.0 69.0 68.6 61.917.5 17.4 14.7 19.6 19.6 16.6 24.5 24.4 20.8 29.9 29.9 25.6 36.0 35.9 30.9 42.8 42.7 36.9 50.3 50.1 43.5 58.6 58.3 50.9

50 19.4 20.7 16.8 21.9 21.9 19.1 27.2 27.2 23.8 33.2 33.2 29.2 39.9 39.8 35.2 47.3 47.2 41.9 55.4 55.2 49.3 64.3 64.1 57.417.0 18.1 14.4 19.1 19.1 16.2 23.8 23.8 20.2 29.0 29.0 24.8 34.8 34.8 29.9 41.3 41.2 35.6 48.4 48.3 41.9 56.2 56.0 48.8

40 18.1 18.1 15.7 20.6 20.6 17.8 25.5 25.5 22.2 31.1 31.0 27.1 37.2 37.2 32.6 44.0 43.9 38.6 51.4 51.3 45.3 59.5 59.3 52.616.6 16.5 14.0 18.6 18.6 15.8 23.1 23.0 19.7 28.1 28.0 24.0 33.6 33.6 28.8 39.7 39.7 34.2 46.4 46.3 40.2 53.7 53.6 46.6

30 16.8 16.8 14.5 19.1 19.1 16.5 23.7 23.6 20.5 28.7 28.7 24.9 34.3 34.3 29.8 40.4 40.4 35.3 47.1 47.1 41.2 54.4 54.4 47.716.0 16.0 13.7 18.0 18.0 15.3 22.3 22.3 19.0 27.0 27.0 23.2 32.3 32.3 27.8 38.1 38.1 32.8 44.4 44.4 38.4 51.2 51.2 44.4

20 15.6 15.6 13.4 17.5 17.5 15.1 21.7 21.7 18.7 26.3 26.3 22.7 31.3 31.3 27.1 36.8 36.8 31.9 42.8 42.8 37.2 49.3 49.3 42.915.4 15.4 13.2 17.3 17.3 14.9 21.4 21.4 18.4 25.9 25.9 22.3 30.9 30.9 26.7 36.4 36.4 31.4 42.3 42.3 36.6 48.7 48.7 42.3

15 15.0 15.0 13.0 16.9 16.9 14.6 20.9 20.9 18.0 25.3 25.3 21.9 30.1 30.1 26.1 35.4 35.4 30.7 41.1 41.1 35.7 47.3 47.3 41.115.0 15.0 13.0 16.9 16.9 14.6 20.9 20.9 18.0 25.3 25.3 21.9 30.1 30.1 26.1 35.4 35.4 30.7 41.1 41.1 35.7 47.3 47.3 41.1

Notes:V=basic wind speed (mph), Figure 6-1L=horizontal building dimension measured parallel to direction of wind (ft)B=horizontal building dimension measured normal to direction of wind (ft)

L

BWind h

ph

p15

11/5/2009

12


Wind Load Equations

Pressure (psf):pz = p0 (1 - z / h) + (z / h) ph

Story Shear (pounds):vz = 0.5(h - z) [(p0 (1 - z / h) + ph (1 + z / h)]

Overturning Moment (ft.-pounds):mz = 1/3 (h - z)2 [0.5p0 (1 – z / h) + ph (1 + 0.5 z / h)]

p0

ph

zpz

zvz

zmz


Dealing with Torsion


Sources of Wind Torsion

• Inherent torsion– Center of pressure not at center of rigidity (eip)– Center of mass not at center of rigidity (eim)

• Accidental torsion– Variation in center of pressure caused by

turbulence (ea)


Causes - Torsional Wind Loading

• Center of pressure not at center of rigidityStrive for eip = 0eip ≤ 0.15B

• Center of mass not at center of rigidityStrive for eim = 0 - 0.05Beim ≤ 0.15B

• Accidental wind torsionea = 0.15B at 0.75W


Minimizing the Effects Torsional Wind Loads

• Align the center of pressure and center of rigidityas close as possible (Goal is zero inherent torsion). Maximum eccentricity eip = 0.15B

• Avoid putting too much lateral load resistance at or near the center of the building. Spread some resistance at building perimeter if possible.

