Solution Hibbeler 5 - Resistencia dos materiais- cap 9.pdf, Exercícios de Mecânica dos sólidos

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9-1. Prove that the sum of the normal stresses O +to,m o, +oyisconstant. Stress Transformation Equations : Applying Eqs. 9-1 and 9.3 Of the text G-a, g+a= cos 28 +1,,sin 20 :TO, 9,-0, TCP 00826 1 sin20 G+o AQED.) 9-2. The state of stress at a point in a member is shown on the element. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec 9.1. X amasinço! ME sadio NZ NeZE-=0 48-+(844sin 4O)cos 40º- (SaAsin 40º) (B4Acos 40º)cos 50º = O AF =-4.05244 Jeos 50º - (344cos 40ºcos 40º + AEB -=0 AB--(84sin 409)sin 40º — (SAAsin 40º) (B44cos 40º)sin 50º = O AE, =-0.404484 ) sim 50º + (344cos 40º)sin 40º + Mao ad =-0404ksi Ans The negative signs indicate that the sense of o, to that shown on FBD. 9-3 Solve Prob. 9-2 usin . g the stress. “quations developed in Sec. 92. + rttnsformation and 15: are opposite a=Sksi o=3ki ty=Bksi 0=130º o «418 Eos 20+ tysin 20 Sêcos 260º +Bsin260º=-405ksi Ans | “ .5+3 E The negative sign indicates O, is a compressive stress. Lsin 20 + ty cos 26 )sin 260º + Bcos 260º = 0.404 ksi Ans The negative sign indicates 7, is in the — y' direction