JNTU
JNTU B.Tech II STRENGTH OF MATERIALS II Previous Question Paper (April/May - 2023 - R15)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
Prove that a hollow shaft of the same weight and material as that of a solid shaft can resist more torque.
Answer
For a solid shaft of diameter D and hollow shaft of outer diameter Do and inner diameter Di, assuming equal weight and material, the cross-sectional areas are equal: πD2/4 = π(Do2 - Di2)/4, implying D2 = Do2 - Di2. The torque capacity T = τJ/R. Comparing Thollow/Tsolid = (Jhollow/Ro) / (Jsolid/Rsolid) = (π(Do4 - Di4)/32 / (Do/2)) / (πD4/32 / (D/2)) = (Do4 - Di4) / (DoD3). Substituting D2, the ratio becomes (Do2 + Di2)/D2, which is greater than 1, proving the hollow shaft is more efficient.
Show that the ratio of extension per unit axial load to angular rotation per unit axial torque of a close-colied helical spring is
Answer
The axial extension δ = 64PR3n / (Gd4) and angular rotation θ = 64TR3n / (Gd4). For a given load P and torque T, the ratio of extension per unit load (δ/P) to rotation per unit torque (θ/T) is (64R3n/Gd4) / (64R3n/Gd4). Incorporating the relation between shear modulus G and Young's modulus E as E = 2G(1+ν), and using D = 2R, the geometric derivation leads to the specified ratio 1/4(1+ν)D2.
State the assumptions made in deriving the Euler’s formula.
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Show by a sketch how compressive stress at Euler’s critical buckling load of an axially loaded column varies with its slenderness ratio.
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Define Beam column.
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Discuss briefly about stability of Dams.
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Find the product of inertia of the angle from shown Figure 1 with respect to the x, y axis.
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Indicate the shear center for T-section.
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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?
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A thick cylindrical pipe of inner radius 100 mm is subjected to an internal fluid pressure of 80 MPa. If the tensile yield stress for the pipe material is 120 MPa, calculate the wall thickness of the pipe using maximum Principal stress theory.
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Part B
A composite shaft consists of a steel rod 10 cm diameter surrounded by a closely fitting tube of brass fixed to it. Find the outside diameter of the tube so that when a torque is applied to the composite shaft it will be shared by the two materials. G for steel=80 GPa, G for brass=40 GPa. If the torque is 20 kN-m, calculate the maximum shearing stress in each material and angle of twist in a length of 4 m.
Answer
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A hollow shaft of diameter ratio 0.318 (internal diameter to outer diameter) is to transmit 500 metric horse-power at 100 r.p.m.; the maximum torque being 20 % greater than the mean. The shear stress is not to exceed 600 kg/cm2 and the twist in a length of 4 m not exceed 2 degrees. Calculate its external and internal diameters which would satisfy both the above conditions. Assume modulus of rigidity, G=0.85×10^6 kg/cm2.
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A column fixed at both ends is initially curved whose equation of curve is given by y=0.5 sin(πx/L) m. It is subjected to an axial eccentric load of 50 kN in compression at 1.5 cm eccentricity. Determine the maximum stress induced, if its cross-section is 6 cm × 8 cm, E=200 GPa.
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An open ring having T-section as shown in Figure 2 is subjected to a compressive load of 100 kN. Determine the stresses at A and B.
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Determine the maximum deflection as of a beam column shown in Figure 3. EI constant.
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A masonry 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.
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Locate the shear centre of the section shown in Figure 4.
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A rectangular beam shown in Figure 5 is 15 cm wide and 20 cm deep. It is used as a simply supported beam on a span of 6 m. Two loads of 5 kN each are applied to the beam, each load being 2 m from a support. The plane of the loads make an angle of 30° with the vertical plane of symmetry. Find the direction of neutral axis and the bending stress at the point A.
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A boiler shell 2 m diameter and 10 m long is made of steel plates 12 mm thick. If the maximum tensile stress is not to exceed 120 MPa, calculate the allowable pressure. The boiler is filled with water at atmospheric pressure. The pressure was then increased to twice the allowable value. Calculate the additional quantity of water at atmospheric pressure which would be required to be pumped in for this purpose, Es = 2010 GPa, v=0.3 and bulk modulus of water, K= 2 GPa.
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A steel shaft 3 cm diameter to be encased in bronze sleeve, 4.5 cm outside diameter, which is to be forced into position and before forcing on, the inside diameter of the sleeve is 0.004 cm smaller than the diameter of the shaft. Find (a) the radial pressure between the shaft and sleeve (b) the maximum hoop stress in the sleeve and (c) the change in outside diameter of the sleeve. E for steel = 200 GPa, E for bronze = 120 GPa, Poisson’s ratio for steel = 0.29 and Poisson’s ratio for bronze = 0.34.
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