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Stregth of Materials

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Most Frequently Asked Questions

Top recurring IOE board exam questions for Stregth of Materials with verified mark schemes, formula notation, and recurrence frequency.

Showing 30 of 30 top repeated questions

Simple Stress and Strain

7 Questions

#1Repeated 4 Times[6 Marks]Simple Stress and Strain

Derive the mathematical relationship between the elastic constants: Young's Modulus ($E$), Shear Modulus ($G$), Bulk Modulus ($K$), and Poisson's ratio ($\nu$): $E = 2G(1+\nu) = 3K(1-2\nu) = \frac{9KG}{3K+G}$.

Appeared in:2083 Baishakh2082 Baishakh2081 Bhadra2078 Bhadra

#2Repeated 4 Times[8 Marks]Simple Stress and Strain

A rigid bar $ABC$ is hinged at one end and supported by vertical steel and copper/aluminum rods. Determine the forces developed in each rod and vertical displacement under an applied vertical load.

Appeared in:2083 Baishakh2081 Bhadra2080 Baishakh2078 Bhadra

#3Repeated 3 Times[8 Marks]Simple Stress and Strain

Explain Theories of Failure for isotropic ductile and brittle materials: Maximum Principal Stress Theory (Rankine), Maximum Shear Stress Theory (Tresca), and Maximum Distortion Energy Theory (von Mises).

Appeared in:2082 Bhadra2080 Chaitra2077 Magh

#4Repeated 3 Times[8 Marks]Simple Stress and Strain

Derive the relationships between Elastic Constants: Young's Modulus of Elasticity ($E$), Shear Modulus ($G$), Bulk Modulus ($K$), and Poisson's Ratio ($\nu$): $E = 2G(1 + \nu) = 3K(1 - 2\nu)$.

Appeared in:2082 Bhadra2081 Chaitra2078 Bhadra

#5Repeated 3 Times[8 Marks]Simple Stress and Strain

Calculate Thermal Stresses and strains developed in a composite bar made of copper and steel components rigidly connected together at both ends when subjected to a uniform temperature change $\Delta T$.

Appeared in:2082 Bhadra2080 Chaitra2079 Chaitra

#6Repeated 2 Times[6 Marks]Simple Stress and Strain

Derive the expression for total elongation of a uniformly tapering circular bar of length $L$ tapering from diameter $d_1$ to $d_2$ under axial tensile load $P$: $\delta = \frac{4PL}{\pi E d_1 d_2}$.

Appeared in:2080 Baishakh2078 Bhadra

#7Repeated 2 Times[8 Marks]Simple Stress and Strain

A compound bar consisting of a steel tube and an internal copper rod is rigidly connected at both ends. Determine the thermal stresses developed in steel and copper when the temperature rises by $\Delta T$.

Appeared in:2080 Baishakh2078 Bhadra

Geometric Properties of Sections

3 Questions

#1Repeated 5 Times[8 Marks]Geometric Properties of Sections

For a given unsymmetrical structural section (angle section, Z-section, channel section), determine centroid $(\bar{x}, \bar{y})$, moments of inertia $I_x, I_y$, product of inertia $I_{xy}$, and calculate principal moments of inertia ($I_u, I_v$) and orientation of principal axes.

Appeared in:2083 Baishakh2082 Baishakh2081 Bhadra2080 Baishakh2078 Bhadra

#2Repeated 3 Times[8 Marks]Geometric Properties of Sections

State the Parallel Axis Theorem and Perpendicular Axis Theorem. Calculate the centroid and second moments of area ($I_{xx}, I_{yy}$) of an asymmetrical T-section or channel section.

Appeared in:2082 Bhadra2081 Chaitra2076 Chaitra

#3Repeated 2 Times[4 Marks]Geometric Properties of Sections

State and prove the Parallel Axis Theorem for product of inertia ($I_{xy} = I_{\bar{x}\bar{y}} + A \bar{x}\bar{y}$).

