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MEngC R.S.E Part-I Civil study materials
MEngC R.S.E Part-I Civil study resources

MEngC R.S.E Part-I Civil practice questions

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Question 1Structural Analysis and Mechanics

For a simply supported beam of span L carrying a central point load W, what is the maximum bending moment?

  1. WL/4 Correct answer.
  2. WL²/8
  3. WL/8
  4. WL/2

Explanation

The reactions are each W/2, and the maximum moment occurs under the load at midspan, giving (W/2)(L/2) = WL/4. This is a standard result for a central point load on a simple span.

Question 2Structural Analysis and Mechanics

In a truss analysis, a joint has three members meeting at it, two of which are collinear and no external load or support reaction acts at the joint. What is the force in the third (non-collinear) member?

  1. Indeterminate without member stiffnesses
  2. Equal to half the sum of the collinear forces
  3. Equal to the larger of the two collinear forces
  4. Zero Correct answer.

Explanation

Resolving perpendicular to the line of the two collinear members leaves only the third member contributing, so its force component must vanish, meaning the member carries zero force. This is the standard zero-force member rule for trusses.

Question 3Structural Analysis and Mechanics

Which quantity is defined as the integral of area about an axis, ∫y² dA, and governs a beam's resistance to bending about that axis?

  1. Second moment of area Correct answer.
  2. Section modulus
  3. Radius of gyration
  4. Polar moment of inertia

Explanation

The second moment of area (moment of inertia) is ∫y² dA and appears directly in the flexure formula σ = My/I. It measures how area is distributed about the neutral axis.

Question 4Structural Analysis and Mechanics

A cantilever of length 2 m carries a point load of 10 kN at its free end. What is the bending moment at the fixed support?

  1. 5 kN·m
  2. 20 kN·m Correct answer.
  3. 40 kN·m
  4. 10 kN·m

Explanation

The fixed-end moment equals load times lever arm, 10 kN × 2 m = 20 kN·m. The moment is maximum at the support and zero at the free end.

Question 5Structural Analysis and Mechanics

According to Hooke's law in its one-dimensional form, the relationship between axial stress σ and axial strain ε for a linear elastic material is:

  1. σ = Eε Correct answer.
  2. σ = Eε²
  3. σ = E/ε
  4. σ = ε/E

Explanation

Hooke's law states stress is proportional to strain through Young's modulus, σ = Eε. The constant of proportionality E has units of stress.

Question 6Structural Analysis and Mechanics

For a statically determinate plane truss with j joints and m members, which relationship must hold for internal determinacy?

  1. m = 2j + 3
  2. m = 3j − 2
  3. m = 2j − 3 Correct answer.
  4. m = j + 3

Explanation

A plane truss needs two equations per joint, giving 2j equations, minus three support reactions, so m = 2j − 3 for full determinacy. This is the standard counting rule for simple plane trusses.

Question 7Structural Analysis and Mechanics

The maximum shear stress in a beam of rectangular cross-section occurs at which location?

  1. At the top fibre
  2. At the bottom fibre
  3. At the neutral axis Correct answer.
  4. At one-quarter depth

Explanation

Shear stress varies parabolically over a rectangular section, being zero at the extreme fibres and maximum at the neutral axis. The peak value is 1.5 times the average shear stress.

Question 8Structural Analysis and Mechanics

A simply supported beam of span 6 m carries a uniformly distributed load of 4 kN/m over its full length. What is the maximum bending moment?

  1. 36 kN·m
  2. 24 kN·m
  3. 18 kN·m Correct answer.
  4. 12 kN·m

Explanation

For a full-span UDL, maximum moment is wL²/8 = 4 × 36 / 8 = 18 kN·m. This occurs at midspan.

Question 9Structural Analysis and Mechanics

The degree of static indeterminacy of a fixed-end beam (both ends fixed) with no internal hinges, considering only reactions, is:

  1. 2
  2. 1
  3. 4
  4. 3 Correct answer.

Explanation

A fixed-end beam has six reaction components (three per support) and three available equilibrium equations, giving 6 − 3 = 3 degrees of static indeterminacy.

Question 10Structural Analysis and Mechanics

Using the principle of virtual work, the deflection at a point on a structure is obtained by integrating which product over the member length?

