Page 310 - Advanced Design Examples of Seismic Retrofit of Structures

Example of a Steel Frame Building Retrofitted Chapter 5 299

where:
M OT ¼total overturning moment induced on the element by seismic forces
applied at and above the level under consideration;
M ST ¼stabilizing moment produced by dead loads acting on the element;
C 1 and C 2 ¼coefficients defined in Section 5.6.1; and
J ¼a coefficient defined in Section 5.5.5.2.
Alternatively, the load combination represented by Eq. (5.19) shall be per-
mitted for evaluating the adequacy of dead load alone to resist the effects of
overturning.

M OT
0:9M ST > (5.19)
C 1 C 2 μ OT
where:
μ OT ¼10.0 for collapse prevention (CP);
¼8.0 for life safety (LS); and
¼4.0 for immediate occupancy (IO).
For the main building:

V 2 X ¼ 342:55 Tonð Þ V 2 y ¼ 313:74 Tonð Þ
,
V 1 X ¼ 1549:68 Tonð Þ V 1 y ¼ 1224:82 Tonð Þ
ð
M ST X ¼ 131:97 15:65ð Þ + 660:13 19:275Þ ¼ 14789:33 T mÞ
ð
ð
ð
M ST Y ¼ 131:97 7:55ð Þ + 660:13 7:55Þ ¼ 5980:35 T mÞ
ð
ð
M OT X ¼ 342:55 7:1ð Þ + 1549:68 3:75Þ ¼ 8243:4T mÞ
ð
M OT Y ¼ 313:74 7:1ð Þ + 1224:82 3:75Þ ¼ 6820:62 T mÞ
ð
M OT X 8243:4
M ST X > ) 14789:33 > ¼ 2453:4T mÞ
ð
C 1 C 2 J 1:4 1:2 2
6820:62
M OT Y
M ST Y > ) 5980:35 > ¼ 2029:94 T mÞ
ð
C 1 C 2 J 1:4 1:2 2
8243:4
M OT X
0:9M ST X > ) 0:9 14789:33 ¼ 13310:4 >
C 1 C 2 R OT 1:4 1:2 8
¼ 613:34 T mÞ
ð
6820:62
M OT Y
0:9M ST Y > ) 0:9 5980:35 ¼ 5382:31 >
C 1 C 2 R OT 1:4 1:2 8
ð
¼ 507:48 T mÞ
For the sports building:
V x ¼ V y ¼ 251:31 Tonð Þ
M ST X ¼ 177:6 5 ¼ 888 T mð Þ
M ST Y ¼ 177:6 8 ¼ 1420:8T mð Þ
M OT X ¼ M OT Y ¼ 251:31 5:55 ¼ 1394:77 T mð Þ