747_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

747_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 741 SECTION 9.5 Method of Superposition 741 Problem 9.5-19 A stekel beam ABC is simply supported at A and held by a high-strength steel wire at B (see figure). A load P 240 lb acts at the free end C. The wire has axial rigidity EA 1500 103 lb, and the beam has flexural rigidity EI 36 106 lb-in.2 What is the deflection dC of point C due to the load P? Wire 20 in. P = 240 lb Beam B A C 20 in. 30 in. Solution 9.5-19 Beam supported by a wire (2) ASSUME THAT THE WIRE STRETCHES T tensile force in the wire P (b + c) b dB d–C P 240 lb b Beam: EI 36 Wire: EA 1500 20 in. c 30 in. h 20 in. 106 lb-in.2 Ph(b + c) EAb Th EA dB a Ph(b + c)2 b+c b b EAb2 (downward) (3) DEFLECTION AT POINT C 103 lb dC ¿ dc ¿¿ dc c) c P(b (1) ASSUME THAT POINT B IS ON A SIMPLE SUPPORT c2 3 EI h(b c) d EAb2 ; Substitute numerical values: dC ¿ dC 0.10 in. + 0.02 in. 0.12 in. ; Pc3 Pc3 b ¿ uBc (Pc) a bc 3EI 3EI 3EI Pc2 (b + c) (downward) 3EI Problem 9.5-20 The compound beam shown in the figure consists of a cantilever beam AB (length L) that is pin-connected to a simple beam BD (length 2L). After the beam is constructed, a clearance c exists between the beam and a support at C, midway between points B and D. Subsequently, a uniform load is placed along the entire length of the beam. What intensity q of the load is needed to close the gap at C and bring the beam into contact with the support? q D A C B L Moment release L c L ...
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