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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, E = 200 GPa, I = 51.6 x 106 m4
SOLUTION
64
51.4 10
I
mm=× (Table B.9).
Use Table B.14 (case 1): ( ) ( )
BBPBQ
θ
θθ
=
+
where,
2
() () 2
BP CP Pa
EI
θθ
==−
22
(2 ) 2
() () 2
BQ DQ Qa Qa
EI EI
θθ
==− =−
Therefore,
22
(4)
2
BaPQ
EI
θ
=+
23
96
(2) (10 20)10
2(200 10 )(51.6 10 )
−
+
=××
3
5.81 10 rad
−
=×
A
P
=
+
B
Actual
Loading
Q
a
a
C
Equivalent Loadings
a
D
A
P
B
C
A
B
Q
D
1
/
1
100%