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)
Use Table B.14: ( ) ( )
BBIBII
θ
θθ =+
where,
22 2 2
() ()[()]
() ()
66
BI BII
Pa L a P L a L L a
EIL EIL
θθ
−−−−
==
Thus, 23 2 23
(23)
6
BPaL a L a La a
EIL
θ =−+−+
()
2
Pa La
EI
=−
3
6
4 10 (3 12) (10 3)(12)
2(10 10 )(72)
××
=−
×
3
8.4 10 rad
−
=×
SOLUTION (10.59)
Continued on next slide
Loading II
Loading I
A
C
P
=
+
B
Actual
Loading
P
a
a
D
L
A
C
P
B
a
A
L
-a
B
P
D
A
P
=
+
B
Actual
Loading
Loading II
2a
P
2
A
C
P
B
C
A
Loading I
B
C
P

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
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.
Use Table B.14:
() ()
BBIBII
θ
θθ =+
where,
22
(4 )
() 16
BI Pa Pa
EI EI
θ ==
22
(4 )
() 24 6
BII Pa a Pa
EI EI
θ ==
Thus,
22
6
BPa Pa
EI EI
θ =+ 2
7
6Pa EI
=
32
6
7(4 10 )(3 12)
6(10 10 )(72)
××
=×
3
8.4 10 rad
−
=×