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ENCE 252Bachelor in Civil Engineering · Semester 41 Paper Available

Theory of Structures II

Past examination question papers and complete curriculum syllabus for Theory of Structures II (ENCE 252), Bachelor in Civil Engineering Semester 4 under Institute of Engineering (IOE), Tribhuvan University.

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Most Frequently Asked Questions

Top recurring IOE board exam questions for Theory of Structures II with verified mark schemes, formula notation, and recurrence frequency.

Showing 30 of 30 top repeated questions

Theorem of Displacements

3 Questions
#1Repeated 5 Times[6 Marks]Theorem of Displacements
State and theoretically prove Maxwell's theorem of reciprocal deflections and Betti's law. Discuss their practical importance in structural analysis.
Appeared in:2081 Baishakh2080 Bhadra2078 Bhadra2075 Ashwin2071 Bhadra
#2Repeated 5 Times[8 Marks]Theorem of Displacements
State Castigliano's first and second theorems. Use Castigliano's theorem to determine the reactions, slopes, and deflections of a propped cantilever beam and a two-span continuous beam.
Appeared in:2083 Baishakh2082 Bhadra2081 Baishakh2079 Bhadra2076 Ashwin
#3Repeated 3 Times[6 Marks]Theorem of Displacements
State and explain Castigliano's Theorem of Least Work and Principle of Stationary Total Potential Energy in displacement-based structural mechanics.
Appeared in:2082 Bhadra2081 Chaitra2076 Chaitra

Force Method

4 Questions
#1Repeated 5 Times[8 Marks]Force Method
Derive the Three-Moment Equation (Clapeyron's theorem) for a continuous beam. Analyze a continuous beam with support settlement using the three-moment equation and draw its BMD.
Appeared in:2083 Baishakh2081 Baishakh2080 Baishakh2078 Bhadra2074 Ashwin
#2Repeated 5 Times[12 Marks]Force Method
Describe the Flexibility Matrix Method (Force Method) with system governing equations. Compute the redundants and member forces of an indeterminate plane truss subjected to external joint loads, temperature rise in members, and member fabrication lack of fit.
Appeared in:2083 Baishakh2082 Bhadra2081 Baishakh2080 Bhadra2078 Kartik
#3Repeated 4 Times[10 Marks]Force Method
Analyze a portal frame with pinned or fixed supports using the force method (consistent deformation method) and draw the bending moment, shear force, and axial force diagrams.
Appeared in:2082 Bhadra2080 Baishakh2076 Ashwin2073 Shrawan
#4Repeated 3 Times[8 Marks]Force Method
Analyze a continuous beam of two unequal spans with support settlement using the Force Method (Method of Consistent Deformations). Select redundant reactions, form compatibility equations using flexibility coefficients ($f_{ij}$), and draw final SFD and BMD.
Appeared in:2082 Bhadra2081 Chaitra2078 Bhadra

Analysis of Indeterminate Arches

4 Questions
#1Repeated 4 Times[10 Marks]Analysis of Indeterminate Arches
Analyze a two-hinged parabolic arch subjected to concentrated point loads and UDL using the elastic center method. Derive the expression for horizontal thrust H taking rib shortening into account.
Appeared in:2082 Bhadra2080 Baishakh2078 Bhadra2075 Ashwin
#2Repeated 4 Times[8 Marks]Analysis of Indeterminate Arches
Analyze a fixed parabolic arch subjected to temperature variation and yielding of abutments. Determine the bending moment, normal thrust, and radial shear at the crown and support sections.
Appeared in:2082 Bhadra2079 Bhadra2076 Ashwin2072 Kartik
#3Repeated 3 Times[8 Marks]Analysis of Indeterminate Arches
Analyze a Two-Hinged Parabolic Arch using the Force Method. Derive the formula for horizontal thrust $H = \frac{\int \frac{M_0 y dx}{E I}}{\int \frac{y^2 dx}{E I}}$ under central point load and uniformly distributed load, accounting for temperature change $\Delta T$.
Appeared in:2082 Bhadra2080 Chaitra2078 Bhadra
#4Repeated 3 Times[8 Marks]Analysis of Indeterminate Arches
Explain Fixed Arches (Symmetric fixed parabolic arch). Formulate the three compatibility equations to determine redundant forces ($H, V, M$) using the Elastic Center Method.
Appeared in:2082 Bhadra2081 Chaitra2076 Chaitra