Appeared in:2081 Bhadra2078 Bhadra

Principal Stress Analysis in 2D Planes

2 Questions

#1Repeated 4 Times[8 Marks]Principal Stress Analysis in 2D Planes

For a two-dimensional state of plane stress subjected to normal stresses $\sigma_x, \sigma_y$ and shear stress $\tau_{xy}$, determine: (a) Principal stresses $\sigma_1, \sigma_2$ and orientation of principal planes, (b) Maximum in-plane shearing stress $\tau_{\max}$, and (c) Verify results using Mohr's Circle of stress.

Appeared in:2083 Baishakh2082 Baishakh2081 Bhadra2080 Baishakh

#2Repeated 3 Times[8 Marks]Principal Stress Analysis in 2D Planes

Derive expressions for Principal Stresses ($\sigma_1, \sigma_2$), maximum shear stress $\tau_{max} = \frac{\sigma_1 - \sigma_2}{2}$, and principal plane angle ($\theta_p$) for a 2D stress element ($\sigma_x, \sigma_y, \tau_{xy}$). Draw and explain Mohr's Circle of Stresses.

Appeared in:2082 Bhadra2081 Chaitra2076 Chaitra

Thin Walled Vessels

2 Questions

#1Repeated 4 Times[8 Marks]Thin Walled Vessels

Prove that circumferential (hoop) stress in a thin cylinder subjected to internal fluid pressure $p$ is twice the longitudinal stress ($\sigma_h = \frac{pd}{2t}, \sigma_L = \frac{pd}{4t}$). Derive formulas for volumetric strain and change in internal volume.

Appeared in:2083 Baishakh2082 Baishakh2081 Bhadra2078 Bhadra

#2Repeated 3 Times[8 Marks]Thin Walled Vessels

Derive formulas for Circumferential (Hoop) Stress $\sigma_h = \frac{p d}{2t}$ and Longitudinal Stress $\sigma_l = \frac{p d}{4t}$ in a thin cylindrical pressure vessel under internal fluid pressure $p$. Calculate maximum shear stress and volumetric strain.

Appeared in:2082 Bhadra2080 Chaitra2078 Kartik

Torsion

3 Questions

#1Repeated 4 Times[8 Marks]Torsion

Derive the torsion formula $\frac{T}{J} = \frac{\tau}{R} = \frac{G\theta}{L}$. Prove that a hollow circular shaft has greater torque transmission capacity and stiffness than a solid shaft of identical weight and material cross-sectional area.

Appeared in:2083 Baishakh2082 Baishakh2081 Bhadra2078 Bhadra

#2Repeated 3 Times[8 Marks]Torsion

A hollow steel shaft having outer diameter $D$ and inner diameter $d$ transmits specified power at given RPM. If maximum shear stress is limited to $\tau_{\text{allow}}$ and twist angle to $\theta_{\text{allow}}$, determine suitable shaft dimensions.

Appeared in:2082 Baishakh2081 Bhadra2078 Bhadra

#3Repeated 3 Times[8 Marks]Torsion

Derive the Torsion Equation for circular solid and hollow shafts: $\frac{T}{J} = \frac{\tau}{r} = \frac{G \theta}{L}$. Calculate the power transmitted $P = \frac{2\pi N T}{60}$ and polar section modulus ($Z_p$) for a solid shaft.

Appeared in:2082 Bhadra2081 Chaitra2079 Chaitra

Theory of Flexure

9 Questions

#1Repeated 4 Times[8 Marks]Theory of Flexure

Determine the slope and deflection at the free end of a cantilever beam or at the center of a simply supported beam subjected to point loads and UDL using Macaulay's method or Moment-Area theorems.

Appeared in:2083 Baishakh2082 Baishakh2081 Bhadra2078 Bhadra

#2Repeated 4 Times[10 Marks]Theory of Flexure

For a given planar frame carrying concentrated loads and UDL, compute support reactions and draw Axial Force Diagram (AFD), Shear Force Diagram (SFD), and Bending Moment Diagram (BMD) indicating salient points and points of contraflexure.

