622_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 622_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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616 CHAPTER 7 Analysis of Stress and Strain Problem 7.6-2 Solve the preceding problem if the element is steel ( = 200 GPA, ) with dimensions = 300 mm, = 150 mm, and = 150 mm and the stresses are , , and . s z ±² 40 MPa s y ±² 40 MPa s x ±² 60 MPa c b a ³± 0.30 E Solution 7.6-2 Triaxial stress (a) M AXIMUM SHEAR STRESS (b) C HANGES IN DIMENSIONS Eq. (7-53 c): â z ± s z E ² ³ E ( s x + s y ) ±² 50.0 * 10 ² 6 Eq. (7-53 b): â y ± s y E ² ³ E ( s z + s x ) ±² 50.0 * 10 ² 6 Eq. (7-53 a): â x ± s x E ² ³ E ( s y + s z ) ±² 180.0 * 10 ² 6 t max ± s 1 ² s 3 2 ± 10.0 MPa ; s 3 ±² 60 MPa s 1 ±² 40 MPa s 2 ±² 40 MPa E ± 200 GPa ³± 0.30 (steel) a ± 300 mm b ± 150 mm c ± 150 mm s z ±² 40 MPa s x ±² 60 MPa s y ±² 40 MPa (c) C HANGE IN VOLUME Eq. (7-56): (d) S TRAIN ENERGY U ± u ( abc ) ± 50.0 N # m ± 50.0 J ; ± 0.00740 MPa Eq. (7-57 a): u ± 1 2 ( s x â x + s y â y + s z â z ) ¢ V ± e ( abc ) ±² 1890 mm 3 (decrease) ; V ± abc e ± 1 ² 2 ³ E ( s x + s y + s z ) ±² 280.0 * 10 ² 6 ¢ c ± c â z ±² 0.0075 mm. (decrease) ¢ b ± b â y ±² 0.0075 mm (decrease) ¢ a ± a â x ±² 0.0540 mm (decrease)
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Unformatted text preview: M ; Problem 7.6-3 A cube of cast iron with sides of length = 4.0 in. (see figure) is tested in a laboratory under triaxial stress . Gages mounted on the testing machine show that the compressive strains in the material are and Determine the following quantities: (a) the normal stresses , and acting on the , and faces of the cube; (b) the maximum shear stress in the material; (c) the change in the volume of the cube; and (d) the strain energy stored in the cube. (Assume = 14,000 ksi and .) Probs. 7.6-3 and 7.6-4 ³ ± 0.25 E U ¢ V t max z x , y s z s x , s y P y ± P z ± ² 37.5 * 10 ² 6 . P x ± ² 225 * 10 ² 6 a y x z a a a O 07Ch07.qxd 9/27/08 1:22 PM Page 616...
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