737_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

737_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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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 C a P Solution 9.5-3 Cantilever beam with extension Table G-1, Cases 4 and 6 PL3 3EI PL2 2EI (a) dB (b) uB PaL2 2EI PaL EI 0 0 a L a L 2 3 1 2 ; ; 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 k1 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 L RB k2 dC dC 0+ 1# (dA + dB) 2 6.25 mm Upward ; ...
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