sm10 63

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PROBLEM (10.63) An S 250 x 38 shape beam (see table B.9) is loaded as shown in Fig. P10.63.
Calculate the slope at B.
Given: a = 2 m,
P = 2Q = 10 kN,
I = 51.6 x 106 m4
E = 200 GPa,
SOLUTION
I = 51.4 × 106 mm 4 (Table B.9).
P
A
Q
a C a D a
B
Actual
Loading
=
Q
P
A
C
B
+
A
D
B
Equivalent Loadings
Use Table B.14 (case 1): θ B = (θ B ) P + (θ B )Q
where,
Pa 2
(θ B ) P = (θC ) P = −
2 EI
Q(2a ) 2
2Qa 2
(θ B )Q = (θ D )Q = −
=−
2 EI
EI
Therefore,
a2
θB =
( P 2 + 4Q)
2 EI
(2) 2 (10 + 20)103
=
= 5.81× 10−3 rad
9
−6
2(200 ×10 )(51.6 × 10 )
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