sm10 58 59

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PROBLEMS (10.58 and 10.59) A simply supported beam AB is loaded as shown in Fig. P10.58
and P10.59. Calculate the angle of rotation at end B.
Given: P=4 kips,
a=3 ft, L=10 ft,
E=10x106 psi,
I=72 in.4
SOLUTION (10.58)
P
a
P
a
A
B
D
C
Actual
Loading
=
L
P
P
A
a C
+A
B
D B
L-a
Loading I
Loading II
Use Table B.14: θ B = (θ B ) I + (θ B ) II
where,
Pa( L2 − a 2 )
P( L − a )[ L2 − ( L − a ) 2 ]
(θ B ) I =
(θ B ) II =
6 EIL
6 EIL
P
(aL2 − a 3 + 2 L2 a − 3La 2 + a 3 )
6 EIL
Pa
=
( L − a)
2 EI
4 × 103 (3 × 12)
=
(10 − 3)(12) = 8.4 ×10−3 rad
6
2(10 ×10 )(72)
Thus, θ B =
SOLUTION (10.59)
P
A
P
2
C 2a
B
P
A
C
Loading I
=
Actual
Loading
P
B + A
C
B
Loading II
Continued on next slide
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Use Table B.14:
θ B = (θ B ) I + (θ B ) II
where,
P(4a) 2 Pa 2
(θ B ) I =
=
16 EI
EI
2
Pa(4a)
Pa 2
(θ B ) II =
=
24 EI
6 EI
Thus,
Pa 2 Pa 2 7 Pa 2
=
θB =
+
EI 6 EI 6 EI
7(4 ×103 )(3 ×12) 2
=
= 8.4 ×10−3 rad
6
6(10 ×10 )(72)
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
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