Practice SetStrength of Materials

Strength of Materials MCQ Practice Set — 50 Questions with Answers

50 exam-oriented Strength of Materials multiple-choice questions with the correct answer and a clear explanation for each. Frequently asked in AE Level Civil Engineering, JE Level Civil Engineering. Solve the full set below for free — no login required.

  1. 1
    Strength of MaterialsMEDIUM

    In a 'statically indeterminate' structure, 'compatibility' equations ensure:

    AForces are in equilibrium only
    BDeformations are geometrically consistent with support conditions and member continuity — no gaps or overlaps
    CStresses are below yield
    DThe structure is safe against buckling

    Answer: B. Deformations are geometrically consistent with support conditions and member continuity — no gaps or overlaps

    Explanation: Compatibility (geometric) equations: ensure deformations are consistent — no gaps or overlaps at joints, supports are satisfied (zero displacement where constrained), continuous members remain connected. In force method (flexibility method): redundant forces chosen such that deformations at released points are compatible (closure conditions). Compatibility + equilibrium + constitutive = complete solution.

  2. 2
    Strength of MaterialsMEDIUM

    The 'section classification' of steel sections in IS 800 (plastic/compact/semi-compact/slender) depends on:

    AMaterial yield strength only
    Bb/t ratios of compression elements relative to ε = √(250/fy) — governs whether plastic, compact, semi-compact, or slender
    COnly member length
    DConnection type (welded vs bolted)

    Answer: B. b/t ratios of compression elements relative to ε = √(250/fy) — governs whether plastic, compact, semi-compact, or slender

    Explanation: IS 800 Table 2: section class depends on b/t ratios of compression elements (flanges, webs). Plastic (Class 1): can form plastic hinges with full rotation capacity (b/t ≤ 8.4ε, ε = √(250/fy)). Compact (Class 2): attain Mp but limited rotation. Semi-compact (Class 3): elastic moment only (Me). Slender (Class 4): local buckling before yield — effective section needed. Classification determines design method.

  3. 3
    Strength of MaterialsMEDIUM

    The 'virtual work principle' states that for a system in equilibrium, if it undergoes a virtual displacement:

    AExternal work = 0 always
    BVirtual work of external forces = virtual internal strain energy for equilibrium (δW_ext = δW_int)
    CStresses must be zero
    DDisplacement must be real, not virtual

    Answer: B. Virtual work of external forces = virtual internal strain energy for equilibrium (δW_ext = δW_int)

    Explanation: Principle of virtual work: for a system in equilibrium, the total virtual work done by all external forces through any compatible virtual displacement = virtual strain energy stored = 0 (for virtual work of external forces minus internal work). Used as: (1) equilibrium check; (2) computing deflections (unit load method). The virtual displacement must be kinematically admissible (compatible with constraints).

  4. 4
    Strength of MaterialsHARD

    In the 'Muller-Breslau principle', the influence line for a function (reaction, shear, moment) is the:

    AFree body diagram of the structure
    BDeflected shape when the restraint is removed and unit deformation applied — direct graphical construction of IL
    CThe loading pattern itself
    DBending moment under full loading

    Answer: B. Deflected shape when the restraint is removed and unit deformation applied — direct graphical construction of IL

    Explanation: Muller-Breslau: the influence line for any function X in a structure is the deflected shape of the structure when the restraint corresponding to X is removed and a unit displacement (for reactions/shears) or unit rotation (for moments) is applied in the direction of X. Extremely powerful: find IL shape without calculating ordinates individually. For propped reaction: remove prop, apply unit settlement = IL for reaction.

  5. 5
    Strength of MaterialsMEDIUM

    The 'direct stiffness' global matrix after assembly is generally:

    ADiagonal only — zero off-diagonal terms
    BSymmetric and banded (non-zeros near diagonal); singular until BCs applied — rigid body motion possible
    CAlways upper triangular from assembly
    DFull dense matrix with all non-zero terms

    Answer: B. Symmetric and banded (non-zeros near diagonal); singular until BCs applied — rigid body motion possible

    Explanation: Assembled global stiffness matrix [K]: (1) Symmetric: Kij = Kji (reciprocal theorem); (2) Banded: non-zero only near diagonal (elements near each other share DOF); (3) Singular before boundary conditions (rigid body modes possible); (4) Positive semi-definite. After applying boundary conditions (zeroing rows/columns of restrained DOF): becomes positive definite, non-singular → solvable. Bandwidth minimized by node numbering algorithms.

