#1Repeated 4 Times[4 Marks]Introduction
What are the two basic approaches of structural analysis? Explain the principle of superposition and its limitations with illustrative examples.
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ENCE 202Bachelor in Architecture · Semester 31 Paper Available
Theory of Structures I
Past examination question papers and complete curriculum syllabus for Theory of Structures I (ENCE 202), Bachelor in Architecture Semester 3 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 I with verified mark schemes, formula notation, and recurrence frequency.
Showing 30 of 30 top repeated questions
Introduction
3 Questions#2Repeated 4 Times[4 Marks]Introduction
Explain the criteria for static determinacy, indeterminacy and stability of planar and spatial structures with neat sketches and examples.
Appeared in:2082 Kartik2078 Chaitra2075 Baisakh2072 Magh
#3Repeated 3 Times[6 Marks]Introduction
Differentiate between Static Indeterminacy ($D_s$) and Kinematic Indeterminacy ($D_k$). Formulate degree of static indeterminacy ($D_s = D_{se} + D_{si}$) and kinematic indeterminacy for plane frames, space frames, and pin-jointed trusses with rigid and semi-rigid joints.
Appeared in:2082 Bhadra2081 Chaitra2076 Chaitra
Strain Energy Method
4 Questions#1Repeated 5 Times[6 Marks]Strain Energy Method
Derive an expression for strain energy stored in a straight beam due to bending moment, axial force and shear force.
Appeared in:2080 Chaitra2079 Chaitra2078 Chaitra2075 Bhadra2071 Magh
#2Repeated 4 Times[6 Marks]Strain Energy Method
A 50 kg load drops by 10 cm on a simply supported beam of 4 m span having width 30 mm and depth 150 mm. E = 200 GPa. Use strain energy method to determine the maximum dynamic deflection and maximum bending stress induced in the beam.
Appeared in:2082 Kartik2079 Chaitra2076 Baisakh2073 Magh
#3Repeated 3 Times[8 Marks]Strain Energy Method
State Castigliano's First and Second Theorems. Apply Castigliano's Theorem to find the vertical and horizontal deflection at the free end of a curved quarter-circular cantilever beam or portal frame.
Appeared in:2082 Bhadra2081 Chaitra2078 Bhadra
#4Repeated 3 Times[8 Marks]Strain Energy Method
Explain Strain Energy stored due to axial force, bending moment ($U = \int \frac{M^2 dx}{2EI}$), shear force, and torsion. State and prove Betti's Law and Maxwell's Reciprocal Deflection Theorem.
Appeared in:2082 Bhadra2080 Chaitra2076 Chaitra
Virtual Work Method
4 Questions#1Repeated 5 Times[6 Marks]Virtual Work Method
State and prove the principle of virtual work (unit load method) for determining deflections in trusses and beams.
Appeared in:2082 Kartik2079 Chaitra2078 Chaitra2075 Baisakh2071 Bhadra
#2Repeated 5 Times[10 Marks]Virtual Work Method
For a pin-jointed plane truss, calculate the vertical and horizontal deflection at a loaded joint due to: (i) external joint loads, (ii) a temperature change of 20°C in bottom chord members, and (iii) a fabrication lack of fit where one diagonal member is 3 mm too long. Take A = 800 mm^2, E = 200 GPa, and α = 1.2 × 10^-5 /°C.
Appeared in:2081 Chaitra2082 Kartik2078 Chaitra2076 Baisakh2074 Bhadra
#3Repeated 3 Times[8 Marks]Virtual Work Method
Explain the Principle of Virtual Work (Unit Load Method) for trusses: $\Delta = \sum \frac{n N L}{A E}$. Determine the vertical deflection of a loaded lower chord joint of a statically determinate plane pin-jointed truss.
Appeared in:2082 Bhadra2080 Chaitra2077 Magh
#4Repeated 3 Times[8 Marks]Virtual Work Method
Use the Unit Load Method (Dummy Unit Load method) to determine the vertical deflection and slope at the mid-span of a simply supported beam with non-prismatic variable flexural rigidity $E I$.
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Deflection of Beams
2 Questions#1Repeated 5 Times[8 Marks]Deflection of Beams
State and prove Mohr's Moment-Area theorems. Determine the slope and deflection at the center and overhanging tip of a simply supported overhanging beam using moment-area method.
Appeared in:2082 Kartik2081 Chaitra2080 Chaitra2079 Chaitra2075 Bhadra
#2Repeated 5 Times[8 Marks]Deflection of Beams
Explain the conjugate beam method and its relationships with the real beam. Determine the slope and deflection at the free end and intermediate points of a stepped cantilever beam using the conjugate beam method.
Appeared in:2081 Chaitra2080 Chaitra2078 Chaitra2075 Baisakh2071 Magh
Influence Lines for Simple Structures
5 Questions#1Repeated 5 Times[6 Marks]Influence Lines for Simple Structures
Define Influence Line Diagram (ILD) and describe its practical importance in the design of bridges and moving load structures. Determine the criteria for absolute maximum bending moment in a simply supported girder.