Slope Deflection Method

3 Questions
#1Repeated 5 Times[10 Marks]Slope Deflection Method
Write down the slope-deflection equations for a prismatic beam member including the effect of support settlement. Analyze a two-span continuous beam where an intermediate support yields by a specified amount and draw the final BMD.
Appeared in:2083 Baishakh2082 Bhadra2081 Baishakh2080 Bhadra2078 Bhadra
#2Repeated 5 Times[12 Marks]Slope Deflection Method
Analyze a single-bay, single-story portal frame with sidesway using the slope deflection method. Formulate the joint equilibrium and shear equations, determine the end moments, and sketch the deflected shape.
Appeared in:2083 Baishakh2080 Baishakh2079 Bhadra2075 Ashwin2071 Bhadra
#3Repeated 3 Times[10 Marks]Slope Deflection Method
Analyze an indeterminate rigid portal frame with lateral sway using the Slope-Deflection Method. Set up slope-deflection equations, joint equilibrium equations, and column shear equation to solve for rotational and sway displacements, and sketch BMD.
Appeared in:2082 Bhadra2080 Chaitra2077 Magh

Moment Distribution Method

4 Questions
#1Repeated 5 Times[6 Marks]Moment Distribution Method
Explain the terms: Stiffness factor, Distribution factor, Carry-over factor, and Carry-over moment in the Moment Distribution Method. Prove that the carry-over factor for a prismatic member with fixed far end is +1/2.
Appeared in:2080 Bhadra2078 Bhadra2076 Ashwin2074 Ashwin2070 Chaitra
#2Repeated 5 Times[12 Marks]Moment Distribution Method
Analyze a rigid frame with sidesway subjected to vertical and lateral loads using the moment distribution method. Perform non-sway and sway distribution, calculate the sway correction factor, and plot the final bending moment diagram.
Appeared in:2082 Bhadra2081 Baishakh2080 Baishakh2078 Bhadra2073 Shrawan
#3Repeated 3 Times[8 Marks]Moment Distribution Method
Analyze a two-span continuous beam with overhangs using the Moment Distribution Method (Hardy Cross Method) considering non-prismatic sections and support sinking. Determine distribution factors and draw final BMD.
Appeared in:2082 Bhadra2081 Chaitra2079 Chaitra
#4Repeated 3 Times[10 Marks]Moment Distribution Method
Analyze a single-bay, single-story portal frame subjected to lateral unsymmetrical loading using the Moment Distribution Method with sway correction.
Appeared in:2082 Bhadra2080 Chaitra2076 Chaitra

Stiffness Matrix Method

4 Questions
#1Repeated 5 Times[8 Marks]Stiffness Matrix Method
Describe the Direct Stiffness Matrix Method for structural analysis. Formulate the member stiffness matrix in local coordinates and derive the transformation matrix to assemble the global structure stiffness matrix.
Appeared in:2083 Baishakh2082 Bhadra2081 Baishakh2079 Bhadra2076 Ashwin
#2Repeated 5 Times[12 Marks]Stiffness Matrix Method
Analyze a two-span continuous beam or rigid-jointed plane frame using the stiffness matrix method. Determine the unknown joint displacements, calculate member end actions, and plot the BMD.
Appeared in:2083 Baishakh2082 Bhadra2081 Baishakh2080 Bhadra2078 Kartik
#3Repeated 3 Times[10 Marks]Stiffness Matrix Method
Analyze a continuous beam using the Direct Stiffness Matrix Method. Assemble the global structure stiffness matrix $[K]$, displacement vector $\{\Delta\}$, and equivalent joint load vector $\{P\}$, and solve for unknown joint displacements and member end forces.
Appeared in:2082 Bhadra2081 Chaitra2078 Kartik
#4Repeated 3 Times[10 Marks]Stiffness Matrix Method
Apply the Direct Stiffness Matrix Method to analyze a pin-jointed plane truss. Formulate member stiffness matrices in local and global coordinate systems using transformation matrix $[T]$: $[K_m] = [T]^T [k_m] [T]$.
Appeared in:2082 Bhadra2080 Chaitra2077 Magh

