637_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 637_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 7.7 Plane Strain 631 Problem 7.7-12 Solve the preceding problem if the plate is made of aluminum with and , the stress is , the angle is , and the strain is 946 * 10 6 . P 21° f 86.4 MPa s x 1/3 E 72 GPa Solution 7.7-12 Aluminum plate in biaxial stress U NITS : All stresses in MPa. S TRAIN IN BIAXIAL STRESS (E QS . 7-39) (1) (2) (3) S TRAINS AT ANGLE (E Q . 7-71a) Solve for s y : s y 21.55 MPa (4) + a 1 2 b a 1 72,000 b a 115.2 4 3 s y b cos 42° 946 * 10 6 a 1 2 b a 1 72,000 b a 57.6 + 2 3 s y b â x 1 â x + â y 2 + â x â y 2 cos 2 u + g xy 2 sin 2 u f 21° â z E ( s x s y ) 1/3 72,000 (86.4 s y ) â y 1 E ( s y s x ) 1 72,000 ( s y 28.8) â x 1 E ( s x s y ) 1 72,000 (86.4 1 3 s y ) Strain gage: f 21° â 946 * 10 6 1/3 E 72 GPa s x 86.4 MPa g xy 0 s y ? M AXIMUM IN - PLANE SHEAR STRESS S TRAINS FROM

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