  6. 6
    Strength of MaterialsMEDIUM

    The 'approximate analysis' of building frames under lateral loads (portal frame method) assumes:

    AAll members have same stiffness (EI uniform)
    BInflection points at mid-height of columns and mid-span of beams; interior columns resist double shear of exterior
    COnly horizontal loads exist
    DAll beam moments are zero

    Answer: B. Inflection points at mid-height of columns and mid-span of beams; interior columns resist double shear of exterior

    Explanation: Portal method (lateral loads, low-rise frames): (1) Inflection point at mid-height of each column; (2) Inflection point at mid-span of each beam; (3) Internal columns carry twice the shear of exterior columns (assume each bay is a portal frame). Results in statically determinate sub-frames. Suitable for low-rise frames (< 10 storeys). Cantilever method: assumes column axial force proportional to distance from centroid (for tall frames).

  7. 7
    Strength of MaterialsHARD

    The 'Timoshenko beam' theory differs from Euler-Bernoulli theory by including:

    AOnly bending stress in the flanges
    BTransverse shear deformation and rotatory inertia — critical for deep beams or high-frequency vibration modes
    CAxial deformation only
    DTemperature effects along the beam

    Answer: B. Transverse shear deformation and rotatory inertia — critical for deep beams or high-frequency vibration modes

    Explanation: Timoshenko beam: includes shear deformation (transverse shear strain) AND rotatory inertia. E-B: assumes plane sections perpendicular to beam axis remain plane and perpendicular (no shear deformation). Timoshenko: sections remain plane but NOT necessarily perpendicular (shear angle φ). Important for: deep beams (span/depth < 10), composite beams with weak core, dynamic analysis (higher modes). Shear factor κ: 5/6 for rectangular, 0.9 for circular.

  8. 8
    Strength of MaterialsHARD

    The 'plastic hinge rotation capacity' in steel beams depends on:

    AApplied live load only
    BSection classification (Class 1 plastic), steel grade ductility, and lateral restraint — determines if plastic moment can be maintained during redistribution
    COnly the span of the beam
    DConnection bolt grade only

    Answer: B. Section classification (Class 1 plastic), steel grade ductility, and lateral restraint — determines if plastic moment can be maintained during redistribution

    Explanation: Plastic hinge rotation capacity: needed when Pp (plastic collapse load) requires redistribution. Ductility depends on: (1) Steel grade (higher strength = lower ductility); (2) Section compactness (Class 1: can form and rotate plastic hinge; Class 2: can form but limited rotation; Class 3: reach My only); (3) Lateral restraint (prevent LTB); (4) Web-flange proportions. IS 800 limits Class 1 (plastic): b/t ≤ 8.4ε for flange, d/tw ≤ 84ε for web (ε = √(250/fy)).

  9. 9
    Strength of MaterialsMEDIUM

    If the area of tensile steel reinforcement is doubled in a singly reinforced beam, the moment of resistance of the beam increases by about

    A12%
    B22%
    C32%
    D42%

    Answer: C. 32%

    Explanation: In a balanced or under-reinforced section, the moment of resistance is proportional to the area of steel (Ast) multiplied by the lever arm (d - n/3). While doubling Ast increases the force component, the neutral axis depth (n) also increases, which slightly reduces the lever arm. The net increase in moment of resistance is approximately 32%.

  10. 10
    Strength of MaterialsMEDIUM

    A cantilever beam of length L is subjected to a uniformly distributed load w (load per unit length) over its whole length L and a concentrated load W (upward) at the free end. If the total downward load W_total = wL is equal to the upward concentrated load W, the deflection at the free end is:

    AZero
    BwL^4/8EI (downward)
    CWL^3/3EI (upward)
    DWL^3/8EI (downward)

    Answer: B. wL^4/8EI (downward)

    Explanation: The downward deflection due to UDL is wL^4/8EI. The upward deflection due to point load W at the free end is WL^3/3EI. Since W = wL, the net deflection is (wL^4/8EI) - (wL^4/3EI), which is downward.