Influence Line for Indeterminate Beams

3 Questions
#1Repeated 5 Times[6 Marks]Influence Line for Indeterminate Beams
State and explain the Müller-Breslau principle. Prove that the Müller-Breslau principle is applicable to indeterminate beams as well as determinate structures.
Appeared in:2083 Baishakh2080 Bhadra2078 Bhadra2076 Ashwin2074 Ashwin
#2Repeated 5 Times[8 Marks]Influence Line for Indeterminate Beams
Using the Müller-Breslau principle, draw the influence line diagram for the intermediate support reaction and central bending moment of a two-span continuous beam by computing ordinates at 1 m intervals.
Appeared in:2083 Baishakh2082 Bhadra2080 Baishakh2078 Bhadra2075 Ashwin
#3Repeated 3 Times[8 Marks]Influence Line for Indeterminate Beams
State and explain the Müller-Breslau Principle for indeterminate structures. Draw qualitative and quantitative Influence Line Diagrams for reaction at intermediate support, shear force, and bending moment for a propped cantilever beam.
Appeared in:2082 Bhadra2081 Chaitra2079 Chaitra

Introduction to Plastic Analysis

5 Questions
#1Repeated 5 Times[6 Marks]Introduction to Plastic Analysis
Define plastic hinge, shape factor, load factor, and plastic section modulus. Calculate the shape factor for rectangular, circular, and standard I-sections.
Appeared in:2081 Baishakh2080 Bhadra2078 Bhadra2075 Ashwin2070 Ashad
#2Repeated 5 Times[10 Marks]Introduction to Plastic Analysis
State and explain the Upper Bound (Kinematic) and Lower Bound (Static) theorems of plastic collapse. Determine the plastic moment capacity Mp or collapse load Wc for a portal frame under combined vertical and lateral loading.
Appeared in:2083 Baishakh2082 Bhadra2080 Baishakh2079 Bhadra2076 Ashwin
#3Repeated 3 Times[8 Marks]Introduction to Plastic Analysis
Explain Plastic Analysis of steel structures. Define Plastic Moment capacity ($M_p$), Shape Factor ($S = Z_p / Z_e$), Plastic Hinge, and Upper Bound (Kinematic) and Lower Bound (Static) theorems of plastic collapse.
Appeared in:2082 Bhadra2080 Chaitra2077 Magh
#4Repeated 3 Times[8 Marks]Introduction to Plastic Analysis
Determine the Plastic Collapse Load ($W_c$) for a fixed-ended beam and propped cantilever beam carrying uniformly distributed load using the virtual work kinematic mechanism method.
Appeared in:2082 Bhadra2081 Chaitra2078 Kartik
#5Repeated 3 Times[8 Marks]Introduction to Plastic Analysis
Determine the Plastic Collapse Load for a single-bay portal frame under combined vertical load $W$ and horizontal lateral load $H$, testing beam mechanism, sway mechanism, and combined mechanism.
Appeared in:2082 Bhadra2080 Chaitra2079 Chaitra

Curriculum Syllabus & Course Topics

Sourced from TU curriculum portal
Full Syllabus (PDF)
Chapter-wise Units & Micro-Syllabus Topics (9 Units)