  1. Virtual moment times virtual shear divided by area
  2. Real shear times virtual axial force divided by modulus
  3. Real moment times virtual moment divided by flexural rigidity Correct answer.
  4. Real moment times real moment divided by axial rigidity

Explanation

For bending deflections, virtual work gives δ = ∫(M·m/EI) dx, where M is the real moment and m the moment due to a unit virtual load. The product is divided by EI and integrated along the member.

Question 11Structural Analysis and Mechanics

A propped cantilever of span L carries a uniformly distributed load w over its full length. The reaction at the prop (simple support) is:

  1. wL/2
  2. wL/4
  3. 3wL/8 Correct answer.
  4. 5wL/8

Explanation

Compatibility of deflection at the prop gives a prop reaction of 3wL/8 for a propped cantilever under full-span UDL. The fixed end then carries 5wL/8.

Question 12Structural Analysis and Mechanics

In the slope-deflection method, the fixed-end moment at end A of a prismatic member AB due to a uniform load w over the whole span is:

  1. wL²/12 Correct answer.
  2. wL²/16
  3. wL²/8
  4. wL²/24

Explanation

A fully fixed member under uniform load develops end moments of magnitude wL²/12 at each end, with opposite signs in the sign convention. This is the standard fixed-end moment used in slope-deflection and moment distribution.

Question 13Structural Analysis and Mechanics

A two-hinged parabolic arch of span L and rise h carries a uniformly distributed load w over its entire horizontal span. The horizontal thrust is:

  1. wL²/(8h) Correct answer.
  2. wL/(8h)
  3. wL²/(2h)
  4. wL²/(4h)

Explanation

For a two-hinged parabolic arch under full uniform load, the horizontal thrust is wL²/(8h), obtained by taking moments about a hinge for the half-arch. Under this loading the arch is funicular to the parabola, so bending moments are zero.

Question 14Structural Analysis and Mechanics

A circular shaft of diameter d transmits torque T. The maximum shear stress in the shaft is given by:

  1. 32T/(πd³)
  2. T d/(πd⁴)
  3. 8T/(πd³)
  4. 16T/(πd³) Correct answer.

Explanation

The torsion formula gives τ = T r / J with r = d/2 and J = πd⁴/32, so τmax = 16T/(πd³). This is the standard result for a solid circular shaft.

Question 15Structural Analysis and Mechanics

Euler's buckling load for a pin-ended column of length L and flexural rigidity EI is:

  1. 4π²EI/L²
  2. π²EI/(4L²)
  3. π²EI/L² Correct answer.
  4. π²EI/(2L²)

Explanation

The Euler load for a pin-ended (both ends hinged) column is π²EI/L², corresponding to an effective length equal to L. Other end conditions scale this by the effective length factor.

Question 16Structural Analysis and Mechanics

In the moment distribution method, the distribution factor for a member at a joint is computed as:

  1. The sum of member stiffnesses divided by the member stiffness
  2. The member stiffness divided by the sum of stiffnesses of all members meeting at the joint Correct answer.
  3. The carry-over factor times the member stiffness
  4. The fixed-end moment divided by the total moment at the joint

Explanation

The distribution factor is the ratio of a member's rotational stiffness to the total stiffness at the joint, so the factors at a joint sum to unity. Each unbalanced moment is shared in proportion to these factors.

Question 17Structural Analysis and Mechanics

A simply supported beam of span L carries a point load W at a distance a from the left support. The deflection under the load is:

  1. W a b /(3EIL)
  2. W a² b² /(3EIL) Correct answer.
  3. W a³ b³ /(3EIL²)
  4. W a² b² /(EIL)

Explanation

For a point load at distance a from one support with b = L − a, the deflection under the load is W a² b² /(3EIL). This follows from virtual work or integration of the moment equation.

Question 18Structural Analysis and Mechanics

A rectangular section beam of width b and depth d is bent about its horizontal centroidal axis. The section modulus is:

  1. bd³/12
  2. bd/6
  3. bd²/12
  4. bd²/6 Correct answer.

Explanation

The second moment of area about the centroidal axis is bd³/12, and dividing by the extreme fibre distance d/2 gives section modulus bd²/6. This is used directly in the flexure formula.