  11. 11
    Strength of MaterialsMEDIUM

    With a decrease in lateral stiffness of a regular typical building, the design horizontal seismic coefficient will

    Aincrease
    Bdecrease
    Cremain unchanged
    Ddepends on the height

    Answer: B. decrease

    Explanation: According to IS 1893, the design horizontal seismic coefficient (Ah) is proportional to the spectral acceleration (Sa/g). A decrease in lateral stiffness increases the natural period (T). For most structures in the constant acceleration or velocity range, an increase in T leads to a decrease in Sa/g, thus decreasing Ah.

  12. 12
    Strength of MaterialsMEDIUM

    The latest start of an activity is always

    Aequal to the latest event time of the preceding node
    Bless than the latest event time of the preceding node
    Cgreater than or equal to the latest event time of the preceding node
    Dindependent of the latest event time of the preceding node

    Answer: C. greater than or equal to the latest event time of the preceding node

    Explanation: For an activity i-j, the latest start time is LST = TL(j) - duration. The latest event time of the preceding node, TL(i), is the minimum of the latest start times of activities leaving that node. Hence an activity's LST is always greater than or equal to TL(i), with equality for at least one controlling outgoing activity.

  13. 13
    Strength of MaterialsMEDIUM

    A beam AB of length 10 m having both ends fixed is acted upon by a concentrated load of 10 tonnes at C at a distance of 4 m from A. The B.M. at C is

    A11.52 t-m (Hogging)
    B14.4 t-m (Hogging)
    C9.6 t-m (Sagging)
    D11.52 t-m (Sagging)

    Answer: D. 11.52 t-m (Sagging)

    Explanation: For a fixed beam with load P at distance a from A and b from B (L=a+b), the moment at C is M_c = (P * a² * b²) / L³. Here P=10, a=4, b=6, L=10. M_c = (10 * 16 * 36) / 1000 = 5.76 t-m. The original options provided are inconsistent with standard structural analysis formulas for fixed beams.

  14. 14
    Strength of MaterialsMEDIUM

    In case of mild steel, the value of the stress at elastic limit is

    ASame as that at limit of proportionality
    BMore than that at limit of proportionality
    CLess than that at limit of proportionality
    DIndependent and cannot be compared

    Answer: A. Same as that at limit of proportionality

    Explanation: For mild steel, the limit of proportionality and the elastic limit are practically identical, though the elastic limit is theoretically slightly higher.

  15. 15
    Strength of MaterialsMEDIUM

    The maximum deflection in a steel beam is limited to

    AL/360
    BL/325
    CL/250
    DL/150

    Answer: A. L/360

    Explanation: According to IS 800:2007, the maximum deflection for beams supporting brittle cladding is generally limited to L/300, and for general cases, it is often L/360.

  16. 16
    Strength of MaterialsMEDIUM

    Which of the following bends will cause the maximum head loss?

    A30° bend
    B60° bend
    C90° bend
    DU-bend

    Answer: D. U-bend

    Explanation: Head loss in a pipe bend increases with the angle of the bend. A U-bend (180°) causes more head loss than a 90° bend.

  17. 17
    TorsionEASY

    Power transmitted by a shaft rotating at N rpm with torque T (N·m):

    AP = 2πNT/60
    BP = NT/60
    CP = πNT/30
    DP = 2NT/60

    Answer: A. P = 2πNT/60

    Explanation: P = T×ω = T×(2πN/60) = 2πNT/60 watts. Or P = 2πNT/60000 kW.

  18. 18
    Columns and StrutsEASY

    Effective length L_e for a column fixed at one end and hinged at the other:

    AL
    B0.5L
    C0.7L
    D2L

    Answer: C. 0.7L

    Explanation: Effective lengths: Pin-pin = L; Fixed-fixed = 0.5L; Fixed-free = 2L; Fixed-hinged = 0.7L (≈L/√2).

