Civil Engineering MCQ – Theory of Structures

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:

a) P = π²EI/L²
b) P = π²EI/(KL)²
c) P = EI/L²
d) P = EI/(KL)²

Answer:

a) P = π²EI/L²

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:

a) bd³/12
b) db³/12
c) bd³/3
d) db³/3

Answer:

a) bd³/12

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:

a) WL³/3EI
b) WL⁴/8EI
c) PL³/3EI
d) PL⁴/8EI

Answer:

c) PL³/3EI

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:

a) WL/4
b) WL/8
c) WL²/4
d) WL²/8

Answer:

d) WL²/8

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:

a) Compression failure
b) Lateral deflection
c) Torsional rotation
d) Shear failure

Answer:

b) Lateral deflection

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:

a) Zero
b) Maximum
c) Minimum
d) Equal to the mid-span moment

Answer:

b) Maximum

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:

a) Zero
b) Equal to the total load on the beam
c) Half the total load on the beam
d) More than half the total load on the beam

Answer:

c) Half the total load on the beam

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:

a) PL²/2EI
b) PL³/2EI
c) PL/2EI
d) PL/3EI

Answer:

a) PL²/2EI

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:

a) Span of the arch
b) Rise of the arch
c) Load on the arch
d) All of the above

Answer:

d) All of the above

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:

a) 1
b) 2
c) 3
d) 4

Answer:

c) 3

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:

a) L
b) L/2
c) 2L
d) L/4

Answer:

c) 2L

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:

a) Equal to the point load
b) Half the point load
c) Zero
d) Double the point load

Answer:

a) Equal to the point load

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?

a) Euler's buckling theory
b) Castigliano's theorem
c) The three-moment equation
d) Mohr's circle

Answer:

b) Castigliano's theorem

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:

a) Square root of (Area/Moment of Inertia)
b) Square root of (Moment of Inertia/Area)
c) Moment of Inertia/Area
d) Area/Moment of Inertia

Answer:

b) Square root of (Moment of Inertia/Area)

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:

a) Plane sections remain plane
b) Material is isotropic
c) Stress is proportional to strain
d) All of the above

Answer:

a) Plane sections remain plane

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:

a) Horizontal thrust only
b) Bending moment only
c) Shear force only
d) Both horizontal thrust and bending moment

Answer:

a) Horizontal thrust only

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:

a) Its load-carrying capacity
b) Its tendency to buckle
c) Its weight
d) Its length

Answer:

b) Its tendency to buckle

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:

a) The supports
b) The center
c) One-third of the span from either support
d) Any point of application of load

Answer:

b) The center

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:

a) The total work done by external forces is zero
b) The total work done by internal forces is zero
c) The total work done by both internal and external forces is zero
d) The total work done is maximum

Answer:

c) The total work done by both internal and external forces is zero

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:

a) The method of joints
b) The method of sections
c) Euler's formula
d) Castigliano's theorem

Answer:

a) The method of joints

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:

a) Determining the effect of moving loads
b) Analyzing static loads
c) Calculating deflections
d) Designing foundations

Answer:

a) Determining the effect of moving loads

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:

a) Sudden failure under load
b) Expansion due to moisture
c) Gradual deformation under sustained load
d) Cracking due to thermal changes

Answer:

c) Gradual deformation under sustained load

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:

a) P = π²EI/L²
b) P = π²EI/(2L)²
c) P = 2π²EI/L²
d) P = 4π²EI/L²

Answer:

b) P = π²EI/(2L)²

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:

a) f = (1/2π)√(3EI/mL³)
b) f = (1/2π)√(EI/3mL³)
c) f = (1/2π)√(3mL³/EI)
d) f = (1/2π)√(EI/m3L³)

Answer:

a) f = (1/2π)√(3EI/mL³)

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:

a) WL²/8
b) WL²/16
c) WL²/24
d) WL²/32

Answer:

b) WL²/16

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:

a) 5wL⁴/384EI
b) wL⁴/384EI
c) 5wL⁴/384πEI
d) wL⁴/384πEI

Answer:

a) 5wL⁴/384EI

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:

a) wL³/6EI
b) wL³/8EI
c) wL³/2EI
d) wL³/3EI

Answer:

a) wL³/6EI

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:

a) Equal to the total load
b) Greater than the total load
c) Less than the total load
d) Zero