• Avoid having the torsional period as the first period (should be third period for normal 100-200 ft buildings in plan)

• Study mode shapes• Conform to minimum period recommendations


Wind Torsion

c.p.

c.r.

c.r.

B

d2j = d21 d23 d22

0.15B e2

W 0.75W

d 1i =

d1i

d 1

3 d 1

2

L e 1

Prin

cipa

l axi

s 1 Principal axis 2

y

x

k2j = k21 k22 k23

k13

k1i = k11

k12

Control location and stiffness of outerMWFRS’s

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13


Wind Torsion

B = horizontal plan dimension of the building normal to the wind L = horizontal plan dimension of the building parallel to the wind c.r. = center of rigidity, c.p. = center of wind pressure k1i = stiffness of frame I parallel to major axis 1 k2j = stiffness of frame J parallel to major axis 2 d1i = distance of frame I to c.r. perpendicular to major axis 1 d2j = distance of frame J to c.r. perpendicular to major axis 2 e1 = distance from c.p. to c.r. perpendicular to major axis 1 e2 = distance from c.p. to c.r. perpendicular to major axis 2 J = polar moment of inertial of all MWFRS wind frames in the building W = wind load as required by standard V1i = wind force in frame i parallel to major axis 1 V2j = wind force in frame j parallel to major axis 2 x0, y0 = coordinates for center of rigidity from the origin of any convenient x,y axes


Wind Torsion

∑

∑

∑

∑

=

=

=

= == n

ii

n

iii

n

ii

n

iii

k

kyy

k

kxx

11

111

0

11

111

0

∑ ∑= =

+=n

i

m

jjjii dxdxJ

1 1

222

211

( ) ( )( )J

dkBeW

k

kWV iin

ii

ii

111

11

11

15.075.075.0 ++=∑

=

( ) ( )( )J

dkBeW

k

kWV jj

m

jj

jj

222

12

22

15.075.075.0 ++=

∑=


Accidental Wind TorsionASCE 7-05

W

BR

0.5R 0.5R

e = 0.15B

V1 V2

k1 k2

Elastic shear center

k1 = k2


Lateral Deflection

δ1 δ2δmax

X axis

k1

k2 δavg = 0.5(δ1 + δ2)

δmax from computer analysis

Y axis

ea= 0.15B


Minimizing Torsional Effects

• Place MWFRS’s to minimize inherent torsion

• Maintain :δmax

δavg = 0.5(δ1 + δ2)≤ 1.4 under wind and

seismic loading -including req’d code eccentricty


Controlling Wind Torsion

( ) ( )∑∑==

−≥

−≥ m

jj

jn

ii

i

keB

JdandkeB

Jd

122

2

111

1

45.045.0

(see similar equations for using simplified seismic provisions ASCE 7-05 Section 12.14.1.1)

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Simplified Method For square buildings with L/B=1.0, the combined stiffness of the two most separated linesof the MWFRS in each direction shall be at least two thirds of the total stiffness in each principal axis direction. For rectangular buildings, as L/B increases from 1.0 to 2.0 ordecreases from 1.0 to 0.5, the combined stiffness of the two most separated lines of theMWFRS in each direction shall be proportionally increased from two thirds of the total stiffness to at least 80% of the total stiffness in each principal axis direction.

For square buildings with L/B = 1.0, the distance between the two most separated lines ofthe MWFRS in each major axis direction shall be at least two thirds of the dimension of thebuilding perpendicular to the axis direction under consideration. For rectangular buildings as L/B increases from 1.0 to 2.0 or decreases from 1.0 to 0.5, the distance between the two mostseparated lines of the MWFRS in each principal axis direction shall be proportionally increased from two thirds of the dimension of the building perpendicular to the axis directionunder consideration to 100% of the dimension.

