sm10 62

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.
________________________________________________________________________
PROBLEM (*10.62) A nonprismatic cantilever beam with flexural rigidity 2EI in part AC and
flexural rigidity EI in part BC carries a uniform load of intensity w (Fig. P10.62). What is the deflection at
the free end ?
*SOLUTION
Use Table B.14 (cases 3.1, and 2):
4322
(2) ( 2)(2) ( 8)(2)
8(2) 3(2) 2(2)
CwL wL L wL L
vEI EI EI =− − − 4
17
768
wL
EI
=−
322
(2) ( 2)(2) ( 8)(2)
6(2 ) 2(2 ) 2
CwL wL L wL L
EI EI EI
θ =− − − 3
7
96
wL
EI
=−
Thus,
4
(2)
()
28()
BCC
LwL
vv EI
θ =+ −
444
17 7
768 192 128
wL wL wL
EI EI EI
=− − −
4
17
256 wL EI
=↓
L/
2
A
2
wL
w
A
2EI
2
8
wL
w
=
+
B
Actual
Loading
C
Equivalent Loadings
C
B
L/
2
EI
w
C