588_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

588_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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582 CHAPTER 7 Analysis of Stress and Strain Problem 7.2-19 At a point in a structure subjected to plane stress , the stresses are s x ±² 4100 psi, s y ± 2200 psi, and t xy ± 2900 psi (the sign convention for these stresses is shown in Fig. 7-1). A stress element located at the same point in the structure (but oriented at a counterclockwise angle u 1 with respect to the x axis) is subjected to the stresses shown in the figure ( s b , t b , and 1800 psi). Assuming that the angle u 1 is between zero and 90˚, calculate the normal stress s b , the shear stress t b , and the angle u 1 1800 psi Ox y t b s b u 1 Solution 7.2-19 For Find Stress Angle s x 1 ± s x + s y 2 + s x ² s y 2 cos (2 u ) + t xy sin (2 u ) u 1 s b ± s x + s y ² 1800 psi s b 3700 psi ; s b s b , t b , and u 1 s x 1 ± 1800 psi s y 1 ± s b t x 1 y 1 ± t b u ± u 1 : t xy ± 2900 psi s x 4100 psi s y ± 2200 psi S OLVE NUMERICALLY : Shear Stress t b ± 3282 psi ; t b s x ² s y 2 sin 1 2 u 1 2 + t xy cos 1 2 u 1 2 t b 2 u 1 ± 87.32° u 1 ± 43.7° ; + 2900 psi sin 1 2 u 1 2 1800 psi 950 psi ² 3150 psi cos 1 2 u 1 2 Principal Stresses and Maximum Shear Stresses When solving the problems for Section 7.3, consider only the in-plane stresses (the stresses in the xy plane).
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