  19. 19
    TorsionMEDIUM

    A hollow shaft (D_o=100mm, D_i=50mm) vs solid shaft (D=100mm), same material and torque. Hollow shaft weight saving:

    A75%
    B25%
    C50%
    D12.5%

    Answer: B. 25%

    Explanation: Weight ∝ cross-sectional area. Solid: π×100²/4. Hollow: π(100²−50²)/4 = π×7500/4. Saving = (100²−(100²−50²))/100² = 2500/10000 = 25%.

  20. 20
    Strength of MaterialsMEDIUM

    The 'consistent deformation' (compatibility) method for redundant beams removes redundants and applies:

    APrescribing displacement at all nodes
    BUnit redundant forces and compatibility equations: δ_load + Σfij×Xj = 0 → solve for redundants
    CReplacing structure with equivalent plates
    DUsing finite elements only

    Answer: B. Unit redundant forces and compatibility equations: δ_load + Σfij×Xj = 0 → solve for redundants

    Explanation: Force method (flexibility/compatibility): (1) Remove redundants to get released (statically determinate) structure; (2) Find displacements at released points due to external loads (free body terms); (3) Apply unit values of redundants and find influence coefficients (flexibility coefficients fij); (4) Write compatibility equations: δ_released + Σ(fij × Xj) = 0; (5) Solve for redundants X. Then all internal forces by superposition.

  21. 21
    Strength of MaterialsMEDIUM

    In 'combined bending and torsion' for a circular shaft, the 'equivalent twisting moment' Teq is:

    ATeq = M + T
    BTeq = √(M² + T²) — combines bending and torsion effects for max shear stress check
    CTeq = (M + T)/2
    DTeq = M × T

    Answer: B. Teq = √(M² + T²) — combines bending and torsion effects for max shear stress check

    Explanation: For shaft with bending M and torque T: Equivalent torque Teq = √(M²+T²) (used with τ formula: τ = Teq×r/J for max shear). Equivalent bending moment Meq = (M + √(M²+T²))/2 (used with bending stress σ = Meq/Z). Principal stress: σ1,2 = σ_b/2 ± √((σ_b/2)²+τ²). Design shafts for: Teq and τ ≤ τ_allow, or Meq and σ ≤ σ_allow.

  22. 22
    Strength of MaterialsHARD

    In 'finite element analysis' (FEA), the 'isoparametric formulation' uses:

    ADifferent functions for geometry and displacement
    BSame shape functions N_i for both geometric mapping and displacement interpolation — allows curved element boundaries
    COnly triangular elements
    DAnalytical integration only

    Answer: B. Same shape functions N_i for both geometric mapping and displacement interpolation — allows curved element boundaries

    Explanation: Isoparametric element: same shape functions N_i used for both geometry (x,y) and displacement (u,v): x=ΣN_i×x_i, u=ΣN_i×u_i. Allows curved element sides (essential for curved boundaries). Integration: numerical Gauss quadrature in natural coordinates (ξ,η). 4-node quadrilateral → bilinear; 8-node serendipity → quadratic. Jacobian J transforms from physical to natural coordinates.

  23. 23
    Strength of MaterialsMEDIUM

    The 'slope' at the free end of a cantilever beam of span L, EI, under end point load P is:

    Aθ = PL³/(3EI) (this is the deflection formula)
    Bθ = PL²/(2EI) — slope at free end of cantilever under end point load
    Cθ = PL/(EI)
    Dθ = 2PL²/(EI)

    Answer: B. θ = PL²/(2EI) — slope at free end of cantilever under end point load

    Explanation: Cantilever deflection: slope at free end θ = PL²/(2EI); deflection at free end δ = PL³/(3EI). For cantilever under UDL w: θ = wL³/(6EI), δ = wL⁴/(8EI). Mohr''s theorems: (1) change in slope = area of M/EI diagram; (2) deflection = moment of M/EI area about reference. Standard results used in superposition (e.g. propped cantilever analysis).

