JNTU
JNTU B.Tech II Year STRENGTH OF MATERIALS I Previous Question Paper (November/December - 2018 - 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
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A steel bar of circular section tapers from 22 mm diameter to 12 mm diameter in a length of 750 mm. Determine the elongation of the bar due to the action of an axial load of 25 kN. Use E = 200 GPa.
Answer
The elongation of a tapered bar is given by the formula:
Given P = 25,000 N, L = 750 mm, E = 200,000 N/mm², d₁ = 22 mm, and d₂ = 12 mm:
Explain the various types of stresses and strains.
Answer
Stresses include Normal stress (tensile or compressive) acting perpendicular to the cross-section, and Shear stress acting parallel to the surface. Strains are categorized as Linear strain (change in length per unit length) and Shear strain (change in angle between two perpendicular lines).
Classify the beams based on support conditions.
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Obtain the relationship between bending moment and rate of loading.
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Distinguish between bending moment and moment of resistance.
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A solid circular section of diameter 100 mm is subjected to shear force of 60 kN. Determine the ratio of mean shear stress to the maximum shear stress.
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The member of a plane truss is subjected to an axial tensile stress of 50 MPa. Find the magnitude and location of the plane carrying maximum shear stress.
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Explain the maximum strain energy theory of failure.
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Distinguish between a real beam and a conjugate beam.
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Derive the relation between moment and curvature of a flexural member.
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Part B
Draw the stress-strain diagram for mild steel and explain the salient features.
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A rigid beam of weight 600 N is held in a horizontal position by three vertical wires, one each attached to the ends of the beam and the third wire to the middle of its length. The outer wires are brass of 2 mm diameter and the centre of steel 1 mm diameter. Find the stress in each wire. Assume that all wires are of the same length. Adopt modulus of elasticity for steel is 2 x 105 N/mm2 and modulus of elasticity for brass is 0.9 x 105 N/mm2.
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A steel rod, 2.5 m long and 20 mm diameter, is enclosed in a brass tube of same length, 40 mm external diameter and 30 mm internal diameter. At the bottom of the composite bar is provided with rigid collar at the bottom and the other end is attached to the roof. A sliding force of 1.25 kN is dropped axially on the collar from a height of 250 mm. Determine the maximum instantaneous elongation of the bar and the maximum stress induced in each component of the composite bar.
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A simply supported beam of span 6 m carries uniformly distributed load of 20 kN/m over a length of 3 m from 2 m from the left hand support and two point loads 25 kN and 45 kN at 1 m and 4 m from the right hand support respectively. Draw the shear force and bending moment diagrams.
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Draw the shear force and bending moment diagrams for a beam of span 6 m supported and loaded as shown in figure 1.
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A simply supported beam of span 6 m has an I-section as shown in figure 2. The beam is subjected to uniformly distributed load 25 kN/m over the entire span. Determine the following:
Maximum bending stress
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Bending stress at a point 100 mm from the top surface of the beam.
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Radius of curvature at the section of maximum bending moment. Use E = 2 x 105 N/mm2.
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A steel beam has cross-section as shown in figure 3. The beam section is subjected to a shear force of 200 kN. Draw the shear stress distribution across the depth of the section. Also determine ratio of the maximum shear stress to the mean shear stress. The total depth of the section is 250 mm.
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The state of stress at a point of a strained member is shown in figure 4. Determine the:
magnitude and the direction of principal stresses
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magnitude and plane carrying the maximum shear stress and
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stresses acting on a plane making an angle 45 degrees with respect to vertical in the clockwise direction.
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A bolt in a connection is subjected to an axial tension of 10 kN together with a shear force of 4 kN. Determine the diameter of the bolt using maximum principal stress theory and maximum shear strain energy theory. The yield stress of the bolt material is 240 N/mm2. Use E = 200 x 103 MPa and the Poisson’s ratio = 0.3. Adopt factor of safety equal to 3.
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A cantilever beam of span 2.4 m has constant flexural rigidity. The beam is subjected to a concentrated load of 10 kN at its mid-span together with udl of intensity 5 kN/m acting from free end to the mid-span. Using moment-area method, determine the slope and the deflection at the mid-span section of the beam.
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Determine the slope at the right support and the deflection under the point of action of the concentrated load of a beam supported and loaded as shown in figure 5. Use conjugate beam method.
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