582CHAPTER 7Analysis of Stress and StrainProblem 7.2-19At a point in a structure subjected to plane stress, the stresses are sx±²4100 psi, sy±2200 psi, and txy±2900 psi (the sign convention for thesestresses is shown in Fig. 7-1). A stress element located at the same point in the structure(but oriented at a counterclockwise angle u1with respect to the xaxis) is subjected tothe stresses shown in the figure (sb, tb, and 1800 psi).Assuming that the angle u1is between zero and 90˚, calculate the normal stress sb, theshear stress tb, and the angle u11800 psiOxytbsbu1Solution 7.2-19ForFindStressAngle sx1±sx+sy2+sx²sy2cos (2u)+txysin (2u)u1sb±sx+sy²1800 psisb3700 psi;sbsb, tb, and u1sx1±1800 psisy1±sbtx1y1±tbu±u1:txy±2900 psisx4100 psisy±2200 psiSOLVE NUMERICALLY:Shear Stress tb±3282 psi;tbsx²sy2sin 12u12+txycos 12u12tb2u1±87.32°u1±43.7°;+2900 psi sin 12u121800 psi950 psi²3150 psi cos12u12Principal Stresses and Maximum Shear StressesWhen solving the problems for Section 7.3, consider only the in-plane stresses (the stresses in the xy plane).
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