  24. 24
    Strength of MaterialsMEDIUM

    The 'temperature stress' in a bar fixed at both ends is:

    Aσ = E×α×ΔT×L (includes length)
    Bσ = E×α×ΔT (compressive) — restrained expansion creates stress proportional to thermal strain
    CZero (temperature causes no stress)
    Dσ = α×ΔT only (no E needed)

    Answer: B. σ = E×α×ΔT (compressive) — restrained expansion creates stress proportional to thermal strain

    Explanation: Temperature stress: bar fixed at both ends, temperature rises by ΔT. Free thermal strain = αΔT, but restrained → compressive stress developed = E×αΔT (compressive because bar wants to expand but cannot). No strain in bar. If one end is free: expansion ΔL = αΔTL, no stress. For prestress: temperature stress important in bridges where expansion joints are limited.

  25. 25
    Strength of MaterialsHARD

    The 'collapse load' for a fixed-fixed beam of span L under central point load W is:

    AW = 8Mp/L
    BW = 16Mp/L — three hinges (both ends + midspan) mechanism gives collapse load
    CW = 4Mp/L
    DW = 12Mp/L (this applies to fixed-pinned)

    Answer: B. W = 16Mp/L — three hinges (both ends + midspan) mechanism gives collapse load

    Explanation: Fixed-fixed beam under central W: collapse mechanism needs 3 plastic hinges (both fixed ends + midspan). At collapse: W×L/4 = Mp (from virtual work: W×δ = Mp×θ + Mp×2θ + Mp×θ = 4Mp×θ, δ = L/4×θ). So W_collapse = 16Mp/L. For fixed-pinned: W = 12Mp/L (2 hinges only). Plastic analysis always > elastic analysis because Mp > Me.

  26. 26
    Strength of MaterialsHARD

    The 'funicular polygon' for a set of concentrated loads gives the shape of:

    ABending moment diagram only
    BThe cable shape under those specific loads — pure tension in cable segments (or compression in equivalent arch)
    CDeflection of a beam
    DShear force diagram

    Answer: B. The cable shape under those specific loads — pure tension in cable segments (or compression in equivalent arch)

    Explanation: Funicular polygon: graphical method combining force polygon (vector polygon of loads + reactions) with space diagram to find the shape a cable or arch must take to carry those specific concentrated loads in pure tension or compression (no bending). For a cable: funicular polygon = cable shape. Rays from pole in force polygon correspond to cable segments. Useful for finding reactions and cable geometry.

  27. 27
    Propped Cantilever ReactionMEDIUM

    A propped cantilever beam of span L with a uniformly distributed load w per unit length has a prop reaction at the free end of:

    A3wL/8
    B5wL/8
    CwL/2
    DwL/4

    Answer: A. 3wL/8

    Explanation: Propped cantilever with UDL w: prop reaction R = 3wL/8 (at the simply supported end). Fixed end reaction = 5wL/8, fixed end moment = wL^2/8. This is a standard one-degree statically indeterminate beam solved by compatibility (deflection at prop = 0). Bending moment at fixed end = wL^2/8 (hogging).

  28. 28
    Strength of Materials and Structural AnalysisMEDIUM

    The core or kern of a section is the area within which load causes:

    APlastic collapse only
    BNo tensile stress anywhere in section
    CMaximum shear at surface
    DZero compressive stress

    Answer: B. No tensile stress anywhere in section

    Explanation: If resultant passes through kern, stress remains compressive throughout.

  29. 29
    Strength of Materials and Structural AnalysisEASY

    Effective length of a column fixed at one end and free at other is:

    A2L
    BL/2
    CL/sqrt(2)
    DL

    Answer: A. 2L

    Explanation: A cantilever column has effective length twice its unsupported length.

  30. 30
    Strength of Materials and Structural AnalysisEASY

    Effective length of a column hinged at both ends is:

    A2L
    B0.5L
    CL
    D0.7L

    Answer: C. L

    Explanation: Pin-ended column has effective length equal to actual length.

  31. 31
    Strength of Materials and Structural AnalysisMEDIUM

    Middle third rule applies to:

    AOpen channel flow
    BRectangular section under eccentric compression
    CFlexible pavement
    DTorsion of circular shaft

    Answer: B. Rectangular section under eccentric compression

    Explanation: Resultant within middle third avoids tension at base.

