07-03ChapGere.0014

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Problem 7.5-6 A rectangular plate in biaxial stress (see figure) is subjected to normal stresses s x 5 90 MPa (tension) and s y 52 20 MPa (compression). The plate has dimensions 400 3 800 3 20 mm and is made of steel with E 5 200 GPa and n 5 0.30. (a) Determine the maximum in-plane shear strain ± max in the plate. (b) Determine the change D t in the thickness of the plate. (c) Determine the change D V in the volume of the plate. SECTION 7.5 Hooke’s Law for Plane Stress 465 Solution 7.5-6 Biaxial stress s x 5 90 MPa s y 52 20 MPa E 5 200 GPa ±5 0.30 Dimensions of Plate: 400 mm 3 800 mm 3 20 mm Shear Modulus (Eq. 7-38): (a) M AXIMUM IN - PLANE SHEAR STRAIN Principal stresses: s 1 5 90 MPa s 2 52 20 MPa Eq. (7-26): Eq. (7-35): g max 5 t max G 5 715 3 10 2 6 t max 5 s 1 2 s 2 2 5 55.0 MPa G 5 E 2(1 1 n ) 5 76.923 GPa (b) C HANGE IN THICKNESS Eq. (7-39c): D t 5 « z t 52 2100 3 10 2 6 mm (Decrease in thickness) (c) C HANGE IN VOLUME From Eq. (7-47): V 0 5 (400)(800)(20) 5 6.4 3 10 6 mm 3 Also,
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