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07-03ChapGere.0012

# 07-03ChapGere.0012 - A-PDF Split DEMO Purchase from...

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Hooke’s Law for Plane Stress When solving the problems for Section 7.5, assume that the material is linearly elastic with modulus of elasticity E and Poisson’s ratio . Problem 7.5-1 A rectangular steel plate with thickness t 0.25 in. is subjected to uniform normal stresses x and y , as shown in the figure. Strain gages A and B , oriented in the x and y directions, respectively, are attached to the plate. The gage readings give normal strains x 0.0010 (elongation) and y 0.0007 (shortening). Knowing that E 30 10 6 psi and 0.3, determine the stresses x and y and the change t in the thickness of the plate. Solution 7.5-1 Rectangular plate in biaxial stress SECTION 7.5 Hooke’s Law for Plane Stress 463 y x y x O B A t 0.25 in. x 0.0010 y 0.0007 E 30 10 6 psi 0.3 Substitute numerical values: Eq. (7-40a): s x E (1 n 2 ) ( e x ne y ) 26,040 psi Eq. (7-40b): Eq. (7-39c): t z t 32.1 10 6 in. (Decrease in thickness) e z n E ( s x s y ) 128.5 10 6 s y E (1 n 2 ) ( e y ne x ) 13,190 psi Problem 7.5-2 Solve the preceding problem if the thickness of the steel plate is t 10 mm, the gage readings are
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