Solution -Cont. - dm2_080208

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(7) Check deflection of possible local mechanisms.
(a) Roof girder mechanism (investigate W12 x 35 from
Step 5).
TN = 2 [pi] (KLM m/KE)1/2
From Section 1 and Table 10
KLM = (.77 + .78)/4 + .66/2 = 0.72
m
= W/g = [(12.66 x 17) + 35]/(32.2 x 144)
= 0.0539 lb-sec2/in2 or
= 53,964 lb-ms2/in2
KE = 307EI/L4 = 307 x 30 x 106 x 285/(16.5x12)4
= 1707.8 psi
TN = 2[pi](0.72 x 53,694/1707.8)1/2 = 30.0 ms
T/TN = 78/30.0 = 2.60
ru = 16Mp/L2 = (16 x 104)/16.52 = 6.11 k/ft.
B = pb
= (2.5)(17)(144)/1,000
= 6.12 k
B/ru = 6.12/6.11 = 1.0
Xm/XE = 3.40 > 3
N.G.
Check end rotation of girder.
XE = ru/KE = 6.11/(1.71 x 12) = 0.30 in
Km = 3.40 x 0.30 = 1.02 in
tan [theta] = Xm/(L/2) = 1.02/(8.25)(12) = 0.0103
[theta] = 0.6deg. < 1deg.
O.K.
(b) Exterior column mechanism (investigate W14 x 82 from
Step 5).
TN = 2[pi](KLMm/KE)1/2
From Section 1 and Table 10
KLM = (.78 + .78)/4 + 0.66/2 = 0.72
2.08-191

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