Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech II Year ELEMENTS OF MECHANICAL ENGINEERING Previous Question Paper (March - 2021 - R15 / R13)
Answer any five questions. All questions carry equal marks.
Main
Define E, K and N and derive relation between E and N.
Answer
E (Young's Modulus) is the ratio of longitudinal stress to longitudinal strain within the elastic limit. K (Bulk Modulus) is the ratio of direct stress to volumetric strain. N (Modulus of Rigidity) is the ratio of shear stress to shear strain. The relation between E and N is derived using a square element subjected to pure shear stress τ. The shear strain is φ = τ/N. By considering the diagonal extension, the normal strain on the diagonal is ε = φ/2 = τ/(2N). In terms of principal stresses, the strain on the diagonal is ε = (τ/E) - (-τ/E) * ν = τ(1+ν)/E. Equating these, τ/(2N) = τ(1+ν)/E, which yields E = 2N(1+ν).
Derive the strain and stress for a vertical bar due to self-weight.
Answer
Consider a vertical bar of length L, cross-sectional area A, and weight density ρ. For an elemental length dx at a distance x from the bottom, the weight acting on it is W = ρ * A * x. The stress at this section is σ = W/A = ρ * x. The maximum stress occurs at the top (x = L), where σ_max = ρ * L. The strain at any section is ε = σ/E = (ρ * x)/E. The total elongation δL is the integral of ε dx from 0 to L: δL = ∫(ρ * x / E) dx = (ρ * L^2) / (2E). Since the total weight W_total = ρ * A * L, the expression can also be written as δL = (W_total * L) / (2 * A * E).
State Hooks law.
Answer
Sign in to view the complete answer paper.
A copper rod of 40 mm diameter is surrounded tightly by a cast iron tube of 80 mm external diameter; the ends being firmly fastened together. Calculate the sharing of load when subject to a compressive load of 30 kN. Also, calculate the decrease in length of the composite system if it is 2 m long. Take ECU = 75 GPa and ECI = 175 GPa.
Answer
Sign in to view the complete answer paper.
A horizontal beam AD, 10 m long, carries a uniformly distributed load of 360 N/m run, together with a concentrated load of 900 N at the left-hand end A. The beam is supported at B, 1 m from A, and at C, which is the right-hand half of the beam, x m from D. Determine the value of x if the mid-point of the beam is a point of inflexion. Plot BM diagram.
Answer
Sign in to view the complete answer paper.
What are the assumptions made in simple theory of bending? Derive relation between bending moment and bending stress.
Answer
Sign in to view the complete answer paper.
A closed cylindrical drum 500 mm in diameter and 2 m long has a shell thickness of 12 mm. If it carries a fluid under a pressure of 2 N/mm2, calculate the longitudinal and hoop stress in the drum wall and also determine the change in diameter, change in length and change in volume of the drum. Take E = 200 GPa and 1/m = 0.3.
Answer
Sign in to view the complete answer paper.
A circular disc of uniform thickness, rotating about its axis. Derive the expression for radial and circumferential stresses.
Answer
Sign in to view the complete answer paper.
List out the difference between four stroke and 2 stroke engines.
Answer
Sign in to view the complete answer paper.
A petrol engine uses per kWh 0.26 kg of fuel of calorific value 44000 kJ/kg. The mechanical efficiency is 78% and the compression is 5.6 to 1. Calculate: i) brake thermal efficiency ii) indicated thermal efficiency.
Answer
Sign in to view the complete answer paper.
Derive the equation for length of open belt.
Answer
Sign in to view the complete answer paper.
A pulley is driven by a flat belt running at a speed of 600 m/min. The coefficient of friction between the pulley and the belt is 0.3 and the angle of lap is 1600. If the maximum tension in the belt is 700 N, find the power transmitted by a belt.
Answer
Sign in to view the complete answer paper.