JNTU
JNTU B.Tech II STRENGTH OF MATERIALS I Previous Question Paper (February - 2024 - 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
Define elasticity.
Answer
Elasticity is the property of a material by virtue of which it regains its original shape and size after the removal of the external deforming force, provided the stress does not exceed the elastic limit.
Determine the Young’s Modulus of a brass rod of diameter 30 mm and of length 300 mm which is subjected to a tensile load of 30 kN when the extension of the rod is equal to 0.3 mm.
Answer
Given: Diameter d = 30 mm, Length L = 300 mm, Load P = 30 kN = 30000 N, Extension δL = 0.3 mm.
Area A = (π/4) * d^2 = (π/4) * 30^2 = 706.86 mm^2.
Stress σ = P / A = 30000 / 706.86 = 42.44 N/mm^2.
Strain ε = δL / L = 0.3 / 300 = 0.001.
Young's Modulus E = σ / ε = 42.44 / 0.001 = 42440 N/mm^2 or 42.44 GPa.
Define point of contraflexure.
Answer
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Derive the relationship between load and shear force.
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Draw the shear stress distribution across the depth of a T-section beam.
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A high-strength steel [E = 200 GPa] tube having an outside diameter of 80 mm and a wall thickness of 3 mm is bent into a circular curve having a 52-m radius of curvature. Determine the maximum bending stress developed in the tube.
Answer
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What is Maximum Principal Stress Theory?
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Derive the stress expression for an oblique plane within a rectangular body under the influence of shear stress.
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Sketch the conjugate beam for the continuous beam shown in Figure. 1
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Write the equations for the maximum deflection of a simply supported beam subjected to a point load and UDL at mid-span.
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Part B
Derive the total extension of a uniformly tapering rod of diameter D1 & D2 and length L when it is subjected to an axial load P.
Answer
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A steel rod 6 m long and 40 mm in diameter is subjected to an axial tensile load of 75 kN. Determine the change in length, diameter, and volume of the rod. Take E = 200 GPa and Poisson’s ratio = 0.25.
Answer
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Analyse and construct the shear-force and bending moment diagrams for the beam shown in Figure. 2. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams.
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A horizontal beam 10 m long is carrying a uniformly distributed load of 1 kN/m. The beam is supported on two supports 5 m apart. Find the position of the supports, so that B.M. on the beam is as small as possible. Also draw the S.F. and B.M. diagrams and label all significant points on each diagram by clearly differentiating straight-line and curved portions.
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A 5 m long simply supported beam carries a uniformly distributed load of 12 kN/m as shown in Figure. 3 (a) and its cross-sectional dimensions are shown in Figure.3 (b). Determine the following: At section a-a, determine the magnitude of shear stress in the beam at point D; At section a-a, determine the magnitude of shear stress in the beam at point E; Maximum horizontal shear stress that occurs in the beam at any location.
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Two vertical forces are applied to a simply supported beam as shown in Figure. 4 (a) having the cross-section shown in Figure. 4 (b). Determine the maximum tension and compression bending stresses produced in segment CD of the beam.
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Consider a point in a structural member which is subjected to plane stress. Normal and shear stresses acting on horizontal and vertical planes at the point are shown in Figure. 5. Determine the principal stresses and maximum in-plane stress acting at the point. Determine the absolute maximum shear stress at the point.
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Determine the diameter of a bolt which is subjected to an axial pull of 10 kN together with a transverse shear force of 5 kN using the following theories: Maximum principal stress; Maximum principal strain; Maximum shear stress. Assume elastic limit in tension = 225 MPa, factor of safety = 3 & Poisson’s ratio = 0.3.
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Use double-integration method for the beam shown in Figure. 6 and determine the following: Equation of elastic curve for the beam; Slope at the point A and B; Deflection at mid-span. Assume that EI to be constant.
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Use conjugate beam method to find the maximum deflection for the beam shown in Figure.7. Assume E = 200 GPa and I = 60 × 10^6 mm^4.
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