Answer:

b) Greater than the total load

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?

a) δ = PL³/48EI
b) δ = PL⁴/48EI
c) δ = PL³/3EI
d) δ = PL⁴/3EI

Answer:

a) δ = PL³/48EI

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:

a) The rise of the arch
b) The span of the arch
c) The type of loading
d) Both the rise and span of the arch

Answer:

c) The type of loading

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:

a) Determining the reactions in beams
b) Calculating deflections in beams
c) Analyzing trusses
d) Determining the moment of inertia

Answer:

b) Calculating deflections in beams

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:

a) Shear force diagrams
b) Bending moment diagrams
c) Deflection analysis
d) Determining the point of contraflexure

Answer:

c) Deflection analysis

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:

a) πd⁴/64
b) πd⁴/32
c) πr⁴/4
d) πr⁴/2

Answer:

a) πd⁴/64

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:

a) Along which the bending stress is zero
b) Along which the shear stress is maximum
c) That divides the section into two equal areas
d) At the outermost fibers of the beam

Answer:

a) Along which the bending stress is zero

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:

a) Higher
b) Lower
c) Same
d) Unpredictable

Answer:

b) Lower

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:

a) 1.5
b) 2.0
c) 1.0
d) 2.5

Answer:

a) 1.5

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:

a) Analyze external forces
b) Calculate internal member forces
c) Determine the deflection of the truss
d) Find the reaction forces

Answer:

b) Calculate internal member forces

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:

a) Buckling and direct stress
b) Shear stress and bending
c) Axial and torsional loads
d) Temperature effects

Answer:

a) Buckling and direct stress

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:

a) Its ductility
b) Its hardness
c) Its stiffness
d) Its malleability

Answer:

c) Its stiffness

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:

a) Is supported at more than two points
b) Has a variable cross-section
c) Carries a uniform load
d) Spans over multiple supports without intermediate hinges

Answer:

a) Is supported at more than two points

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:

a) A slight upward curvature
b) The maximum bending moment
c) The point of zero shear force
d) The depth of the beam

Answer:

a) A slight upward curvature

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:

a) The ratio of lateral strain to longitudinal strain
b) The ratio of longitudinal strain to lateral strain
c) The ratio of shear strain to normal strain
d) The ratio of normal strain to shear strain

Answer:

a) The ratio of lateral strain to longitudinal strain

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:

a) Internal forces can be determined from equilibrium equations alone
b) Deflection analysis is required to determine internal forces
c) The number of reactions exceeds the number of equilibrium equations
d) Additional constraints are needed to prevent movement

Answer:

a) Internal forces can be determined from equilibrium equations alone

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:

a) Energy absorbed by a structure under loading
b) Potential energy due to the structure's weight
c) Kinetic energy due to the structure's movement
d) Thermal energy generated due to stress

Answer:

a) Energy absorbed by a structure under loading

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:

a) Shear stress is maximum
b) Bending stress is maximum
c) Application of load does not cause twisting
d) Shear force and bending moment are zero

Answer:

c) Application of load does not cause twisting

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?

a) Moment distribution method
b) Method of joints
c) Conjugate beam method
d) Slope deflection method

Answer:

d) Slope deflection method

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:

a) Instantaneous elastic deformation
b) Immediate plastic deformation
c) Long-term increase in deformation under sustained load
d) Sudden brittle failure

Answer:

c) Long-term increase in deformation under sustained load

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:

a) Represent a real hinge in the structure
b) Analyze structures under elastic deformation
c) Define the point where a structure yields under load
d) Calculate the thermal effects in beams

Answer:

c) Define the point where a structure yields under load

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:

a) The maximum reaction in a beam
b) The effect of moving loads on a structure
c) The fixed-end moments in a beam
d) The location of plastic hinges

Answer:

b) The effect of moving loads on a structure

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:

a) Its resistance to axial deformation
b) Its resistance to volumetric deformation
c) Its resistance to shear deformation
d) Its resistance to bending

Answer:

c) Its resistance to shear deformation

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.

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