#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.
Appeared in:2080 Chaitra2079 Chaitra2076 Baisakh2074 Bhadra
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Theory of Structure I
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Most Frequently Asked Questions
Top recurring IOE board exam questions for Theory of Structure 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 $E I$.
Appeared in:2082 Bhadra2081 Chaitra2079 Chaitra
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.
Appeared in:2082 Bhadra2081 Chaitra2078 Kartik
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