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ENME 251Bachelor in Agriculture Engineering · Semester 41 Paper Available

Strength of Materials

Past examination question papers and complete curriculum syllabus for Strength of Materials (ENME 251), Bachelor in Agriculture Engineering Semester 4 under Institute of Engineering (IOE), Tribhuvan University.

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Note: This question paper file (3rd sem) was archived from an IOE exam session for the common Strength of Materials curriculum.

3rd-sem_Strength of Material.pdf

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Most Frequently Asked Questions

Top recurring IOE board exam questions for Strength 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

Curriculum Syllabus & Course Topics

Sourced from TU curriculum portal
Full Syllabus (PDF)
Chapter-wise Units & Micro-Syllabus Topics (8 Units)

  1. 1. Simple Stress and Strain

    • 1.1Introduction to strength of materials
    • 1.2Deformable bodies, external forces, internal stresses and strains
    • 1.3Types of stresses: Normal stress, shear stress, bearing stress
    • 1.4Material behavior under axial loading: Stress-strain diagram for mild steel, yield stress, proportional limit, elastic limit, Hooke’s law, Young’s modulus of elasticity, strain hardening, ultimate stress/strength, ductility, toughness, elastic and inelastic strains, concept of factor of safety and allowable/permissible stress
    • 1.5Stress-strain behavior for ductile and brittle materials, proof stress
    • 1.6Fatigue and creep strength
    • 1.7Thermal stress and strain in simple, compound, composite and indeterminate bars
    • 1.8Lateral strains and Poisson’s ratio
    • 1.9Shear deformation and shear angle; Hooke’s law for shearing deformations, modulus of rigidity
    • 1.10Multi-axial loading and generalized Hooke’s law
    • 1.11Definitions of isotropic, anisotropic and orthotropic materials
    • 1.12Volumetric stress-strain, bulk modulus
    • 1.13Relationships between elastic constants
    • 1.14Saint-Venant’s principle and stress concentrations
    • 1.15Elongation of bars under axial loadings: Uniform and varying cross- sections, tapered sections, compound and composite bars
    • 1.16Use of compatibility equations for axially loaded indeterminate bars

  2. 2. Geometric Properties of Sections

    • 2.1Axes of symmetry
    • 2.2Centre of gravity of plane and built-up sections
    • 2.3Moment of inertia of standard and built-up sections
    • 2.4Parallel and perpendicular axis theorems
    • 2.5Polar moment of inertia
    • 2.6Radius of gyration
    • 2.7Product moment of inertia
    • 2.8Principal axes and principal moment of inertia
    • 2.9Mohr’s circle for principle moment of inertia

  3. 3. Principal Stress Analysis in 2D Planes

    • 3.1Stresses in inclined plane: Normal stress under uniaxial loading, Normal and shear stress subjected to two mutually perpendicular planes
    • 3.2Principal planes and principal stresses
    • 3.3Relationships between normal and shear stresses
    • 3.4Maximum shear stresses
    • 3.5Mohr’s circle diagram for principal stresses

  4. 4. Principal Strain Analysis

    • 4.1Plane strain: Normal and shear strains in inclined planes
    • 4.2Principal strains, maximum in-plane shear strains and their positions
    • 4.3Mohr’s circle diagram for plane strain
    • 4.4Absolute maximum shear strain
    • 4.5Strain rosettes
    • 4.6Modes of failure for different materials
    • 4.7Introduction of failure theories

  5. 5. Thin Walled Vessels

    • 5.1Introduction and characteristics
    • 5.2Types of stresses and strains in cylindrical and spherical pressure vessels
    • 5.3Calculation of stresses and strains in pressure vessels

  6. 6. Torsion

    • 6.1Introduction to torsion
    • 6.2Stress-strain behavior in torsion
    • 6.3Derivation of torsion formula for a circular shaft
    • 6.4Torsional moments: Series and parallel combination of shafts and composite shaft
    • 6.5Torsional stress in shafts, torsional resilience
    • 6.6Comparison between solid and hollow shafts
    • 6.7Power transmitted by shafts
    • 6.8Statically indeterminate shafts
    • 6.9Introduction to non-circular shafts
    • 6.10Combined bending and torsion

  7. 7. Theory of Flexure

    • 7.1Introduction to flexure
    • 7.2Coplanar and pure bending
    • 7.3Derivation of bending equation
    • 7.4Distribution of bending stress across the different beam cross-sections
    • 7.5Analysis of beams for symmetric and composite sections
    • 7.6Shear equation, shear stress variation in rectangular, circular, I and T sections
    • 7.7Concept of slope and deflection in beams using double integration method: Simply supported and cantilever beams

  8. 8. Column Theory

    • 8.1Introduction: Buckling and stability of columns
    • 8.2Classification based on slenderness ratio
    • 8.3Effect of support conditions and effective length
    • 8.4Derivation of Euler’s formula for different end conditions, limitations and applicability
    • 8.5Intermediate columns: Rankine’s hypothesis
    • 8.6Introduction to uniaxial and biaxial eccentric loading, condition for no tension

Examination Scheme & Marks Distribution

Evaluation Structure

  • Final Board Theory Exam: 60 Marks (Pass mark: 24)
  • Internal Assessment: 40 Marks (Pass mark: 16)
  • Practical / Lab Exam: 25 or 50 Marks (Continuous lab evaluation + viva, where applicable)

* This is the general current IOE 60/40 scheme; verify course-specific details in the syllabus above.

Exam Preparation Guidelines

  • Review the available past examination paper to understand question styling, typical derivation topics, and marks allocation.
  • Cross-reference key answers with official syllabus units, standard textbooks, and lecture notes.
  • Structure answers with labeled diagrams, concise bullet points, and highlight final answers in numerical solutions.

Frequently Asked Questions (Strength of Materials)

Q: How can I download Strength of Materials past question papers?

You can preview or download the Strength of Materials question papers (PDF) directly using the built-in viewer on this page with zero redirects or paywalls.

Q: What is the pass mark for Strength of Materials?

The general current scheme is a 60-mark final theory exam and a 40-mark internal assessment, with pass marks of 24 and 16. Verify the course-specific syllabus above.

Q: Where can I find the complete syllabus for this subject?

The available chapter-wise syllabus and topic breakdown is indexed in the Syllabus section above, with links to the curriculum PDF source.

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