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578_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 578_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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572 CHAPTER 7 Analysis of Stress and Strain Problem 7.2-3 Solve Problem 7.2-1 for an element in plane stress subjected to stresses s x 5700 psi, s y 2300 psi, and t xy 2500 psi, as shown in the figure. Determine the stresses acting on an element oriented at an angle u 50˚ from the x axis, where the angle u is positive when counterclockwise. Show these stresses on a sketch of an element oriented at the angle u . Solution 7.2-2 s x 1 119.2 MPa ; s x 1 s x + s y 2 + s x s y 2 cos (2 u ) + t xy sin (2 u ) u 30° s x 100 MPa s y 80 MPa t xy 28MPa s y 1 60.8 MPa ; s y 1 s x + s y s x 1 t x 1 y 1 5.30 MPa ; t x 1 y 1 s x s y 2 sin(2 u ) + t xy cos(2 u ) 2300 psi 2500 psi 5700 psi Solution 7.2-3 s x 1 1243 psi ; s x 1 s x + s y 2 + s x s y 2 cos (2 u ) + t xy sin (2 u ) u 50° s x 5700 psi s y 2300 psi t xy 2500 psi s y 1 6757 psi ; s y 1 s x + s y s x 1 t x 1 y 1 1240 psi ; t x 1 y 1 s x s y 2 sin (2 u ) +

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578_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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