JNTU
JNTU B.Tech II STRENGTH OF MATERIALS - II Previous Question Paper (March - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
Derive the equation of torsion from fundamentals.
Answer
Consider a circular shaft of radius R and length L subjected to a torque T. Under torsion, a cross-section rotates by an angle θ relative to another cross-section at distance L. For a fiber at radius r, the shear strain γ is given by:
From Hooke's Law for shear, the shear stress τ is τ = Gγ, where G is the modulus of rigidity. Substituting γ:
Consider an elemental ring of radius r and thickness dr. The area is dA = 2πr dr. The resisting force dF = τ dA = (Gθ/L)r(2πr dr). The resisting torque dT = dF × r = (Gθ/L)2πr3 dr. Integrating over the entire cross-section from 0 to R:
where Ip = πD4/32 is the polar moment of inertia. Thus, the torsion equation is:
Find the power that can be transmitted by a 60mm diameter shaft at 160rpm, if the permissible shear stress is 80N/mm2 and the maximum torque is 30% greater than the mean torque.
Answer
Given: Diameter D = 60 mm, Speed N = 160 rpm, Permissible shear stress τ = 80 N/mm2, Tmax = 1.3 Tmean.
First, calculate the polar moment of inertia Ip:
Using the torsion equation τ = (Tmax × R) / Ip, where R = 30 mm:
Calculate mean torque Tmean:
Calculate power P transmitted:
A steel close coiled helical spring is subjected to an axial couple of 60kN-mm. The mean coil diameter of the spring is 75mm and the diameter of the spring wire is 8mm. If the number of coils of the spring is 15, find the bending stress induced in the wire and the increase in the number of turns.
Answer
Sign in to view the complete answer paper.
For a close-coiled helical spring subjected to an axial load of 300N having 12 coils of wire diameter of 16mm, and made with coil diameter of 250mm, find: (i) axial deflection, (ii) strain energy stored, (iii) maximum torsional shear stress in the wire. Take modulus of rigidity as 80GN/m2.
Answer
Sign in to view the complete answer paper.
Derive an expression for Euler’s critical load of a column with one end fixed and the other end hinged from the first principles.
Answer
Sign in to view the complete answer paper.
Determine the section of a cast iron hollow cylindrical column 3m long with both ends fixed, if it carries an axial load of 800kN. The ratio of internal to external diameter of the column is 5/8. Use Rankine’s formula by taking Rankine’s constant as 1/1600 and working crushing strength of material as 550N/mm2.
Answer
Sign in to view the complete answer paper.
Explain in brief about Prof. PERRY’S formula.
Answer
Sign in to view the complete answer paper.
Distinguish between Direct stress and Bending stress by means of diagram.
Answer
Sign in to view the complete answer paper.
A column is rectangular in cross section 400 × 500 mm. The column carries an eccentric loading of 460kN on one diagonal at a distance of quarter diagonal length from a corner. Calculate the stresses at all four corners. Also draw stress distribution diagram for any side.
Answer
Sign in to view the complete answer paper.
A square chimney, 30 m high, has a flue opening of size 1.5 m × 1.5 m. Find the minimum width required at the base for no tension if the masonry weights 20 kN/m3 and the wind pressure is 1.5kN/m2. The permissible stress in the masonry is 1kN/m2.
Answer
Sign in to view the complete answer paper.
A thin steel cylindrical shell of thickness 10mm, 1.5m diameter and 4.5m long is carrying a fluid at a pressure of 3.5N/mm2. Find the change in diameter, length and volume of the cylinder. Assume E = 2×105 N/mm2 and Poisson’s ratio = 0.25.
Answer
Sign in to view the complete answer paper.
A simply supported beam of span 4.5m has an I cross-section of size 150mm × 250mm × 10mm. The beam is subjected to a concentrated load of 125kN at the mid-span in a plane making an angle 300 with respect to vertical and passing through the centroid of the section. Determine the maximum stress developed in the section.
Answer
Sign in to view the complete answer paper.