11/5/2009 1 Designing for Wind/Seismic SEAoT State Conference 2009 Austin, Texas Designing for Wind/Seismic Wind Versus Seismic Which Controls? by Larry Griffis P.E. Walter P. Moore and Associates, Inc. Designing for Wind/Seismic 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 Designing for Wind/Seismic The Code Designing for Wind/Seismic 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” Designing for Wind/Seismic 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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• Mean roof height h ≤ 60 feet• Mean roof height h does not exceed
least horizontal dimension
Designing for Wind/Seismic
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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Designing for Wind/Seismic
Simple Diaphragm Building
floordiaphragms
Main Wind ForceResisting System
( MWFRS)
Designing for Wind/Seismic
The Basis of Simplification
Designing for Wind/Seismic
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
Designing for Wind/Seismic
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)
Designing for Wind/Seismic
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.
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
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Designing for Wind/Seismic
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
Designing for Wind/Seismic
Dealing with Torsion
Designing for Wind/Seismic
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)
Designing for Wind/Seismic
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
Designing for Wind/Seismic
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
Designing for Wind/Seismic
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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Designing for Wind/Seismic
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
Designing for Wind/Seismic
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 ++=
∑=
Designing for Wind/Seismic
Accidental Wind TorsionASCE 7-05
W
BR
0.5R 0.5R
e = 0.15B
V1 V2
k1 k2
Elastic shear center
k1 = k2
Designing for Wind/Seismic
Lateral Deflection
δ1 δ2δmax
X axis
k1
k2 δavg = 0.5(δ1 + δ2)
δmax from computer analysis
Y axis
ea= 0.15B
Designing for Wind/Seismic
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
Designing for Wind/Seismic
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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Designing for Wind/Seismic
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.
Designing for Wind/Seismic
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
Designing for Wind/Seismic
Seismic Detailing – Always(even when wind controls)
• Table 12.2-1 – System Requirements• Avoid horizontal 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
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Designing for Wind/Seismic
Example Problem10 story Concrete Building
• Hotel with large ballroom• Downtown St. Louis Missouri• Exposure C – wind• Site Class D - seismic
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)
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
Designing for 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
Designing for 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
Designing for 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
Designing for Wind/Seismic
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