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581_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 581_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 1:18 PM Page 575 SECTION 7.2 Plane Stress Solution 7.2-8 sx 46 MPa u 42.5° sx1 sx1 sy sx + sy 13 MPa cos (2u) + txy sin (2u) + 2 21 MPa 2 2 sx + sy ; sx1 7.1 MPa ; y Problem 7.2-9 The polyethylene liner of a settling pond is subjected to stresses sx 350 psi, sy 112 psi, and txy 120 psi, as shown by the plane-stress element in the first part of the figure. Determine the normal and shear stresses acting on a seam oriented at an angle of 30° to the element, as shown in the second part of the figure. Show these stresses on a sketch of an element having its sides parallel and perpendicular to the seam. sin (2u) + txy cos (2u) 14.6 MPa sy1 ; 51.9 MPa sy1 sy sx tx1y1 tx1y1 sy sx txy 112 psi 30° 350 psi O x 120 psi Seam Solution 7.2-9 Plane stress (angle ) sx u sx1 sy 350 psi sx + sy sy sx + 2 2 sy sx 2 163 psi sy1 txy 120 psi 30° 187 psi tx1y1 112 psi sx + sy cos 2u + txy sin 2u ; sin 2u + txy cos 2u ; sx1 275 psi ; The normal stress on the seam equals 187 psi ; tension. The shear stress on the seam equals 163 psi, acting clockwise against the seam. ; 575 ...
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