sm10 115

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PROBLEM (10.115) Compute the slope and deflection at point D of the cantilever beam seen in
Fig. P10.113 for a W 460 x 74 shape beam (see Table B.8).
Given: w = 150 kN/m, a = 1 m, E = 200 GPa.
SOLUTION
Table B.8: 64
333 10
I
mm=× See solution of Prob.10.113:
333
123
622
wa wa wa
AAA
EI EI EI
=− =− =−
The distances from point D to the centroid of each area are
111
34 32 53
x
axaxa===
Thus,
333
96
7 7(150 10 )(1)
6 6(200 10 )(370 10 )
DB wa
EI
θθ
−
×
== = ××
3
2.36 10 rad
−
=×
/112233DA D
tvAxAxAx== + +
or
44
41
(3 18 20)
24 24
Dwa wa
vEI EI
=− + + = ↓
Substituting the given data:
34
96
41 150 10 (1) 3.85
24 (200 10 )(333 10 )
D
vmm
−
×
==↓
××