7.

8.


Wind Torsion

c.p.

c.r.

c.r.

B

d2j = d21 d23 d22

0.15B e2

W 0.75W

d 1i =

d1i

d 1

3 d 1

2

L e 1

Prin

cipa

l axi

s 1 Principal axis 2

y

x

k2j = k21 k22 k23

k13

k1i = k11

k12

Control location and stiffness ofouter MWFRS’s

Maximize distance


Seismic Detailing – Always(even when wind controls)

• Table 12.2-1 – System Requirements• Avoid horizontal structural irregularities

Table 12.3-1• Avoid vertical structural irregularities

Table 12.3-2


Horizontal Structural Irregularities


Vertical Structural Irregularities


Steps in Preliminary Design• Obtain wind p from simplified method• Obtain seismic base shear from ELF method• Compute base shears for each• Obtain forces at each level• Draw/compare story V, M diagrams for building• Minimize torsion• Seismic detailing - always

11/5/2009

15


Example Problem10 story Concrete Building

• Hotel with large ballroom• Downtown St. Louis Missouri• Exposure C – wind• Site Class D - seismic


Steps in Preliminary Design

Seismic:• Obtain site latitude , longitude

Latitude: 38.63 deg,Longitude: -90.20 deg

2. Obtain SDS, SD1

http://earthquake.usgs.gov/research/hazmaps/design/

http://www.travelgis.com/geocode/



Fa = 1.337 SDS = 0.516 gFv = 2.131 SD1 = 0.238 g

3. Determine Occupancy Category:(from ASCE 7-05 Table 1-1)



• Occupancy Category III4. Determine seismic design category:

(from Tables 11.6-1, 11.6-2)



• Seismic Design Category (SDC) D

SDS = 0.516 g

SD1 = 0.238 g



5. Determine Importance Factor (seismic)(Table 11.5-1 ASCE 7-05)

6. Determine structural system type(Table 12.2-1 ASCE 7-05)

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Structural System Selection

• Special Shear wall + IMF (Dual System)R = 6 Ω = 2.5 CD = 5

Seismic Design Category RestrictionsSystem Category R Ωo Cd A B C D E F

Concrete:1 Shear Wall Frame Interaction SW/Frame Interaction 4 1/2 2 1/2 4 NL NL NP NP NP NP

(Ord SW + Ord MF)2 Ordinary Shear Wall Building Frame System 5 2 1/2 4 1/2 NL NL NL NP NP NP3 Ordinary Shear Wall + IMF Dual System 5 1/2 2 1/2 4 1/2 NL NL NL NP NP NP4 Ordinary Shear Wall + SMF Dual System 6 2 1/2 5 NL NL NL NP NP NP5 Special Shear Wall + Int MF Dual System 6 1/2 2 1/2 5 NL NL NL 160 / 240 100 / 160 1006 Special Shear Wall + SMF Dual System 7 2 1/2 5 1/2 NL NL NL NL NL NL7 Special Moment Frame Moment Frame 8 3 5 1/2 NL NL NL NL NL NL



7. Determine Building Period Ta

Ta = 0.02 h0.75 = 0.02 (100)0.75

• Ta = 0.632 seconds

8. Obtain Seismic Response Coefficient Cs


Steps in Preliminary DesignDesign Response Spectrum

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5

Period (sec)

Spec

ytra

l Acc

eler

atio

n (%

g)

Ta=0.632

Sa = SD1 / (Ta)



0724.0

25.15.6632.0

238.01 =⎟⎠⎞

⎜⎝⎛

=⎟⎠⎞

⎜⎝⎛

=

IRT

SC Ds

• CS = 0.0724



Building Density

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80

No. Floors

Bld

g. D

ensi

ty (p

cf)

