Civil Engineering students can access a comprehensive set of MCQ (Multiple Choice Questions) and answers related to the Theory of Structures. These resources are tailored to help students prepare for GATE exams, various technical interviews, competitive examinations, and other entrance exams. The Theory of Structures MCQ section is a crucial chapter for both Civil Engineering and GATE students.

## 1. Euler's formula for the critical load of a long column is given by:

### Answer:

### Explanation:

Euler's formula for the critical (buckling) load of a long column is P = π²EI/L², where E is the modulus of elasticity, I is the moment of inertia, and L is the effective length of the column.

## 2. The moment of inertia of a rectangular section about an axis through its base is:

### Answer:

### Explanation:

The moment of inertia of a rectangular section about an axis through its base is given by bd³/12, where b is the base width and d is the depth of the rectangle.

## 3. The deflection at the free end of a cantilever beam carrying a point load at the free end is given by:

### Answer:

### Explanation:

The deflection (δ) at the free end of a cantilever beam carrying a point load P at the free end is given by δ = PL³/3EI, where L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia.

## 4. The maximum bending moment in a simply supported beam with a uniformly distributed load W over its entire span L is:

### Answer:

### Explanation:

The maximum bending moment (M) in a simply supported beam with a uniformly distributed load over its entire span is given by M = WL²/8.

## 5. The term "buckling" in column analysis refers to:

### Answer:

### Explanation:

Buckling in column analysis refers to the sudden lateral deflection or sideway bending of a column under compressive load.

## 6. In a fixed beam, the moments at the supports are:

### Answer:

### Explanation:

In a fixed beam, the moments at the supports are maximum due to the restraint provided at the ends.

## 7. A propped cantilever beam is subjected to a uniform distributed load. The reaction at the prop is:

### Answer:

### Explanation:

In a propped cantilever with a uniform distributed load, the reaction at the prop is typically half the total load on the beam, due to the static equilibrium of forces.

## 8. The slope at the free end of a cantilever beam carrying a point load at the free end is given by:

### Answer:

### Explanation:

The slope (θ) at the free end of a cantilever beam carrying a point load P at the free end is given by θ = PL²/2EI, where L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia.

## 9. In a three-hinged arch, the horizontal thrust is influenced by:

### Answer:

### Explanation:

In a three-hinged arch, the horizontal thrust is influenced by the span, rise, and load on the arch.

## 10. The degree of static indeterminacy of a beam fixed at both ends is:

### Answer:

### Explanation:

A beam fixed at both ends has three degrees of static indeterminacy – two moments and one horizontal reaction at each support.

## 11. The effective length of a column fixed at one end and free at the other is:

### Answer:

### Explanation:

For a column that is fixed at one end and free at the other, the effective length is considered as twice the actual length (2L) for buckling analysis.

## 12. In a simply supported beam with a point load at the center, the maximum shear force is:

### Answer:

### Explanation:

In a simply supported beam with a point load at the center, the maximum shear force is equal to the magnitude of the point load.

## 13. The concept of strain energy is used in which of the following theorems?

### Answer:

### Explanation:

Castigliano's theorem uses the concept of strain energy for determining displacements in structures.

## 14. The radius of gyration of a column section is defined as:

### Answer:

### Explanation:

The radius of gyration (r) of a column section is defined as the square root of the ratio of its moment of inertia (I) to its cross-sectional area (A), r = sqrt(I/A).

## 15. The fundamental assumption in the theory of simple bending is:

### Answer:

### Explanation:

The fundamental assumption in the theory of simple bending is that plane sections before bending remain plane after bending.

## 16. A two-hinged parabolic arch subjected to a symmetrically placed load will have:

### Answer:

### Explanation:

A two-hinged parabolic arch with symmetrical loading experiences horizontal thrust but no bending moment due to its shape and symmetry.

## 17. The slenderness ratio of a column is a measure of:

### Answer:

### Explanation:

The slenderness ratio of a column is a measure of its tendency to buckle and is determined by its effective length and cross-sectional dimensions.

## 18. The maximum deflection of a uniformly loaded simply supported beam occurs at:

### Answer:

### Explanation:

The maximum deflection in a simply supported beam carrying a uniform load occurs at the center of the span.

## 19. The principle of virtual work states that for a deformable body in equilibrium:

### Answer:

### Explanation:

The principle of virtual work states that for an elastic body in equilibrium, the total virtual work done by both internal and external forces is zero.

## 20. In a truss structure, zero-force members can be determined by:

### Answer:

### Explanation:

Zero-force members in a truss structure can be identified using the method of joints, which involves analyzing the equilibrium of forces at each joint.

## 21. The concept of influence lines is primarily used for:

### Answer:

### Explanation:

Influence lines are used in structural analysis to determine the effect of moving loads on various response quantities like bending moments, shear forces, and deflections in a structure.

## 22. Creep in concrete refers to:

### Answer:

### Explanation:

Creep in concrete is the term used to describe the gradual time-dependent deformation of concrete under sustained load.

## 23. The critical load for a column with one end fixed and the other free is given by:

### Answer:

### Explanation:

For a column with one end fixed and the other free, the critical load (buckling load) is given by P = π²EI/(2L)², where L is the actual length of the column.

## 24. The formula for the fundamental frequency of vibration of a cantilever beam is:

### Answer:

### Explanation:

The fundamental frequency of vibration (f) of a cantilever beam is given by f = (1/2π)√(3EI/mL³), where E is the modulus of elasticity, I is the moment of inertia, m is the mass per unit length, and L is the length of the beam.

## 25. In a simply supported beam carrying a triangular load with the vertex at the center, the maximum bending moment is:

### Answer:

### Explanation:

For a simply supported beam with a triangular load with the vertex at the center, the maximum bending moment is WL²/16, where W is the total load and L is the length of the beam.

