JNTU
JNTU B.Tech II STRENGTH OF MATERIALS - I Previous Question Paper (October - 2020 - R16)
Answer any five questions. All questions carry equal marks.
Main
A tensile load of 40KN is acting on a rod of diameter 40mm and of length 4.0m. A bore of diameter 20mm is made centrally on the rod. To what length the rod should be bored, so that the total extension will increase 30% under the same tensile load. Take
Answer
Given data:
Load (P) = 40 kN = 40,000 N
Outer diameter (D) = 40 mm
Inner diameter (d) = 20 mm
Total length (L) = 4,000 mm
Young's modulus (E) = 2 × 105 N/mm2
Area of solid rod (A1) = (π/4) × 402 = 1256.64 mm2
Area of bored section (A2) = (π/4) × (402 - 202) = 942.48 mm2
Original extension (δL) = (P × L) / (A1 × E) = (40,000 × 4,000) / (1256.64 × 2 × 105) = 0.6366 mm
Increased extension (δL') = 1.30 × 0.6366 = 0.8276 mm
Let 'x' be the length of the bored portion. The remaining length (4000 - x) is the solid rod.
The total extension is the sum of extensions of the two parts:
Substituting the values:
Solving for x:
The rod should be bored to a length of approximately 3600.75 mm.
Two bars A and B of variable diameter as shown in Figure 1 are made of the same material. The bar ‘A’ receives an axial blow which produces a Max. stress of 20KN/cm2. Determine the Maximum stress produced by the same blow on bar ‘B’. If the bar B is also stressed to 20KN/cm2, determine the ratio of strain energies stored in the bar A and B.
Answer
When a bar is subjected to an axial blow (impact load), the strain energy stored in the bar is equal to the work done by the falling weight. The maximum stress induced in a bar of variable cross-section is given by the relation involving the strain energy density. For a bar of length L and varying cross-sectional area A, the strain energy U is expressed as the integral of (σ2 / 2E) dV over the volume. Since the same blow (same energy U) is applied to both bars, the maximum stress σ is proportional to the square root of the stiffness properties of the bars.
For bar A, the maximum stress is σA = 20 kN/cm2. Given the geometry of the bars, the maximum stress produced in bar B (σB) is determined by the ratio of their respective volumes and cross-sectional areas. Assuming the bars are stepped or tapered as per standard variable diameter problems, σB = σA * sqrt(VA / VB), where V is the effective volume capacity to absorb energy.
To determine the ratio of strain energies stored when both bars are stressed to the same limit of 20 kN/cm2, we use the formula for strain energy U = ∫ (σ2 / 2E) dV. Since σ and E are identical for both bars, the ratio of strain energies is equal to the ratio of their volumes:
By calculating the volumes VA and VB based on the provided diameters and lengths in the figure, the ratio is obtained. If the bars have the same material properties and are subjected to the same stress, the energy stored is directly proportional to the total volume of the material in each bar.
Draw the BMD and SFD for the beam shown in Figure 2.
Answer
Sign in to view the complete answer paper.
Draw the B.M and S.F. diagrams for the beam as shown in Figure 3.
Answer
Sign in to view the complete answer paper.
Compare the flexural strength of the following two beams of equal weight:
I-section 20cm×15cm, having 2cm as flange thickness and 1cm as web thickness.
Answer
Sign in to view the complete answer paper.
Rectangular section having depth equal to 1.75width.
Answer
Sign in to view the complete answer paper.
An I-section beam of flanges 20cm×2cm and web 30cm×1cm is acted on by a shearing force of 150KN. Determine:
The maximum and minimum shearing stress in the web
Answer
Sign in to view the complete answer paper.
The maximum shear stress in the flange.
Answer
Sign in to view the complete answer paper.
Determine the slope and deflection at the free end of a cantilever beam loaded as shown in Figure 4 take I = M.I and E = young’s modulus. Use Conjugate beam method.
Answer
Sign in to view the complete answer paper.
What is Mohr’s stress circle? What is the importance of this circle and explain how these circles are drawn for 2D state of stress?
Answer
Sign in to view the complete answer paper.