3. An elastic material fills a cubic-shaped cavity in a rigid metal form. The properties of...

 

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3. An elastic material fills a cubic-shaped cavity in a rigid metal form. The properties of the material are: E = 15000 MPa v = 0.25 = 120 10-6/C (coefficient of thermal expansion) The material is subjected to a uniform temperature increase of 50 C. Determine: i. The stresses developed in the material in xyz- axes system. a = 100 mm Elastic material volume = a ii. The principal stresses in the material. iii. The increase in depth (A). Rigid form Notes: i. ii. i. ii. The rigid form is made of invar steel; that is, it does not experience any thermal expansion or distortion. Material is in state of plane stress; that is, there is no stress in the y-direction and all stresses are in the xz plane (the material is restrained only in the x and z directions). [e] total = [e] elastic (due to stress) + [e]thermal The change in temperature produces normal strains with a magnitude of ethermal = (a)(AT) which is uniform and equal in every direction (AT is the change in temperature). 3. An elastic material fills a cubic-shaped cavity in a rigid metal form. The properties of the material are: E = 15000 MPa v = 0.25 = 120 10-6/C (coefficient of thermal expansion) The material is subjected to a uniform temperature increase of 50 C. Determine: i. The stresses developed in the material in xyz- axes system. a = 100 mm Elastic material volume = a ii. The principal stresses in the material. iii. The increase in depth (A). Rigid form Notes: i. ii. i. ii. The rigid form is made of invar steel; that is, it does not experience any thermal expansion or distortion. Material is in state of plane stress; that is, there is no stress in the y-direction and all stresses are in the xz plane (the material is restrained only in the x and z directions). [e] total = [e] elastic (due to stress) + [e]thermal The change in temperature produces normal strains with a magnitude of ethermal = (a)(AT) which is uniform and equal in every direction (AT is the change in temperature).