Question 19Structural Analysis and Mechanics

A three-hinged arch is statically determinate. How many independent equilibrium conditions are available for its overall analysis, including the internal hinge condition?

  1. 6
  2. 5
  3. 3
  4. 4 Correct answer.

Explanation

A three-hinged arch has four unknowns (two reactions at each support) and four equations: three global equilibrium equations plus the zero bending moment condition at the crown hinge. This makes it statically determinate.

Question 20Structural Analysis and Mechanics

In the stiffness method, the element stiffness matrix for a plane frame member includes which of the following effects?

  1. Only axial deformation
  2. Only bending deformation
  3. Only torsional deformation
  4. Axial, bending and shear deformation through combined terms Correct answer.

Explanation

A plane frame element stiffness matrix couples axial and bending behaviour and can include shear deformation through the shear area. Each degree of freedom at the two nodes interacts with the others.

Question 21Structural Analysis and Mechanics

A beam of uniform flexural rigidity EI is fixed at both ends and carries a central point load W over span L. The fixed-end moment at each support is:

  1. WL/4
  2. WL/12
  3. WL/16
  4. WL/8 Correct answer.

Explanation

For a fixed-fixed beam with a central point load, each fixed-end moment has magnitude WL/8. The midspan moment is WL/8 as well, and the support moments are hogging.

Question 22Structural Analysis and Mechanics

An influence line for the reaction at a support of a simply supported beam is drawn for a unit load moving across the span. The ordinate at a distance x from that support equals:

  1. x(L − x)/L
  2. 1 − x/L Correct answer.
  3. x/L
  4. L/x

Explanation

Taking moments about the far support gives the reaction as 1 − x/L for a unit load at distance x from the support in question. The ordinate is unity at the support and zero at the far end.

Question 23Structural Analysis and Mechanics

A two-span continuous beam with equal spans L is analysed by the three-moment theorem. For a uniform load w on both spans, the hogging moment at the central support is:

  1. wL²/12
  2. wL²/8 Correct answer.
  3. wL²/10
  4. wL²/16

Explanation

Applying the three-moment equation to equal spans with uniform load gives a support moment of wL²/8. The central support moment is hogging and exceeds the simple-span value in magnitude.

Question 24Structural Analysis and Mechanics

In plasticity theory, the shape factor for a rectangular section bent about its centroidal axis, defined as the ratio of plastic moment to yield moment, is:

  1. 1.0
  2. 1.7
  3. 1.5 Correct answer.
  4. 2.0

Explanation

For a rectangle, the plastic modulus is bd²/4 and the elastic section modulus is bd²/6, so the shape factor is 1.5. This reflects the reserve strength between first yield and full plastification.

Question 25Structural Analysis and Mechanics

A cylindrical pressure vessel with closed ends has internal pressure p, radius r and wall thickness t. The hoop and longitudinal stresses are:

  1. 2pr/t and pr/t
  2. pr/(2t) and pr/t
  3. pr/t and pr/t
  4. pr/t and pr/(2t) Correct answer.

Explanation

For a thin-walled closed cylinder, the hoop stress is pr/t and the longitudinal stress is pr/(2t), so the hoop stress is twice the longitudinal stress. This follows from force equilibrium on longitudinal and circumferential cuts.

Question 26Structural Analysis and Mechanics

A cantilever of length L has flexural rigidity EI and carries a single concentrated load P at its free end. What is the vertical deflection at the free end?

  1. PL²/(2EI)
  2. PL³/(3EI) Correct answer.
  3. 5PL⁴/(384EI)
  4. PL³/(8EI)

Explanation

For a cantilever with an end point load, the bending moment diagram is triangular with maximum PL at the fixed support. Integrating M/EI twice with the boundary conditions of zero slope and zero deflection at the fixed end gives the free-end deflection PL³/(3EI).

Question 27Structural Analysis and Mechanics

A solid circular shaft of diameter d is subjected to a bending moment M and a twisting moment T acting simultaneously. According to the maximum shear stress theory, the equivalent twisting moment used for design is:

  1. √(M² + T²) Correct answer.
  2. √(M² − T²)
  3. (M + √(M² + T²))/2
  4. M + T

Explanation

The principal stresses at the extreme fibre combine the direct bending stress 32M/(πd³) and the torsional shear stress 16T/(πd³). The maximum shear stress equals 16/(πd³) times √(M² + T²), so the equivalent twisting moment is √(M² + T²).