Concrete

Steel

Building Wt. (pcf)No. Floors Stl Conc

2 6 1210 6.375 1320 7.125 14.2540 9 17.560 12 2280 16 28

13 pcf

9. Determine estimated building weight W



W = weight density x bldg volume= 13 x [ 150x150x100] / 1000= 29,250 kips

• W = 29, 250 kips10. Determine base shear V

V = Cs W = 0.0724 x 29,250 = 2,118 kips• V = 2,118 kips

11/5/2009

17



11. Distribute base shear up the bldg

V = 2,118 kips

wi = 2,925 kips ea floor

Ta = 0.624 sec > 0.5 seconds

k = 1.07 by interpolation


Steps in Preliminary Design Seismic:

height Cvx Fx V Mft kips kips k-ft.

100 0.1872 395 0 090 0.1673 353 395 395380 0.1475 312 749 1143870 0.128 270 1061 2203960 0.1086 229 1330 3534350 0.0894 189 1560 5094040 0.0705 149 1749 6842430 0.0519 110 1897 8739720 0.0337 71 2007 10746510 0.0161 34 2078 1282440 0 0 2112 149363

Draw Fx, V and M diagram for seismic loading



Wind:1. Determine wind Importance Factor I

(from ASCE 7-05 Table 6-1)

I = 1.15 (wind)



2. Determine design wind pressures from pressure table

ph = 1.15 x 27.7 = 31.9 psfpo = 1.15 x 21.7 = 25.0 psf

ph = 31.9 psfpo = 25.0 psf


Wind Pressure MWFRS (psf) Exposure C

V(mph) 85 90 100 110 120 130 140 150h(ft.), L/B 0.5 1 2 0.5 1 2 0.5 1 2 0.5 1 2 0.5 1 2 0.5 1 2 0.5 1 2 0.5 1 2

160 29.0 28.7 25.9 32.8 32.4 29.3 41.7 41.2 37.3 52.0 51.3 46.6 63.9 62.8 57.2 77.2 75.8 69.1 92.3 90.6 82.5 109.1 106.6 97.421.1 21.0 17.7 24.1 23.8 20.1 30.6 30.2 25.7 38.2 37.6 32.0 46.9 46.1 39.3 56.7 55.6 47.5 67.7 66.3 56.7 80.1 78.2 66.9

150 28.2 28.0 25.2 31.9 31.6 28.5 40.6 40.1 36.3 50.5 49.9 45.3 61.9 61.0 55.5 74.8 73.6 67.1 89.3 87.7 80.0 105.5 103.3 94.420.8 20.6 17.4 23.6 23.4 19.8 30.0 29.7 25.2 37.4 37.0 31.5 45.9 45.2 38.6 55.4 54.5 46.6 66.2 64.9 55.6 78.2 76.5 65.6

140 27.4 27.2 24.5 31.0 30.8 27.7 39.3 39.0 35.2 49.0 48.4 43.9 60.0 59.1 53.8 72.4 71.2 65.0 86.3 84.8 77.5 101.8 99.8 91.320.4 20.3 17.2 23.2 23.1 19.5 29.4 29.2 24.8 36.6 36.2 30.9 44.9 44.2 37.9 54.1 53.3 45.8 64.5 63.4 54.5 76.1 74.7 64.3

130 26.1 26.5 23.7 30.2 29.9 26.9 38.2 37.9 34.2 47.4 46.9 42.5 57.9 57.2 52.1 69.8 68.8 62.8 83.2 81.9 74.8 98.1 96.3 88.220.1 20.0 16.9 22.8 22.6 19.2 28.9 28.6 24.4 35.8 35.5 30.3 43.8 43.3 37.1 52.8 52.0 44.8 62.9 61.9 53.4 74.2 72.8 62.9

