614_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

614_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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608 CHAPTER 7 Analysis of Stress and Strain 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 n . Problem 7.5-1 A rectangular steel plate with thickness t ± 0.25 in. is subjected to uniform normal stresses ² x and ² 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 e x ± 0.0010 (elongation) and e y ±³ 0.0007 (shortening). Knowing that E ± 30 ´ 10 6 psi and µ ± 0.3, determine the stresses ² x and ² y and the change t in the thickness of the plate. s y s x y x O B A Solution 7.5-1 Rectangular plate in biaxial stress S UBSTITUTE NUMERICAL VALUES : Eq. (7-40a): Eq. (7-40b): s y ± E (1 ³µ ) 2 ( â y + µ â x ) ±³ 13,190 psi ; s x ± E (1 ³µ ) 2 ( â x + µ â y ) ± 26,040 psi ; E ± 30 * 10 6 psi µ± 0.3 t ± 0.25 in. â x ± 0.0010 â y ±³ 0.0007 Eq. (7-39c): (Decrease in thickness)
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Unformatted text preview: ¢ t ± â z t ± ³ 32.1 * 10 ³ 6 in. ; â z ± ³ µ E ( s x + s y ) ± ³ 128.5 * 10 ³ 6 Problem 7.5-2 Solve the preceding problem if the thickness of the steel plate is t ± 10 mm, the gage readings are e x ± 480 ´ 10 ³ 6 (elongation) and e y ± 130 ´ 10 ³ 6 (elongation), the modulus is E ± 200 GPa, and Poisson’s ratio is µ ± 0.30. Solution 7.5-2 Rectangular plate in biaxial stress S UBSTITUTE NUMERICAL VALUES : Eq. (7-40a): s x ± E (1 ³ µ ) 2 ( â x + µ â y ) ± 114.1 MPa ; E ± 200 GPa µ ± 0.3 â y ± 130 * 10 ³ 6 t ± 10 mm â x ± 480 * 10 ³ 6 Eq. (7-40b): Eq. (7-39c): (Decrease in thickness) ¢ t ± â z t ± ³ 2610 * 10 ³ 6 mm ; â z ± ³ µ E ( s x + s y ) ± ³ 261.4 * 10 ³ 6 s y ± E (1 ³ µ ) 2 ( â y + µ â x ) ± 60.2 MPa ; Probs. 7.5-1 and 7.5-2 07Ch07.qxd 9/27/08 1:20 PM Page 608...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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