Question 28Structural Analysis and Mechanics

A short column of rectangular cross-section 200 mm × 300 mm carries a vertical compressive load of 600 kN applied at an eccentricity of 50 mm measured along the 300 mm side from the centroidal axis. What is the maximum compressive stress in the section?

  1. 10.0 N/mm²
  2. 20.0 N/mm² Correct answer.
  3. 12.0 N/mm²
  4. 16.0 N/mm²

Explanation

The direct stress is P/A = 600000/(200 × 300) = 10 N/mm². With eccentricity along the 300 mm side, Z = 200 × 300²/6 = 3 × 10⁶ mm³, so Pe/Z = 10 N/mm². Direct and bending stresses add at the more compressed edge, giving 20 N/mm².

Question 29Structural Analysis and Mechanics

A propped cantilever of span L has uniform flexural rigidity EI and carries a concentrated load W at the mid-span. Using the force method with the prop reaction as redundant, what is the prop reaction?

  1. 11W/16
  2. 3W/8
  3. W/2
  4. 5W/16 Correct answer.

Explanation

Releasing the prop gives a cantilever with mid-span load W, whose free-end deflection is 5WL³/(48EI). The upward deflection at the free end due to a unit prop reaction is L³/(3EI). Equating the two gives R = 5W/16.

Question 30Structural Analysis and Mechanics

A portal frame consists of two columns of height h and a beam of span L, all of constant flexural rigidity EI, with fixed bases and rigid beam-column joints. Ignoring axial deformations, what is the degree of kinematic (sway) indeterminacy for a sidesway analysis?

  1. Three independent joint translations, one per joint plus one for beam rotation
  2. One independent joint translation, since the beam is axially rigid and both column tops translate equally Correct answer.
  3. Zero, because the fixed bases prevent all joint translation
  4. Two independent joint translations, one for each column top

Explanation

With fixed bases and axially rigid members, the only possible kinematic freedom beyond joint rotations is a single horizontal sway of the beam level. Both column tops move by the same amount because the beam is inextensible, so the sway degree of freedom is one.

Question 31Structural Design of Concrete Structures

In limit state design of a reinforced concrete flexural member, which pair correctly states the two limit states that must be satisfied?

  1. Yield limit state and rupture limit state
  2. Shrinkage limit state and creep limit state
  3. Collapse limit state and serviceability limit state Correct answer.
  4. Elastic limit state and plastic limit state

Explanation

Limit state design requires the structure to resist the ultimate (collapse) limit state with adequate safety against failure, and to perform satisfactorily at the serviceability limit state for deflection and cracking under working loads. The other pairs are not the standard two-limit-state framework of concrete design codes.

Question 32Structural Design of Concrete Structures

For a singly reinforced rectangular concrete section in flexure, the lever arm between the compressive and tensile resultants is taken as:

  1. z = 0.5 d
  2. z = d − 0.5 x Correct answer.
  3. z = x
  4. z = d + 0.5 x

Explanation

The compressive resultant acts at mid-depth of the rectangular stress block, i.e. at 0.5x from the top fibre, while the tensile steel acts at effective depth d. Hence the lever arm is d − 0.5x, and the moment of resistance is the steel force times this lever arm.

Question 33Structural Design of Concrete Structures

According to the IS 456 stress block for concrete in flexure, the maximum compressive stress in the concrete at the ultimate limit state is taken as:

  1. 0.446 fck Correct answer.
  2. 0.67 fck
  3. 0.85 fck
  4. fck

Explanation

The design stress block uses 0.67 fck divided by the partial safety factor of 1.5 for materials, giving 0.446 fck over a depth of 0.42xu. This is the value adopted for computing the concrete compression resultant in Indian practice.

Question 34Structural Design of Concrete Structures

The primary purpose of providing shear reinforcement (stirrups) in a reinforced concrete beam is to:

  1. Prevent the corrosion of the tension steel
  2. Reduce the long-term creep of the beam
  3. Increase the flexural compressive strength of concrete
  4. Resist diagonal tension and restrain the longitudinal bars Correct answer.

