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Define stress:
Sol.: When body is acted upon by load or external force, it undergoes deformation (that is, change in shape or dimension) which increases gradually. At the time deformation, the material of the body resists the tendency of the load to deform the body, and when load influence is taken over by internal resistance of material of the body, it becomes stable. Internal resistance which is offered by body to meet with the load is called as stress.
Or, the force of resistance per unit area, which is offered by a body against deformation, is called as stress. Stress can be considered as total stress or unit stress. Total stress represent total resistance to an external effect and can be expressed in N,KN etc. Unit stress represents resistance developed by unit area of cross section, and can be expressed in KN/m2.
If external load is applied just in one direction, the stress developed is called as simple stress whereas
If the external loads are applied in over one direction, the stress developed is called as compound stress.
Normal stress ( σ ) = P/A N/m2
1 Pascal(Pa) = 1 N/m2
1KPa = 103 N/m2
1MPa = 106 N/m2
1GPa = 109 N/m2
(Hint Minimization problem -min X1 + X2, s.t. 2X1 + X2 = 12, X1 + 6X2 = 24, 5X1 + 8X2 = 24; X1, X2 = 0).
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