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Unformatted text preview: 09Ch09.qxd 9/27/08 1:32 PM Page 731 731 SECTION 9.5 Method of Superposition Problem 9.5-3 The cantilever beam AB shown in the figure has an extension L BCD attached to its free end. A force P acts at the end of the extension. A B (a) Find the ratio a/L so that the vertical deflection of point B will be zero.
(b) Find the ratio a/L so that the angle of rotation at point B will be zero. D
P Solution 9.5-3 Cantilever beam with extension
Table G-1, Cases 4 and 6
2EI (a) dB
(b) uB PaL2
; Problem 9.5-4 Beam ACB hangs from two springs, as shown
in the figure. The springs have stiffnesses k1 and k2 and the beam
has flexural rigidity EI. RA = k1 dA (a) What is the downward displacement of point C, which is
at the midpoint of the beam, when the moment M0 is
applied? Data for the structure are as follows:
M0 10.0 kN m, L 1.8 m, EI 216 kN m2,
k1 250 kN/m, and k2 160 kN/m.
(b) Repeat (a) but remove M0 and apply uniform load
q 3.5 kN/m to the entire beam. k1 RB = k2 dB k2 M0 A L/2 C L/2 B q = 3.5 kN/m (for Part (b) only) Solution 9.5-4
10.0 kN # m M0
q L 250 kN /m k2 1.8 m
160 kN / m EI 216 kN # m2 dA
dB 22.22 mm
34.72 mm Downward
Upward Table G-2, Case 8 3.5 kN/ m (a) RA M0
L RB dA RA
k1 dB M0
dC 0+ 1#
(dA + dB)
2 6.25 mm Upward ; ...
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