698_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

698_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 08Ch08.qxd 9/18/08 692 11:06 AM Page 692 CHAPTER 8 Applications of Plane Stress Solution 8.5-15 (a) MAXIMUM P 240 lb b 5 ft length of arm h 27 ft height of post r2 4.5 in. t r2 r1 r1 A 2 p (r2 I 2I Q 2 1 r3 2 3 t p 1 r4 2 4 Ip sx 0.257 in. 2 r1 ) r 42 1 s1 7.059 in.2 A s2 67.507 in.4 I s2 135.014 in.4 Ip r 32 1 smax T Vx P cos(30deg) h M P cos(30deg) b T P cos(30deg) Vy Vx P sin(30deg) Vy A 103 psi 4.489 sx + sy + 2 A a txy t sy 2 sx b + t2 xy 2 103 psi 4.534 sx + sy 2 a sy sx 2 2 b + t2 xy 44.593 psi MAXIMUM TENSILE STRESS 9.825 in.3 Q sy 0 s1 4.243 in. REACTIONS AT THE SUPPORT M TENSILE STRESS AND MAXIMUM SHEAR STRESS smax s1 tmax A tmax 2289 psi 4534 psi ; MAXIMUM SHEAR STRESS 6.734 104 lb # in 1.247 4 10 lb # in 207.846 lb a sy sx 2 2 b + t2 xy ; 120 lb (b) ALLOWABLE LOAD P STRESSES AT POINT A sallow tallow 16000 psi 6000 psi The stresses at point A are proportional to the load P. Based on tensile stress: Pallow P sallow smax Pallow 847.01lb Pallow sallow P smax Based on shear stress: Pallow P Pallow sx M r2 I 629.07 lb Pallow 629 lb Pallow 0 sy tallow tmax t sy Vy Q T r2 + Ip I 2t 4.489 t 103 psi 449.628 psi (The shear force Vx produces no stress at point A) ; tallow P tmax ...
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