Appeared in:2082 Kartik2081 Chaitra2079 Chaitra2076 Baisakh2074 Bhadra
#2Repeated 5 Times[8 Marks]Influence Lines for Simple Structures
A train of wheel loads crosses a simply supported girder of span 20 m from left to right. Determine: (i) the maximum bending moment and shear force at a section 8 m from the left support, and (ii) the absolute maximum bending moment developed in the girder.
Appeared in:2082 Kartik2081 Chaitra2079 Chaitra2078 Chaitra2075 Bhadra
#3Repeated 5 Times[8 Marks]Influence Lines for Simple Structures
Draw influence line diagrams for forces in members U1U2, U2L2, and L2L3 of a through-type Pratt truss. Determine the maximum forces in these members when a uniformly distributed load of intensity 20 kN/m and length 6 m passes through the bottom chord.
Appeared in:2082 Kartik2081 Chaitra2080 Chaitra2078 Chaitra2073 Magh
#4Repeated 3 Times[8 Marks]Influence Lines for Simple Structures
Construct Influence Line Diagrams (ILD) for support reactions, shear force, and bending moment at a given section $C$ of a simply supported beam. Calculate the maximum shear force and bending moment caused by a moving train of concentrated wheel loads.
Appeared in:2082 Bhadra2081 Chaitra2078 Kartik
#5Repeated 3 Times[8 Marks]Influence Lines for Simple Structures
Construct Influence Line Diagrams for axial forces in the top chord, bottom chord, and vertical/diagonal web members of a Pratt or Warren truss under a rolling unit load on the bottom deck.
Appeared in:2082 Bhadra2080 Chaitra2077 Magh
Statically Determinate Arches
5 Questions#1Repeated 5 Times[10 Marks]Statically Determinate Arches
A three-hinged parabolic arch of span 40 m and central rise 8 m carries a moving uniformly distributed load of 30 kN/m of length 15 m. With the help of influence lines, calculate the maximum positive and negative bending moments, radial shear and normal thrust at a section 10 m from the left support.
Appeared in:2082 Kartik2081 Chaitra2080 Chaitra2078 Chaitra2075 Baisakh
#2Repeated 4 Times[6 Marks]Statically Determinate Arches
Show that the bending moment at any section of a three-hinged parabolic arch subjected to uniformly distributed load over its entire span is zero everywhere. Deduce the expression for normal thrust and radial shear under this condition.
Appeared in:2081 Chaitra2079 Chaitra2076 Baisakh2074 Bhadra
#3Repeated 3 Times[8 Marks]Statically Determinate Arches
Analyze a Three-Hinged Parabolic Arch with hinges at both springings and crown. Derive the expression for horizontal thrust $H = \frac{w L^2}{8 h}$ under a uniformly distributed load $w$ over the entire span, and prove that the resultant bending moment is identically zero everywhere.
Appeared in:2082 Bhadra2081 Chaitra2079 Chaitra
#4Repeated 3 Times[8 Marks]Statically Determinate Arches
Analyze a Three-Hinged Circular Arch carrying concentrated point loads. Calculate the normal thrust ($N$) and radial shear ($Q$) at a section defined by angular coordinate $\theta$ from the support.
Appeared in:2082 Bhadra2080 Chaitra2078 Bhadra
#5Repeated 3 Times[8 Marks]Statically Determinate Arches
Construct Influence Line Diagrams for horizontal thrust $H$, bending moment, normal thrust, and radial shear at a given section of a Three-Hinged Parabolic Arch.
Appeared in:2082 Bhadra2081 Chaitra2076 Chaitra
Suspension Cable Systems
4 Questions#1Repeated 5 Times[12 Marks]Suspension Cable Systems
A suspension cable of 80 m span and 8 m dip is stiffened by a three-hinged girder. It carries a dead load of 10 kN/m. Determine maximum tension in the cable and maximum bending moment at a section 20 m from the left support in the girder when a moving UDL of intensity 15 kN/m longer than the span passes through the girder. Also draw BMD and SFD for the girder.
Appeared in:2082 Kartik2081 Chaitra2079 Chaitra2078 Chaitra2075 Bhadra
#2Repeated 4 Times[8 Marks]Suspension Cable Systems
A cable is suspended between two supports at different levels with span of 50 m. The left support is 3 m below the right support and the lowest point of the cable is 5 m below the lower support. The cable carries a UDL of 15 kN/m horizontally across the entire span. Calculate the length of the cable, the horizontal thrust, and the maximum tension in the cable.
Appeared in:2080 Chaitra2078 Chaitra2075 Baisakh2071 Magh
#3Repeated 3 Times[8 Marks]Suspension Cable Systems
Derive the cable profile equation for a flexible suspension cable carrying a uniformly distributed load $w$ per horizontal meter. Derive cable tension $T = \sqrt{H^2 + V^2}$, maximum tension at the support, and total cable length $S = L + \frac{8h^2}{3L}$.