Explanation

Stirrups carry the diagonal tensile stresses that develop near supports and also hold the main bars in position, improving bond and ductility. They contribute little to flexural compression capacity and do not control creep or corrosion directly.

Question 35Structural Design of Concrete Structures

In a reinforced concrete column, the minimum eccentricity to be considered in design accounts for:

  1. The buckling of the main steel
  2. The shrinkage of the concrete only
  3. The self-weight of the column
  4. Unavoidable construction tolerances and load misalignment Correct answer.

Explanation

Even a nominally axially loaded column is designed for a minimum eccentricity to cover practical inaccuracies in construction and load application. This ensures the section is designed for a small moment rather than a purely axial force.

Question 36Structural Design of Concrete Structures

Which factor most directly governs the nominal cover to reinforcement in a reinforced concrete member exposed to a moderate environment?

  1. The span-to-depth ratio of the member
  2. The grade of the reinforcing steel
  3. Durability requirements against carbonation and corrosion Correct answer.
  4. The type of formwork used

Explanation

Nominal cover is specified primarily to protect the steel from carbonation, chloride ingress and fire, and is linked to the exposure classification. Steel grade, span-to-depth ratio and formwork type do not set the durability cover.

Question 37Structural Design of Concrete Structures

The characteristic strength of concrete used in design is defined as the value of cube strength below which not more than:

  1. 1 percent of test results are expected to fall
  2. 5 percent of test results are expected to fall Correct answer.
  3. 25 percent of test results are expected to fall
  4. 50 percent of test results are expected to fall

Explanation

Characteristic strength corresponds to the 5th percentile of the strength distribution, i.e. only 5 percent of results are expected to fall below it. Design values are then obtained by dividing by the material partial safety factor.

Question 38Structural Design of Concrete Structures

In a simply supported one-way slab, the main reinforcement is provided:

  1. Along the span direction to resist bending Correct answer.
  2. Equally in both directions
  3. Only at the supports
  4. Along the support direction to resist shear

Explanation

A one-way slab bends mainly in the span direction, so the main steel is placed parallel to the span to resist the flexural tension. Distribution steel is placed perpendicular to the main bars to control cracking and temperature effects.

Question 39Structural Design of Concrete Structures

A singly reinforced rectangular beam has effective depth d = 500 mm and neutral axis depth x = 200 mm at the ultimate limit state. Using the lever arm z = d − 0.5x, the lever arm is:

  1. 300 mm
  2. 250 mm
  3. 450 mm
  4. 400 mm Correct answer.

Explanation

Substituting into z = d − 0.5x gives 500 − 0.5(200) = 500 − 100 = 400 mm. The moment of resistance then follows from the steel force multiplied by this lever arm.

Question 40Structural Design of Concrete Structures

For a beam with width b = 300 mm, effective depth d = 550 mm and concrete grade M25, the limiting neutral axis depth xu,lim/d for Fe 415 steel is 0.48. The limiting neutral axis depth is:

  1. 220 mm
  2. 275 mm
  3. 264 mm Correct answer.
  4. 240 mm

Explanation

The limiting neutral axis depth is obtained as 0.48 × 550 = 264 mm. Sections with x less than this are under-reinforced and governed by steel yielding at the ultimate limit state.

Question 41Structural Design of Concrete Structures

A rectangular beam section is described as under-reinforced when, at the ultimate limit state:

  1. The concrete crushes before the tension steel yields
  2. The tension steel yields before the concrete crushes Correct answer.
  3. The steel and concrete reach failure simultaneously
  4. The section carries no tensile reinforcement

Explanation

In an under-reinforced section the steel yields first and the concrete crushing follows, giving a ductile and desirable mode of failure. This corresponds to a neutral axis depth less than the limiting value.

Question 42Structural Design of Concrete Structures

The design shear strength of concrete τc in a reinforced concrete beam depends mainly on:

  1. The amount of shear reinforcement provided
  2. The percentage of tension steel and the concrete grade Correct answer.
  3. The grade of the steel only
  4. The span of the beam only

Explanation

The concrete shear strength is a function of the longitudinal tension reinforcement percentage and the concrete grade, as tabulated in design codes. Stirrups are additional and do not enter the expression for τc.