120 25.8 25.7 22.9 29.2 29.1 26.1 37.0 36.7 33.0 45.8 45.4 41.1 55.9 55.3 50.2 67.3 66.4 60.6 80.0 78.9 72.1 94.2 92.7 84.919.7 19.6 16.6 22.4 22.2 18.8 28.3 28.1 23.9 35.0 34.7 29.7 42.8 42.3 36.3 51.5 50.8 43.8 61.2 60.4 52.1 72.0 70.9 61.4

110 25.0 24.9 22.2 28.3 28.2 25.2 35.7 36.5 31.9 44.2 43.8 39.6 53.8 53.3 48.4 64.6 63.9 58.3 76.8 75.8 69.3 90.3 89.1 81.619.4 19.3 16.3 21.9 21.8 18.5 27.7 27.5 23.4 34.2 34.0 29.1 41.7 41.3 35.6 50.1 49.5 42.8 59.5 58.8 50.9 70.0 69.0 59.9

100 24.5 24.4 21.8 27.8 27.7 24.8 35.1 34.9 31.4 43.4 43.1 39.0 52.9 52.5 47.7 63.7 63.0 57.5 75.7 74.8 68.4 89.1 87.8 80.619.3 19.2 16.3 21.8 21.7 18.5 27.6 27.4 23.5 34.1 33.9 29.2 41.6 41.2 35.7 50.0 49.5 43.0 59.5 58.7 51.2 70.0 69.0 60.2

90 23.3 23.2 20.6 26.4 26.3 23.3 33.1 32.9 29.4 40.8 40.5 36.4 49.4 49.1 44.4 59.1 58.7 53.3 70.0 69.4 63.2 82.1 81.2 74.218.6 18.6 15.7 21.0 21.0 17.8 26.4 26.3 22.4 32.5 32.4 27.8 39.4 39.2 33.8 47.2 46.9 40.6 55.9 55.4 48.2 65.5 64.8 56.6

80 22.4 22.4 19.7 25.3 25.3 22.4 31.7 31.6 28.2 39.0 38.9 34.7 47.2 46.9 42.2 56.4 56.0 50.6 66.6 66.1 60.0 77.8 77.2 70.418.3 18.2 15.4 20.6 20.6 17.4 25.8 25.7 21.9 31.7 31.6 27.1 38.3 38.1 32.9 45.8 45.5 39.4 54.1 53.7 46.7 63.2 62.7 54.8

70 21.5 21.4 18.8 24.3 24.2 21.3 30.3 30.2 26.8 37.1 37.1 33.0 44.8 44.7 40.0 53.4 53.2 47.8 62.9 62.6 56.6 73.4 72.9 66.217.9 17.8 15.1 20.1 20.1 17.0 25.1 25.1 21.4 30.8 30.7 26.3 37.2 37.1 31.9 44.3 44.1 38.2 52.2 51.9 45.2 60.9 60.5 52.9

60 20.5 20.4 17.8 23.1 23.1 20.2 28.8 28.8 25.3 35.2 35.1 31.1 42.4 42.3 37.7 50.4 50.2 44.9 59.3 59.0 53.0 69.0 68.6 61.917.5 17.4 14.7 19.6 19.6 16.6 24.5 24.4 20.8 29.9 29.9 25.6 36.0 35.9 30.9 42.8 42.7 36.9 50.3 50.1 43.5 58.6 58.3 50.9

50 19.4 20.7 16.8 21.9 21.9 19.1 27.2 27.2 23.8 33.2 33.2 29.2 39.9 39.8 35.2 47.3 47.2 41.9 55.4 55.2 49.3 64.3 64.1 57.417.0 18.1 14.4 19.1 19.1 16.2 23.8 23.8 20.2 29.0 29.0 24.8 34.8 34.8 29.9 41.3 41.2 35.6 48.4 48.3 41.9 56.2 56.0 48.8