  1. 1. Introduction

    • 1.1Types of indeterminate structures
    • 1.2Boundary conditions and degree of freedoms
    • 1.3Static and kinematic indeterminacy
    • 1.4Structure idealization, local and global coordinate systems, deformations and their sign conventions
    • 1.5Determination of degree of static indeterminacy of a system: Use of formula, necessity of visual checking for plane systems in the form of beam, frame, truss and arch
    • 1.6Degree of kinematic indeterminacy of a system and its determination: Use of formula, necessity of visual checking for plane systems in the form of beam, frame, truss and arch
    • 1.7Definitions and explanations of force and displacement, flexibility and stiffness and their relationship

  2. 2. Theorem of Displacements

    • 2.1Force and displacements as cause and effects
    • 2.2Castigliano’s theorems and their applications
    • 2.3Analyses of simple systems like beam, frame and truss
    • 2.4Bending moment, shear force and normal thrust diagrams for beam, truss and frames

  3. 3. Force Method

    • 3.1Definitions and explanations; Specialties of force method and its limitations
    • 3.2Consistent deformation systems; Compatibility equations, primary structures, choice of redundant
    • 3.3Flexibility method: Use in beam, frame and trusses; Yielding of supports in beam, truss and frames; Temperature effects and misfits in truss
    • 3.4Flexibility matrix method
    • 3.5Graph multiplication approach for simple cases
    • 3.6Three moment theorem and its application
    • 3.7Introduction to focal point method

  4. 4. Analysis of Indeterminate Arches

    • 4.1Use of arches in modern constructions
    • 4.2Horizontal reaction for parabolic and circular two-hinged and fixed arches
    • 4.3Bending moment, shear force and normal thrust diagrams
    • 4.4Yielding of supports, temperature effect and rib shortening
    • 4.5Influence line diagrams for horizontal thrust, bending moment at span, normal thrust and radial shear for two hinged arches

  5. 5. Slope Deflection Method

    • 5.1Introduction and sign conventions
    • 5.2Formulation of slope deflection equation
    • 5.3Fixed end moments
    • 5.4Application in beam and frames with support settlements and rotations
    • 5.5Bending moment, shear force and normal thrust diagrams for beam and frames

  6. 6. Moment Distribution Method

    • 6.1Introduction, terminology and development of method
    • 6.2Distribution factors
    • 6.3Carry over moments
    • 6.4Application in beam and frames: Symmetry and anti-symmetry, sway conditions and support yielding
    • 6.5Bending moment, shear force and normal thrust diagrams for beam and frames

  7. 7. Stiffness Matrix Method

    • 7.1Definition of stiffness, choice of redundant and degree of freedoms
    • 7.2Member stiffness matrix for spring, bar, truss and beam elements
    • 7.3Rotation matrices
    • 7.4Analysis of multiple spring connected systems, bar and string combinations, simple two-dimensional trusses
    • 7.5Applications to beams and two-dimensional frames, effects of settlement of support and temperature
    • 7.6Application in space/three-dimensional truss
    • 7.7Bending moment, shear force and normal thrust diagrams for beam and frames
    • 7.8Introduction to structural engineering related software

  8. 8. Influence Line for Indeterminate Beams

    • 8.1Necessity of influence line diagrams
    • 8.2Muller Breslau principle, its physical meaning and use
    • 8.3Influence line diagrams for reactions, bending moment and shear force in various sections of continuous beams (Two to three spans only)
    • 8.4Use of influence line diagrams to calculate reactions, shear forces and bending moments for concentrated force, couple and distributed load

  9. 9. Introduction to Plastic Analysis

    • 9.1Definitions and explanations
    • 9.2Plastic analysis of bending members
    • 9.3Plastic hinge and its length
    • 9.4Load factor, shape factor and plastic modulus
    • 9.5Basic theorems on methods of limit analysis
    • 9.6Collapse loads: partial collapse, complete collapse
    • 9.7Collapse with tied loads for simple cases of statically indeterminate beams (Not more than three spans) and frames (Only portal frames)

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 (Theory of Structures II)

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Q: What is the pass mark for Theory of Structures II?

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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