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GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-VII (NEW) EXAMINATION - WINTER 2018
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Subject Code: 2171916 Date: 15/11/2018
Subject Name: Applied Mechanics of Solid
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1 (a) Define state of stress at a point. [03]
(b) Justify the statement “Principal planes are orthogonal.” [04]
(c) The state of stress at a point is characterized by the components:
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sx =100 MPa, sy =-40 MPa, sz =80 MPa, txy =tyz =tzx =0Determine the extremum values of shear stresses, their associated normal stresses, octahedral shear stress and its associated normal stress. [07]
Q.2 (a) Write the use of FOS in design. [03]
(b) List out the theories of failure and explain any one of them. [04]
(c) Explain strain deviator and its invariants. [07]
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OR
(c) Derive differential equations of equilibrium. [07]
Q.3 (a) Define the state of pure shear. [03]
(b) Explain the plane stress and plane strain. [04]
(c) Explain Airy stress function in polar coordinates. [07]
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OR
Q.3 (a) Explain Circular Polariscope. [03]
(b) What do you mean by the principal of virtual work? [04]
(c) Explain the Mohr’s circle for three dimensional state of stress. [07]
Q.4 (a) Write equilibrium equations for plane stress state. [03]
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(b) Explain stress strain relation in terms of plastic flow. [04]
(c) The cubic-element is subjected to the following state of stress:
sx =100 MPa, sy =-20 MPa, sz =-40 MPa, txy =tyz =tzx =0
Assume the material is homogenous and isotropic. Determine the principal shear strains and octahedral shear strain, take E = 2 x 105 MPa and ? =0.25. [07]
OR
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Q.4 (a) Explain Bouschinger effect. [03]
(b) Write a short note on octahedral stresses. [04]
(c) Explain the stress integration of Drucker - Prager material model. [07]
Q.5 (a) What do you mean by principal of super position? [03]
(b) Explain the general nature of yield locus. [04]
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(c) Derive Saint Venant’s equations of compatibility. [07]
OR
(b) Explain the work hardening of a material. [04]
(c) Explain Normality, Convexity and Uniqueness for an elastic solid. [07]
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