580_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

580_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 574 1:18 PM Page 574 CHAPTER 7 Analysis of Stress and Strain Solution 7.2-6 sx u sx1 sx1 sy 27 MPa 5.5 MPa txy 10.5 MPa 35° sx + sy sy sx + 2 2 sy1 sy1 ; 6.4 MPa 2 tx1y1 cos (2u) + txy sin (2u) sy sx tx1y1 sin (2u) + txy cos (2u) ; 18.9 MPa sx sy sx1 ; 15.1 MPa Problem 7.2-7 The stresses acting on element B in the web of a wide-flange beam are found to be 14,000 psi compression in the horizontal direction and 2600 psi compression in the vertical direction (see figure). Also, shear stresses of magnitude 3800 psi act in the directions shown. Determine the stresses acting on an element oriented at a counterclockwise angle of 40˚ from the horizontal. Show these stresses on a sketch of an element oriented at this angle. 2600 psi B 14,000 psi B 3800 psi Side View Cross Section Solution 7.2-7 sx txy u sx1 sx1 sy 14000 psi 3800 psi 2600 psi 40° tx1y1 sy sx 2 sin (2u) + txy cos (2u) tx1y1 sx + sy sy sx + 2 13032 psi 2 cos (2u) + txy sin (2u) 4954 psi ; sy1 sx + sy sx1 sy1 3568 psi ; ; Problem 7.2-8 Solve the preceding problem if the normal and shear stresses acting on 13 MPa element B are 46 MPa, 13 MPa, and 21 MPa (in the directions shown in the figure) and the angle is 42.5˚ (clockwise). 21 MPa B 46 MPa ...
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