JNTU
JNTU B.Tech II STRENGTH OF MATERIALS - I Previous Question Paper (August/September -2022 - R18)
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Main
The Modulus of rigidity for a material is 0.81×105 MPa. A 10 mm diameter rod was subjected to an axial pull of 10 kN and the change in diameter was observed to be 3×10-3 mm. Calculate Poisson’s ratio and the modulus of elasticity.
Answer
Given: Modulus of rigidity (G) = 0.81 × 105 MPa, Diameter (d) = 10 mm, Axial load (P) = 10 kN = 10,000 N, Change in diameter (δd) = 3 × 10-3 mm.
First, calculate the lateral strain (εlat):
Calculate the axial stress (σ):
Using the relationship between Poisson's ratio (μ) and lateral strain: εlat = -μ × (σ / E). We also know G = E / (2(1 + μ)), so E = 2G(1 + μ). Substituting E into the strain equation:
Now, calculate the modulus of elasticity (E):
Deduce the total extension of a uniformly tapering rod of diameters d and D over a length of L, when the rod is subjected to an axial load ‘P’.
Answer
Consider a small element of length dx at a distance x from the smaller end (diameter d). The diameter dx at this section is given by:
The area of this section is Ax = (π / 4) × dx2. The extension of the small element dx is:
Integrating from x = 0 to x = L:
Let k = (D - d) / L. Then dx = dk / k. The integral becomes:
Determine the values and draw the shear force and bending moment diagrams for the loaded over hanging beam shown in figure 1.
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A beam of I section 400 mm × 200 mm has a web and flange thickness 20 mm. Calculate the maximum intensity of shear stress across the section and sketch the shear stress distribution across the section of the beam, if it carries a shearing force of 300 kN at a section.
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A rectangular beam 200 mm deep is simply supported over a span of 6 m. Determine the uniformly distributed load per meter which the beam may carry, if bending stress should not exceed 100 N/mm2. Take I=8.0×106 mm4.
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Determine the slope at supports and deflection at points B and C by Macaulay’s method shown in figure 2.
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What is the difference between real beam and conjugate beam?
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Write and explain the assumptions made in the theory of simple bending.
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Find the section modulus for a hollow circular section of internal diameter d and external diameter D.
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Prove that the ratio of depth to width of the strongest beams that can be cut from a circular log of diameter, d is 1.414.
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At a point in a strained material, the principal stresses are 100 MN/m2 (tensile) and 40 MN/m2 (compressive). Determine the resultant stress in magnitude and direction on a plane inclined at 600 to the axis of major Principal stress. What is the resultant stress and maximum intensity of shear stress in the material at a point?
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The Principal stresses at a point in an elastic material are 200 N/mm2 (tensile), 100 N/mm2 (tensile) and 50 N/mm2 (compressive). If the stress at the elastic limit in simple tension is 200 N/mm2. Determine whether the failure of the material will occur according to the maximum principal strain theory. Take Poisson’s ratio = 0.3.
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A cantilever beam of length 7m carries a gradually varying load, zero at the free end to 5 kN/m at the fixed end. Draw the S.F and B.M diagrams for the cantilever.
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A horizontal beam of the section is shown in Figure 3, is 3.0m long and is simply supported at the ends. It carries an udl of intensity 6.56 kN/m over the entire span. Determine the stresses developed in the extreme fibers of compression and tension zones. (All dimensions are in mm).
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