JNTU
JNTU B.Tech II Year STRENGTH OF MATERIALS I Previous Question Paper (September/October - 2023 - R16)
Part A is compulsory. In Part B, Answer any one question from each unit.
Part A
Write the equation for the strain energy for a circular solid shaft.
Answer
U = T²L / (2GJ)
where G is the modulus of rigidity and J is the polar moment of inertia (πd⁴/32).
A thin square plate is uniformly deformed as shown in Figure.1. For the deformed plate determine the shear strain γxy at corner R and S.
Answer
List out the important types of loads acting on a structural member.
Answer
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Derive the relationship between shear force, bending moment and loading at a section for a beam.
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Define neutral axis and section modulus.
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A rectangular beam 100 mm wide is subjected to a maximum shear force of 90 kN. Determine the depth of the beam if the maximum shear stress is 5 MPa.
Answer
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Name any two methods used to determine the deflection and slope at a specific section of a structure.
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Distinguish between Macaulay's method and the double integration method for calculating deflections.
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Briefly describe the concepts of normal and tangential stresses on an inclined plane under biaxial stresses.
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Define the concept of "Theories of failure" and identify the significant theories associated with it.
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Part B
Determine the modulus of elasticity for a rod, which tapers uniformly from 30 mm to 15 mm diameter in a length of 400 mm. The rod is subjected to an axial load of 6 kN and extension of the rod is 0.025 mm. Derive the expression for strain energy when the load is applied gradually.
Answer
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A steel rod and two copper rods together support a load of 400 kN as shown in Figure 2. The cross-sectional area of steel rod is 2500 mm2 and of each copper rod is 1600 mm2. Find the stresses in the rods. Take Esteel = 2 × 105 N/mm2 and Ecopper = 1 × 105 N/mm2.
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Analyse and construct the shear-force and bending moment diagrams for the beam shown in Figure 3. Label all significant points on each diagram and identify the maximum moments along with their respective locations.
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Draw the shear-force and bending moment diagrams for the beam shown in Figure 4. Label all significant points on each diagram and identify the maximum moments along with their respective locations.
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A uniformly distributed load of 9 kN/m is applied to a cantilever beam having the cross-section shown. Determine the maximum tension and compression bending stresses produced in the beam.
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The internal shear force V at a certain section of a T-section is 10 kN. Determine the shear stress at point A located 60 mm above the bottom surface and also the maximum horizontal shear stress in the T-section.
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Determine the slope and deflection at point B for the cantilever beam show in Figure 7 using conjugate beam method. Assume E = 200 GPa and I = 60 × 106 mm4.
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Use double-integration method for the beam and loading shown to determine: a) The equation of the elastic curve for the portion AB, b) The deflection midway between the supports, c) The slope at A and B.
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Discuss in detail: a) Maximum principal stress theory, b) Maximum principal strain theory, c) Maximum shear stress theory.
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The stresses shown in Figure 9 act at a point on the free surface structural component. Determine the normal stresses σx and σy and the τxy shear stress at the point.
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