JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year STRENGTH OF MATERIALS - I Previous Question Paper (October - 2020 - R18)
Answer any five questions. All questions carry equal marks.
Main
Derive the relationship between the three elastic constants.
Answer
1. Relationship between E, G, and μ:
Consider a square element subjected to pure shear. The shear strain γ is related to the principal strains. The relationship is:
2. Relationship between E, K, and μ:
Consider a cube subjected to hydrostatic stress σ in all three directions. The volumetric strain εv is the sum of linear strains. The relationship is:
3. Combined relationship:
By eliminating μ from the above equations, we obtain the relationship between all three constants:
Derive an expression for strain energy stored in a body when the load is applied with an impact.
Answer
- Let 'P' be the load, 'h' the height of fall, and 'E' Young's modulus.
- The total energy lost by the falling weight is the potential energy: U = P(h + δ)
- The strain energy stored in the bar is: U = (σ²/2E) * AL
- Equating the potential energy to the strain energy: P(h + δ) = (σ²/2E) * AL
- Substituting δ = (σL / E): P(h + σL/E) = (σ²AL / 2E)
- Rearranging into a quadratic equation in terms of σ: σ² - (2P/A)σ - (2PhE / AL) = 0
- Solving for σ (impact stress): σ = (P/A) * [1 + sqrt(1 + 2AEh / PL)]
A steel tube of internal diameter 100mm and external diameter 125mm is surrounded by a brass tube of external diameter 150mm. The composite bar is subjected to an axial pull of 10KN. Find the load carried by each tube and the stresses and strains developed in them if Es= 200GPa and Eb= 100GPa.
Answer
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A simply supported beam AB of span 10m carries a UDL of 20N/m over 3m from left hand support and also over 4m from the right-hand support. It has also two isolated loads of 20KN and 60KN at 3m and 8m respectively from the left hand support. Draw the B.M and S.F diagrams and calculate the B.M at significant points.
Answer
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Construct S.F.D and B.M.D for a simply supported beam shown in Figure.
Answer
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Obtain the shear stress distribution for a rectangular cross section 230×40mm subjected to a shear force of 40KN. Calculate the maximum and average shear stress.
Answer
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Derive the bending equation from fundamentals
Answer
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Determine slope and deflection of a cantilever loaded with a point at the free end using Moment Area method.
Answer
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Find the deflection at the free end of a cantilever of length ‘L’ subjected to UDL of intensity ‘w’ per unit length over its entire span. Use Double integration method.
Answer
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Derive an expression for the distortion energy per unit volume when a body is subjected to principal stresses σ1, σ2 and σ3.
Answer
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