40 18.1 18.1 15.7 20.6 20.6 17.8 25.5 25.5 22.2 31.1 31.0 27.1 37.2 37.2 32.6 44.0 43.9 38.6 51.4 51.3 45.3 59.5 59.3 52.616.6 16.5 14.0 18.6 18.6 15.8 23.1 23.0 19.7 28.1 28.0 24.0 33.6 33.6 28.8 39.7 39.7 34.2 46.4 46.3 40.2 53.7 53.6 46.6

30 16.8 16.8 14.5 19.1 19.1 16.5 23.7 23.6 20.5 28.7 28.7 24.9 34.3 34.3 29.8 40.4 40.4 35.3 47.1 47.1 41.2 54.4 54.4 47.716.0 16.0 13.7 18.0 18.0 15.3 22.3 22.3 19.0 27.0 27.0 23.2 32.3 32.3 27.8 38.1 38.1 32.8 44.4 44.4 38.4 51.2 51.2 44.4

20 15.6 15.6 13.4 17.5 17.5 15.1 21.7 21.7 18.7 26.3 26.3 22.7 31.3 31.3 27.1 36.8 36.8 31.9 42.8 42.8 37.2 49.3 49.3 42.915.4 15.4 13.2 17.3 17.3 14.9 21.4 21.4 18.4 25.9 25.9 22.3 30.9 30.9 26.7 36.4 36.4 31.4 42.3 42.3 36.6 48.7 48.7 42.3

15 15.0 15.0 13.0 16.9 16.9 14.6 20.9 20.9 18.0 25.3 25.3 21.9 30.1 30.1 26.1 35.4 35.4 30.7 41.1 41.1 35.7 47.3 47.3 41.115.0 15.0 13.0 16.9 16.9 14.6 20.9 20.9 18.0 25.3 25.3 21.9 30.1 30.1 26.1 35.4 35.4 30.7 41.1 41.1 35.7 47.3 47.3 41.1

Notes:V=basic wind speed (mph), Figure 6-1L=horizontal building dimension measured parallel to direction of wind (ft)B=horizontal building dimension measured normal to direction of wind (ft)

L

BWind h

ph

p15Designing for Wind/Seismic


3. Determine Fx , V, M at each floor Wind:

height p Fx V Mft psf kips kips kip-ft

100 31.9 23.9 0 090 31.2 46.7 46 23780 30.5 45.7 92 94170 29.8 44.7 136 210260 29.1 43.6 180 370850 28.4 42.6 222 575140 27.7 41.6 264 822030 27.0 40.5 304 1110420 26.3 39.5 344 1439310 25.6 38.5 383 180760 25.0 18.7 421 22144

Draw Fx, V and M diagram for wind loading

11/5/2009

18


Compare loading diagramsSeismic/Wind Force (Fx) vs Height

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400

Force (kips)

Hei

ght (

ft)

Wind

Seismic


Compare Shear DiagramsStory Shear vs Height

0

10

20

30

40

50

60

70

80

90

100

0.0 500.0 1,000.0 1,500.0 2,000.0 2,500.0

Story Shear (kips)

Hei

ght (

ft)

Wind

Seismic


Compare Moment DiagramsOverturning Moment vs Height

0

10

20

30

40

50

60

70

80

90

100

0 25,000 50,000 75,000 100,000 125,000 150,000

Moment (kip-ft)

Hei

ght (

ft)

Wind Seismic


Conclusions• Seismic loading may control design (even

in the central US!)• High seismic loads from low site

classification (Site Class D) and Importance Factor (I = 1.25)

• Check wind and seismic drift• Seismic detailing – always!• Control location of LLRS for wind and

seismic torsion control


Wrap-Up• Simple procedures for wind and seismic

load calculations• Useful comparisons for preliminary design• Control wind and seismic torsion• Seismic detailing – always!• Minimize vertical and horizontal

irregularities (trade steel/concrete for granite)

seaot 10-09w vs s.ppt topics • asce 7 – simplified wind provisions • asce 7 – seismic...

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