Lower Sloped Roof Areas
Due to symmetry both of the lower sloped roof areas will behave the same in torsion. Only one of the
areas is analyzed and the results are used for both. In addition to the torsion created between the offset
between the centers of mass and rigidity, the transfer of shear into the diaphragm from vertical resisting
elements tributary to the upper roof diaphragm creates torsion. In the transverse direction the braced
moment frames transfer their shear into the horizontal diaphragm. This creates a torsional force equal to
the shear transferred times the distance between the center of application of the moment frame forces and
the center of rigidity (45' 18.81' 26.2' . In the longitudinal direction the offset between the upper shear
-
=
)
walls (along lines B & H) and the lower resisting elements (walls along lines A & I) creates torsional
forces.
Transverse Forces:
Center of Mass in X direction =
45.00
ft.
Center of Rigidity in X direction =
18.81
ft.
Actual Eccentricity in X direction =
26.19
ft.
Perpendicular Span in X direction =
90
ft.
Accidental Eccentricity (5% of Span) =
4.5
ft.
Design Eccentricity in X direction =
30.69
ft.
Seismic Force Tributary to each Diaphragm =
18.1
kips
Eccentricity Torsional Force (V * e) =
554.2
kipft
Shear Force from Upper Roof (moment frames) =
19.24
kips
=4 x 4.81
Distance to Center of Rigidity =
26.19
ft
Torsion Force from Upper Roof =
503.8
kipft
Total Torsion =
1058.0
kipft (1434 KNm)
Rd2
Element
R
d
Rd
Torsional
Force
(kip)
Wall A2-A7
68320
0.00
0
0
0.0
Wall 2A-2D
18918
-18.81
-355848
6693493
-11.8*
Wall 7A-7C
5000
71.19
355950
25340081
11.8
Σ=
32033573
*Note: Negative torsional force contributions are neglected.
Longitudinal Forces:
Center of Mass in Y direction =
5.05 ft.
Center of Rigidity in Y direction =
9.67 ft.
Actual Eccentricity in Y direction =
4.62 ft.
Perpendicular Span in Y direction =
9.67 ft.
Accidental Eccentricity (5% of Span) =
0.4835 ft.
Design Eccentricity in Y direction =
5.11 ft.
Seismic Force Tributary to each Diaphragm =
18.1 kips
Eccentricity Torsional Force (V * e) =
92.25 kipft
Shear Force from Upper Roof (wall line B) =
19.8 kips
Distance to Center of Rigidity =
9.67 ft
Torsion Force from Upper Roof =
191.5 kipft
Total Torsion =
283.7 kipft (385 KNm)
H3-36
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