## 26. The deflection at the center of a simply supported beam carrying a uniform load is given by:

### Answer:

### Explanation:

The deflection (δ) at the center of a simply supported beam carrying a uniform load (w) is given by δ = 5wL⁴/384EI, where L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia.

## 27. The formula for finding the slope at the end of a cantilever beam carrying a uniformly distributed load is:

### Answer:

### Explanation:

The slope at the end of a cantilever beam carrying a uniformly distributed load (w) is given by θ = wL³/6EI, where L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia.

## 28. The maximum shear force in a simply supported beam with an overhanging end carrying a uniformly distributed load over the entire length is:

### Answer:

### Explanation:

The maximum shear force in such a beam occurs at the junction of the overhang and can be greater than the total load on the beam.

## 29. The relationship between load (P), span (L), flexural rigidity (EI), and deflection (δ) in a simply supported beam is given by which formula?

### Answer:

### Explanation:

For a simply supported beam with a central point load, the maximum deflection is given by δ = PL³/48EI, where P is the load, L is the span, E is the modulus of elasticity, and I is the moment of inertia.

## 30. In a two-hinged arch, the horizontal reaction component is influenced primarily by:

### Answer:

### Explanation:

The horizontal reaction in a two-hinged arch is primarily influenced by the type of loading (symmetrical or unsymmetrical) rather than just the geometric parameters of the arch.

## 31. The Macaulay’s method is used for:

### Answer:

### Explanation:

Macaulay’s method is a technique used in structural analysis to calculate the deflection at any point in a beam.

## 32. In structural analysis, the term "conjugate beam" is used in:

### Answer:

### Explanation:

The conjugate beam method is a technique used in structural analysis for determining the deflection of a beam.

## 33. The area moment of inertia for a circular section about its diameter is given by:

### Answer:

### Explanation:

The area moment of inertia (I) for a circular section about its diameter is I = πd⁴/64, where d is the diameter of the circle.

## 34. The neutral axis of a beam cross-section is a line:

### Answer:

### Explanation:

The neutral axis in the cross-section of a beam is the line along which the bending stress is zero. It is the axis that separates the tension and compression zones in the beam.

## 35. The load-carrying capacity of a slender column compared to a short column is:

### Answer:

### Explanation:

Slender columns are more prone to buckling under axial loads compared to short columns, hence they have a lower load-carrying capacity.

## 36. The shape factor of a rectangular section in bending is:

### Answer:

### Explanation:

The shape factor of a rectangular section in bending is 1.5. It indicates the ratio of the plastic moment capacity to the elastic moment capacity of the section.

## 37. In a truss structure, the method of joints is used to:

### Answer:

### Explanation:

The method of joints in truss analysis is used to calculate the internal forces in the members of the truss by considering equilibrium at each joint.

## 38. The Rankine-Gordon formula for columns accounts for:

### Answer:

### Explanation:

The Rankine-Gordon formula is used for columns to account for both buckling (due to slenderness) and direct compressive stress.

## 39. The modulus of elasticity (E) of a material is a measure of:

### Answer:

### Explanation:

The modulus of elasticity (E) is a measure of a material's stiffness or resistance to elastic deformation under load.

## 40. A continuous beam is one that:

### Answer:

### Explanation:

A continuous beam extends over more than two supports, providing greater structural stability and load distribution.

## 41. The term "camber" in beams refers to:

### Answer:

### Explanation:

Camber in beams refers to a slight upward curvature introduced to counteract deflection due to loads and ensure a level surface when loaded.

## 42. The Poisson's ratio of a material is defined as:

### Answer:

### Explanation:

Poisson's ratio is defined as the ratio of lateral strain (transverse contraction) to longitudinal strain (axial extension) in a material under stress.

## 43. A statically determinate structure is one in which:

### Answer:

### Explanation:

A statically determinate structure is one where the internal forces can be determined solely from the equations of static equilibrium without the need for additional information or compatibility equations.

## 44. The concept of 'Strain Energy' in structural analysis refers to:

### Answer:

### Explanation:

Strain energy is the energy absorbed by a structure due to deformation under loading. It is a measure of the work done by the external forces in deforming the structure.

## 45. The shear center in a cross-section of a beam is the point where:

### Answer:

### Explanation:

The shear center is the point in a beam's cross-section where the application of transverse loads will not produce twisting or torsional deformation. It is crucial in designing beams subjected to lateral loads.

## 46. Which method is used for analyzing indeterminate structures based on deflection compatibility?

### Answer:

### Explanation:

The slope deflection method is used for analyzing indeterminate structures. It is based on the deflection compatibility at joints and considers the relationship between moments, rotations, and deflections.

## 47. Creep in materials is described as:

### Answer:

### Explanation:

Creep in materials is a time-dependent, gradual increase in deformation observed under a constant or sustained load, particularly noticeable in materials like concrete and metals at high temperature.

## 48. The 'Plastic Hinge' concept in structural analysis is used to:

### Answer:

### Explanation:

A plastic hinge is a theoretical concept used in structural analysis to represent the location in a structure where it yields or undergoes plastic deformation under load, leading to mechanism formation.

## 49. In structural analysis, 'Influence Lines' are used to determine:

### Answer:

### Explanation:

Influence lines are graphical representations used in structural analysis to determine the effect of moving loads on responses like reactions, shear forces, and bending moments at specific points in a structure.

## 50. The 'Modulus of Rigidity' (G) of a material is a measure of:

### Answer:

### Explanation:

The modulus of rigidity, also known as shear modulus, is a measure of a material's resistance to shear deformation. It is a fundamental property related to the material's elastic response under shear stress.