Appeared in:2083 Baishakh2081 Bhadra2080 Baishakh2078 Bhadra

#3Repeated 3 Times[8 Marks]Theory of Flexure

Derive the Bending Formula (Flexure formula) for beams under pure bending: $\frac{M}{I} = \frac{\sigma}{y} = \frac{E}{R}$. State assumptions in Euler-Bernoulli beam theory and define Section Modulus ($Z$).

Appeared in:2082 Bhadra2081 Chaitra2078 Kartik

#4Repeated 3 Times[8 Marks]Theory of Flexure

Derive the Shear Stress formula for beams: $\tau = \frac{V Q}{I b}$. Plot the shear stress distribution across rectangular, circular, I-section, and T-section beam profiles.

Appeared in:2082 Bhadra2080 Chaitra2077 Magh

#5Repeated 3 Times[8 Marks]Theory of Flexure

Derive the Differential Equation of Beam Deflection $E I \frac{d^2 y}{dx^2} = M(x)$. Apply Macaulay's Method to find slope and deflection at the center of a simply supported beam with asymmetric point loads.

Appeared in:2082 Bhadra2080 Chaitra2076 Chaitra

#6Repeated 3 Times[8 Marks]Theory of Flexure

Apply Moment-Area Theorems (Mohr's Theorems) and Conjugate Beam Method to calculate the maximum deflection and slope for a cantilever beam carrying an end point load and uniformly distributed load.

Appeared in:2082 Bhadra2081 Chaitra2078 Bhadra

#7Repeated 3 Times[8 Marks]Theory of Flexure

Draw the Shear Force Diagram (SFD) and Bending Moment Diagram (BMD) for a simply supported beam with an overhang carrying a uniformly distributed load and point loads. Identify points of zero shear, maximum positive/negative bending moments, and points of contraflexure.

Appeared in:2082 Bhadra2080 Chaitra2078 Kartik

#8Repeated 2 Times[8 Marks]Theory of Flexure

Derive the horizontal shear stress formula in a beam cross-section: $\tau = \frac{V Q}{I b}$. Plot the shear stress distribution across the depth of an I-beam, T-beam, and rectangular beam.

Appeared in:2078 Bhadra2076 Chaitra

#9Repeated 2 Times[6 Marks]Theory of Flexure

Derive the flexure formula for pure bending of beams: $\frac{M}{I} = \frac{\sigma}{y} = \frac{E}{R}$. Define section modulus ($Z$) and moment of resistance.

Appeared in:2080 Baishakh2076 Chaitra

Column Theory

4 Questions

#1Repeated 4 Times[8 Marks]Column Theory

State the assumptions and derive Euler's formula for the critical buckling load of an ideal column of length $L$ and flexural rigidity $EI$ with: (a) Both ends hinged ($P_{\text{cr}} = \frac{\pi^2 EI}{L^2}$), and (b) One end fixed and other end free ($P_{\text{cr}} = \frac{\pi^2 EI}{4L^2}$).

Appeared in:2083 Baishakh2082 Baishakh2081 Bhadra2080 Baishakh

#2Repeated 3 Times[8 Marks]Column Theory

Derive Euler's Critical Buckling Load for an ideal column with both ends hinged: $P_{cr} = \frac{\pi^2 E I}{L^2}$. State effective lengths ($L_e$) for various end conditions and explain the slenderness ratio limitation ($\lambda = L_e / r_{min}$).

Appeared in:2082 Bhadra2080 Chaitra2077 Magh

#3Repeated 3 Times[8 Marks]Column Theory

Explain the Rankine-Gordon Formula for intermediate columns: $\frac{1}{P_R} = \frac{1}{P_c} + \frac{1}{P_E}$. Show that $P_R = \frac{\sigma_c A}{1 + a (L_e / r)^2}$ and compare with Euler's buckling curve.

Appeared in:2082 Bhadra2081 Chaitra2079 Chaitra

#4Repeated 2 Times[6 Marks]Column Theory

Explain the limitations of Euler's formula for short and intermediate columns. Derive the Rankine-Gordon empirical formula $\frac{1}{P_R} = \frac{1}{P_c} + \frac{1}{P_e}$ and define slenderness ratio.

Appeared in:2081 Bhadra2078 Bhadra