Appeared in:2082 Bhadra2080 Chaitra2077 Magh
#4Repeated 3 Times[8 Marks]Suspension Cable Systems
Analyze a Suspension Bridge with a Three-Hinged Stiffening Girder. Calculate the cable tension, uniform upward hanger tension, and draw bending moment and shear force diagrams for the stiffening girder under rolling point loads.
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Simple Space Truss
3 Questions#1Repeated 4 Times[6 Marks]Simple Space Truss
Explain the tension coefficient method for the analysis of space trusses. State the equations of equilibrium and boundary conditions used in the analysis of space frames.
Appeared in:2080 Chaitra2078 Chaitra2076 Baisakh2074 Bhadra
#2Repeated 4 Times[10 Marks]Simple Space Truss
Analyze a tripod space truss supported on spherical hinges at ground level and loaded by a combined vertical and horizontal force at the top apex joint. Determine the tension or compression in all members using tension coefficient method.
Appeared in:2081 Chaitra2079 Chaitra2076 Baisakh2072 Magh
#3Repeated 3 Times[8 Marks]Simple Space Truss
Analyze a Statically Determinate Simple Space Truss using the Method of Tension Coefficients. Determine the member forces for a tripod or transmission tower subjected to horizontal and vertical joint loads.
Appeared in:2082 Bhadra2080 Chaitra2079 Chaitra
Curriculum Syllabus & Course Topics
Sourced from TU curriculum portalChapter-wise Units & Micro-Syllabus Topics (8 Units)
1. Introduction
- 1.1Types of structures based on analysis perspective
- 1.2Idealization of structures, threats and responses
- 1.3Review of determinacy, indeterminacy and stability of plane structures
- 1.4Application of determinate systems in civil engineering infrastructures
2. Strain Energy Method
- 2.1Work and complementary work
- 2.2Strain energy and complementary strain energy
- 2.3Strain energy due to axial, shear, bending and torsion
- 2.4Deformation of beams and frames by real work method
- 2.5Limitations of the real work method
- 2.6Strain energy due to gradually and suddenly applied direct load: Dynamic multipliers
3. Virtual Work Method
- 3.1Introduction to virtual work
- 3.2Derivation of virtual work equation
- 3.3Displacements by the methods of virtual work
- 3.4Direct axial, shear, bending and torsion effects
- 3.5Deformation of trusses due to external loads, temperature effect and misfits
- 3.6Deformation of beams and fames due to external loads and temperature effects
- 3.7Deformation of beams and frames due to support settlements
- 3.8Betti’s law and Maxwell’s reciprocal theorems
- 3.9Application of different effects in beam, frame and truss
4. Deflection of Beams
- 4.1Importance of deflection evaluation
- 4.2Macaulay’s method
- 4.3Moment-area method: Derivation of theorems
- 4.4Conjugate-beam method
- 4.5Deflections by the method of superposition
- 4.6Deflection evaluation of different determinate beams
- 4.7Application of deflection
5. Influence Lines for Simple Structures
- 5.1Importance of influence lines
- 5.2Concept of moving static loads and influence line diagrams (ILD)
- 5.3Influence lines for support reactions and support moments
- 5.4Influence lines for shear force and bending moment in beams
- 5.5Influence lines for support reactions and member forces in trusses
- 5.6ILD for indirect load applications (Panel loadings)
- 5.7Qualitative ILD using Muller-Breslau principle
- 5.8Use of influence line diagrams
- 5.8.1Determination of reactions, bending moments and shear forces (Structural quantity diagram) from ILD due to different loadings: Point load, distributed load, couple, standard load trains
- 5.8.2Most critical position of a loading system for maximum internal force/moment at a beam section
- 5.8.3Determination of most critical position of a loading system for absolute maximum internal forces
6. Statically Determinate Arches
- 6.1Introduction and type of arches
- 6.2Three-hinged structures with supports at the same and different levels
- 6.3Determination of support reactions, shear forces, normal forces and bending moments
- 6.4Analysis of three-hinged arches by the graphical method
- 6.5Use of ILD for reactions, bending moments, radial shear forces and normal thrust
7. Suspension Cable Systems
- 7.1Introduction and type
- 7.2Funicular shape of cable
- 7.3Catenary cables and general cable theorem
- 7.4General cases of parabolic cables and their analysis
- 7.5Elements of a simple suspended and suspension bridges
- 7.6Analysis of three-hinged stiffening girder
- 7.7Use of influence line diagrams
- 7.8Basics of tower structures, wind cables and ties
8. Simple Space Truss
- 8.1Introduction and importance of space truss
- 8.2Boundary conditions and types of supports
- 8.3Analysis of simple space truss by tension coefficient methods
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 I)
Q: How can I download Theory of Structures I past question papers?
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Q: What is the pass mark for Theory of Structures I?
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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