JNTU
JNTU B.Tech II MECHANICS OF SOLIDS AND MECHANICS OF FLUIDS Previous Question Paper (October - 2020 - R16)
Answer any five questions. All questions carry equal marks.
Main
Write the relationship between bulk modulus, rigidity modulus and Poisson’s ratio.
Answer
The relationship between the elastic constants, namely Young's modulus (E), Rigidity modulus (G), Bulk modulus (K), and Poisson's ratio (μ), is defined by the following equations:
By eliminating E from these two equations, the relationship between K, G, and μ is derived as:
A bar of 25mm diameter is subjected to a pull of 40kN. The measured extension on gauge length of 200mm is 0.085mm and the change in diameter is 0.003mm. Calculate the value of Poisson’s ratio and the three moduli.
Answer
Given: Diameter (d) = 25 mm, Load (P) = 40,000 N, Gauge length (L) = 200 mm, Extension (ΔL) = 0.085 mm, Change in diameter (Δd) = 0.003 mm.
- Calculate Longitudinal strain (εL): εL = ΔL / L = 0.085 / 200 = 0.000425
- Calculate Lateral strain (εd): εd = Δd / d = 0.003 / 25 = 0.00012
- Poisson's ratio (μ): μ = εd / εL = 0.00012 / 0.000425 = 0.282
- Stress (σ): Area (A) = (π / 4) * 25^2 = 490.87 mm^2. σ = P / A = 40000 / 490.87 = 81.49 N/mm^2
- Young's Modulus (E): E = σ / εL = 81.49 / 0.000425 = 191,741 N/mm^2 (191.74 GPa)
- Rigidity Modulus (G): G = E / (2(1 + μ)) = 191741 / (2 * (1 + 0.282)) = 74,781 N/mm^2 (74.78 GPa)
- Bulk Modulus (K): K = E / (3(1 - 2μ)) = 191741 / (3 * (1 - 2 * 0.282)) = 147,143 N/mm^2 (147.14 GPa)
What are principal planes?
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A brass bar having cross-sectional area of 1000 mm2 is subjected to axial forces shown in the Figure. Find the total elongation of the bar, Modulus of elasticity of brass 100GN/m2.
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State the assumptions made in the theory of simple bending and derive the bending formula.
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A simply supported beam of span 4m carries a UDL of 6kN/m over the entire span. If the maximum allowable stress due to bending is restricted to 150 N/mm2, determine the cross-sectional dimensions if the section is:
a) Rectangular with depth twice the breadth
b) Solid circular section
c) Hollow circular section having a diameter ratio of 0.6.
Answer
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Derive the torsion equation
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60mm diameter shaft is subjected to torque of 4kNm. Find:
i) Maximum shear stress induced in the shaft
ii) Angle of twist per meter length of the shaft
iii) Shear stress at a distance of 10mm from the axis of the shaft. Take G=8×104 N/mm2.
Answer
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Derive expression for design of shaft under combined torque and bending moment.
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Find the power that can be transmitted by a shaft 60 mm diameter, at 180 r.p.m. if the permissible shear stress is 85 N/mm2.
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Define the following:
a) Atmospheric pressure
b) Gauge pressure
c) Vacuum pressure
d) Absolute pressure.
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Define streak line and streamline.
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Derive the expression for Bernoulli’s equation.
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