JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II STRENGTH OF MATERIALS – II Previous Question Paper (December - 2017 - R13)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit.
Part A
Draw the torsional shear stress distribution in a solid and in a hollow shaft.
Answer
For a solid shaft, the shear stress distribution is linear, starting from zero at the center and reaching a maximum at the outer surface. For a hollow shaft, the distribution is also linear, starting from a non-zero value at the inner radius and increasing to a maximum at the outer radius.
State the difference between torsional failure surfaces in ductile and brittle materials.
Answer
In ductile materials, torsional failure occurs along a plane perpendicular to the axis of the shaft (a plane of maximum shear stress). In brittle materials, failure occurs along a helical surface inclined at 45 degrees to the axis of the shaft, which corresponds to the plane of maximum principal tensile stress.
Write the differential equation for beam column.
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Define slenderness ratio.
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State the secant column formula. In which situation is this formula used?
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Define section modulus.
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Define Shear centre.
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Define hoop stress.
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In which applications are thick-walled cylinders involved?
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A thin spherical vessel 100 mm diameter and 12.5 mm thick is filled with water. More water is pumped in until the pressure reaches 4.2 MPa. How much extra water was required to reach this pressure. Assume E=210 GPa, γ = 0.25.
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Part B
A hollow steel shaft 3 m long must transmit a torque of 25 kN m. The total angle of twist in this length is not to exceed 2.5 degrees and the allowable shearing stress is 90 MPa. Determine the inside and outside diameter of the shaft if G=85 GPa.
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A stiff bar of negligible weight transmits a load P to a combination of 3 springs. The three springs are made of the same material and out of rods of equal diameters. They are of the same length before loading. The number of coils in the three springs are 10, 12 and 15 respectively, while the mean radii of the coils are in the proportion 1:1.2:1.4 respectively. Find the distance x such that the stiff bar remains horizontal after applying the load (figure 1).
Answer
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A bar of length L clamped at its lower end and subject to both vertical and horizontal forces at the upper end, as shown in Figure 2. The vertical force P is equal to one-fourth of the Euler load for this bar. Determine the lateral displacement of the upper end of the bar.
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Determine the horizontal and vertical deflections of the end B of the thin curved beam shown in Figure 3. E=200 GN/m2, width =10 mm, thickness=5 mm, P=2 N.
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A simply supported beam column of 4 cm × 6 cm cross-section 1.5 m long is subjected to an axial load of 8 kN in addition to a transverse concentrate load of 15 kN at a distance of 50 cm from one end. Determine the maximum deflection and the maximum stress in the column. E=200 GPa.
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A mansory dam 9 m high and trapezoidal in section has the top width 1 m and the bottom width 5 m. The face exposed to water is inclined at a slope of 1:10. Test the stability of the dam if the coefficient of friction is 0.6. Density of dam material 2500 kg/m3 and that of water 1000 kg/m3 (figure 4).
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Determine the shear center of the thin walled section indicated in Figure 5. The thickness t is constant.
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Calculate the stresses at points A, B and C of the cross-section of the beam shown in Figure 6.
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A cylindrical shell 2.5 m long and closed at the ends has an internal diameter of 1.25 m and wall thickness of 20 mm. Calculate the change in dimensions when subjected to an internal pressure of 1.5 MPa. Take E=200 GPa, γ =0.3.
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Prove that the maximum hoop stress in a thick cylinder is given by the formula:
Where P = internal pressure, K = outside to inside diameter ratio.
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If a cylinder of internal diameter d, wall thickness t and subjected to internal pressure only, is assumed to be a thin cylinder, what is the greatest value for the ratio t / d if the error in the estimated maximum hoop stress is not to exceed 5 percent?
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