Question 43Structural Design of Concrete Structures

In the design of a short reinforced concrete column subjected to axial load and uniaxial bending, the interaction diagram is used to:

  1. Compute the deflection of the column
  2. Establish the fire rating of the column
  3. Check that the load-moment combination lies within the safe envelope Correct answer.
  4. Determine the shrinkage of the concrete

Explanation

The interaction diagram plots the safe combinations of axial load and bending moment for a given section and reinforcement. A design load point inside the envelope indicates an adequate section.

Question 44Structural Design of Concrete Structures

The development length of a reinforcing bar in tension is primarily required to ensure that:

  1. The bar can develop its design stress without slipping over its anchorage length Correct answer.
  2. The concrete does not shrink around the bar
  3. The bar does not corrode at the ends
  4. The bar remains straight in the member

Explanation

Development length is the embedded length over which bond transfers the bar force to the concrete so the bar can reach its design stress. It is computed from the bar diameter, steel stress and bond strength.

Question 45Structural Design of Concrete Structures

A simply supported beam of effective span 6 m carries a factored moment of 150 kN·m. If the lever arm is 0.9d with d = 500 mm and the design steel stress is 0.87fy, the approximate area of tension steel required is:

  1. 770 mm² Correct answer.
  2. 1200 mm²
  3. 600 mm²
  4. 900 mm²

Explanation

Using M = 0.87fy·Ast·z with z = 0.9 × 500 = 450 mm and fy = 415 MPa, Ast = 150×10^6 / (0.87×415×450) ≈ 770 mm². This illustrates the direct application of the moment of resistance equation.

Question 46Structural Design of Concrete Structures

The purpose of providing lateral ties in a reinforced concrete column is to:

  1. Prevent buckling of the longitudinal bars and confine the concrete Correct answer.
  2. Reduce the self-weight of the column
  3. Improve the surface finish of the column
  4. Increase the axial load capacity by acting as main steel

Explanation

Lateral ties hold the longitudinal bars in position, prevent their buckling and provide confinement that improves ductility. They are not counted as main load-carrying reinforcement.

Question 47Structural Design of Concrete Structures

In a two-way slab with corners prevented from lifting, torsional reinforcement is provided at the corners because:

  1. The supports settle at the corners
  2. Corner twisting induces torsional moments that must be resisted Correct answer.
  3. The corners carry the maximum bending moment
  4. The slab shrinks more at the corners

Explanation

When corners are held down, twisting of the slab at the corners generates torsional moments that require additional reinforcement in the form of corner mesh. This prevents corner cracking and ensures the assumed support conditions are valid.

Question 48Structural Design of Concrete Structures

The serviceability limit state of deflection in a reinforced concrete beam is commonly controlled by:

  1. Increasing the concrete cover
  2. Limiting the span-to-effective-depth ratio Correct answer.
  3. Using a higher grade of formwork
  4. Reducing the stirrup spacing

Explanation

Deflection control is achieved by limiting the span-to-effective-depth ratio, with modification factors for steel percentage and section shape. This avoids the need for explicit deflection calculations in routine design.

Question 49Structural Design of Concrete Structures

The partial safety factor for concrete in the ultimate limit state of flexure, used to obtain the design compressive strength, is:

  1. 1.15
  2. 1.5 Correct answer.
  3. 2.0
  4. 1.0

Explanation

The material partial safety factor for concrete in the ultimate limit state is 1.5, giving the design strength 0.67fck/1.5 = 0.446fck. The factor 1.15 applies to steel, not concrete.

Question 50Structural Design of Concrete Structures

A reinforced concrete beam is over-reinforced. Which statement best describes its behaviour at ultimate load?

  1. Steel yields first and the beam deflects excessively before failure
  2. Concrete crushes while the steel remains below yield, giving a brittle failure Correct answer.
  3. The beam fails by bond slip of the main bars
  4. The beam fails by diagonal tension near the supports

Explanation

In an over-reinforced section the neutral axis is deep and the concrete reaches its limiting strain before the steel yields. Failure is therefore sudden and brittle, which is why codes limit the tension steel to keep sections under-reinforced.