584_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

584_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 578 1:18 PM Page 578 CHAPTER 7 Analysis of Stress and Strain Problem 7.2-13 At a point on the surface of a machine the material y 1600 psi, as is in biaxial stress with sx 3600 psi, and sy shown in the first part of the figure. The second part of the figure shows an inclined plane aa cut through the same point in the material but oriented at an angle u. Determine the value of the angle u between zero and 90° such that no normal stress acts on plane aa. Sketch a stress element having plane aa as one of its sides and show all stresses acting on the element. 1600 psi a u 3600 psi O x a Solution 7.2-13 Biaxial stress STRESS ELEMENT u sx1 sy1 sx sx1 tx1y1 1600 psi txy s sx + sy 3600 psi sy Find angle u for s 0 0 56.31° sx1 sy sx 2 ; 2000 psi sin 2u + txy cos 2u 2400 psi 0. normal stress on plane a-a sx + sy sy sx + 2 2 cos 2u + txy sin 2u 1000 + 2600 cos 2u(psi) For sx1 ‹ 2u 0, we obtain cos 2u 112.62° and u 1000 2600 56.31° Problem 7.2-14 Solve the preceding problem for sx and sy 32 MPa y 50 MPa (see figure). 50 MPa a u 32 MPa O x a ...
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