JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II THEORY OF STRUCTURES Previous Question Paper (March - 2021 - R18)
Answer any five questions. All questions carry equal marks.
Main
A structural member supports loads, which produce, at a particular point, a direct tensile stress of 80 N/mm² and a shear stress of 45 N/mm² on the same plane. Calculate the values and directions of the principal stresses at the point and the maximum stress, stating on which planes this will act.
Answer
Given: Direct tensile stress (σx) = 80 N/mm², Shear stress (τxy) = 45 N/mm², and σy = 0 N/mm² (as it is not specified).
The principal stresses (σ1, σ2) are calculated using the formula:
Substituting the values:
The principal stresses are:
The directions of the principal planes (θp) are given by:
The maximum shear stress (τmax) is calculated as:
The planes of maximum shear stress act at 45° to the principal planes, specifically at θs = θp1 - 45° = -20.82° and θs2 = θp1 + 45° = 69.18°.
A bending moment of 3,000 Nm is applied to the purlin in a plane at an angle of 30° to the vertical y axis. If the sense of the bending moment is such that its components Mx and My both produce tension in the positive xy quadrant, calculate the maximum direct stress in the purlin stating clearly the point at which it acts.
Answer
To calculate the maximum direct stress, we first resolve the applied bending moment M = 3,000 Nm into its components along the principal axes x and y. Given the angle θ = 30° to the vertical y-axis, the components are:
The direct stress σ at any point (x, y) in the cross-section is given by the formula:
Since the problem states that both components produce tension in the positive xy quadrant, the maximum tensile stress occurs at the corner where both x and y coordinates are positive (the extreme fiber in the first quadrant). Assuming a rectangular section with width b and depth d, where Ix = (bd3)/12 and Iy = (db3)/12, the maximum stress is:
The maximum direct stress acts at the extreme fiber located at the corner (x = b/2, y = d/2) in the first quadrant, where the tensile effects of both bending moments are additive.
A rectangular block of material is subjected to a tensile stress of 100 N/mm² on one plane and a tensile stress of 60 N/mm² on a plane at right angle, together with shear stresses of 45 N/mm² on the same plane. Find:
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A beam on simple supports is subjected to a parabolically distributed load of intensity
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What are the basic assumptions in theory of elasticity and derive the equations of equilibrium and compatibility equations?
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A hollow cylindrical cast iron column is 4 m long with both ends fixed. Determine the minimum diameter of the column if it has to carry a safe load of 250 kN with a factor of safety of 5. Take the internal diameter as 0.8 times the external diameter. Take ultimate compressive stress for the column material is 550 N/mm² and a = 1/1600 in Rankine’s formula.
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Calculate the vertical deflection of the joint B and the horizontal movement of the support D in the truss shown. The cross-sectional area of each member is 1800 mm² and Young’s modulus, E, for the material of the members is 200,000 N/mm².
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