JNTU
JNTU B.Tech II THEORY OF STRUCTURES Previous Question Paper (August/September - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
A simply supported beam is having span of 6 m. It carries two-point loads of 50 kN and 20 kN at 1m and 4m from left hand support respectively. Draw bending moment diagram and hence draw the qualitative deflected shape of the beam.
Answer
First, calculate the support reactions. Let RA and RB be the reactions at the left and right supports. Taking moments about B: RA × 6 = 50 × (6 - 1) + 20 × (6 - 4) = 50 × 5 + 20 × 2 = 290. Thus, RA = 48.33 kN. Then, RB = (50 + 20) - 48.33 = 21.67 kN.
Calculate bending moments at load points: M1m = RA × 1 = 48.33 kNm. M4m = RA × 4 - 50 × (4 - 1) = 48.33 × 4 - 150 = 193.32 - 150 = 43.32 kNm.
The bending moment diagram is a triangle-based shape with peaks at 1m (48.33 kNm) and 4m (43.32 kNm), decreasing linearly to zero at the supports. The qualitative deflected shape shows a smooth downward curve sagging between the supports, with the maximum deflection occurring between the two point loads.
A brass bar having cross sectional area of 1000 mm2 is subjected to axial forces as shown in figure 1, find the net deformation in the bar. Take E = 2.05 × 105 N/mm2.
Answer
The net deformation Δ is the algebraic sum of the deformations of individual segments of the bar, given by the formula Δ = Σ(PL / AE). Assuming the bar is divided into segments based on the applied axial forces, let the lengths be L1, L2, L3 and forces be P1, P2, P3.
Given A = 1000 mm2 and E = 2.05 × 105 N/mm2, the product AE = 2.05 × 108 N. The total deformation is calculated as:
Sum the products of force and length for each section, ensuring tensile forces are treated as positive and compressive forces as negative. Divide the resulting sum by 2.05 × 108 N to obtain the net deformation in mm. The final result represents the net change in length of the bar.
Draw stress - strain diagram with all salient points on it for ductile material.
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Calculate the power a shaft of 30 mm diameter that can transmit with a speed of 200 rpm. The permissible shear stress is 120 N/mm2. Take maximum torque as 30% more than the average torque.
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A bar of 30 mm diameter is subjected to a pull of 60 KN. The measured extension on gauge length of 200mm is 0.09mm and the change in diameter is 0.0039. Calculate the Poisson’s ratio and the value of the three moduli.
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A cantilever is 2m long and is subjected to a u.d.l. of 2 kN/m. The cross section of cantilever is tee section with flange 80 mm × 10 mm and web of 10 mm × 120 mm such that its total depth is 130 mm. The flange is at the top and web is vertical. Determine maximum tensile stress and compressive stress developed and their positions.
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A hollow rectangular beam section square in size having outer dimensions 120 mm × 120 mm with uniform thickness of material 20 mm is carrying a shear force of 125 kN. Calculate the maximum shear stress induced in the section.
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An I section beam 350 mm × 200 mm has a web thickness of 12.5 mm and a flange thickness of 25 mm. it carries a shearing force of 200 kN at a section. Sketch the shear stress distribution across the section.
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The cast iron beam is of T- section as show in the figure 2. The beam is simply supported on a span of 6 m. The beam carries a uniformly distributed load of 2kN/m on the entire length (span). Determine the maximum tensile and maximum compressive stress.
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Find the Euler’s crippling load for a hollow cylindrical steel column of 38 mm external diameter and 2.5 mm thick. Take length of the column as 2.3 m and hinged at its both ends. Take E = 205 kN/mm2. Also determine the crippling load by Rankine’s formula using fc = 335N/mm2 and a = 1/7500.
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Derive a relation for the Euler’s crippling load for a column when (a) it has both ends hinged and (b) both ends fixed. Also obtain a relation for the Rankine’s crippling load for columns.
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Analyze the portal frame shown below figure 3. By moment distribution method. Draw BMD.
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Develop the differential equations of equilibrium for 2-D and 3-D problems in elasticity using Cartesian coordinate system with detailed Illustrations.
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Derive Biharmonic equation in terms of Airy’s stress function.
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