  32. 32
    Perry-Robertson FormulaMEDIUM

    Perry-Robertson formula in column design accounts for:

    AMaterial plasticity
    BInitial bow/imperfection of columns
    CEnd fixity only
    DTemperature effect

    Answer: B. Initial bow/imperfection of columns

    Explanation: Perry-Robertson includes initial geometric imperfection (bow) of real columns; used in BS:449.

  33. 33
    Definition of Elastic ModulusEASY

    The modulus of elasticity of a material is defined as:

    AStress/strain within elastic limit
    BStrain/stress within elastic limit
    CUltimate stress/fracture strain
    DYield stress/plastic strain

    Answer: A. Stress/strain within elastic limit

    Explanation: Young's modulus E = σ/ε within the proportional (elastic) limit.

  34. 34
    Strength of MaterialsHARD

    For ductile materials, failure theory commonly used under combined stress is:

    Aminimum strain energy theory
    Bmaximum principal strain theory only
    CEuler theory
    Dmaximum shear stress theory

    Answer: D. maximum shear stress theory

    Explanation: Tresca maximum shear stress theory is often applied to ductile materials.

  35. 35
    Strength of MaterialsHARD

    The flexural rigidity of a beam is:

    AEA
    BM/I
    CGJ
    DEI

    Answer: D. EI

    Explanation: Flexural rigidity is the product of modulus of elasticity and second moment of area.

  36. 36
    Strength of MaterialsHARD

    Rankine's column formula combines:

    Atorsion and bending only
    Bcrushing and buckling effects
    Cfatigue and impact only
    Dshear and creep only

    Answer: B. crushing and buckling effects

    Explanation: Rankine formula is an empirical interaction of crushing load and Euler buckling load.

  37. 37
    Strength of MaterialsHARD

    The neutral axis of a homogeneous beam section under pure bending passes through:

    Apoint of maximum shear only
    Bcentroid of the section
    Ctopmost fibre
    Dbottommost fibre

    Answer: B. centroid of the section

    Explanation: For homogeneous prismatic beams, the neutral axis passes through the centroid.

  38. 38
    Theory of Structures and DesignHARD

    The maximum shear stress in a rectangular beam section is:

    A1.5 times average shear stress
    Bzero at neutral axis
    Cequal to average shear stress
    D2 times average shear stress

    Answer: A. 1.5 times average shear stress

    Explanation: For a rectangle, shear stress distribution is parabolic and maximum at the neutral axis is 1.5 times average shear stress.

  39. 39
    Theory of Structures and DesignHARD

    For a simply supported beam carrying UDL w over full span, maximum deflection is:

    AwL^3/(48EI)
    BwL^4/(8EI)
    CwL^4/(185EI)
    D5wL^4/(384EI)

    Answer: D. 5wL^4/(384EI)

    Explanation: The maximum midspan deflection under full-span UDL is 5wL^4/(384EI).

  40. 40
    Theory of Structures and DesignHARD

    For a rectangular section of width b and depth d, the plastic shape factor in bending about the centroidal axis parallel to b is:

    A1.00
    B1.50
    C1.33
    D2.00

    Answer: B. 1.50

    Explanation: For a rectangle, Zp = bd^2/4 and Ze = bd^2/6, hence shape factor = Zp/Ze = 1.5.

  41. 41
    Theory of Structures and DesignHARD

    The member stiffness at end A of a prismatic beam AB, when end B is hinged, is:

    A2EI/L
    BEI/L
    C3EI/L
    D4EI/L

    Answer: C. 3EI/L

    Explanation: The rotational stiffness is 4EI/L if the far end is fixed and 3EI/L if the far end is hinged.

  42. 42
    Strength of Materials and Structural AnalysisHARD

    Shear stress at the top and bottom fibres of a rectangular beam section is:

    AZero
    BInfinite
    CMaximum
    DEqual to average shear

    Answer: A. Zero

    Explanation: Shear stress distribution is parabolic and becomes zero at extreme fibres.

  43. 43
    Strength of Materials and Structural AnalysisHARD

    In plastic analysis, shape factor is the ratio of:

    ALoad to deflection
    BPlastic moment to yield moment
    CShear to bending moment
    DYield stress to ultimate stress

    Answer: B. Plastic moment to yield moment

    Explanation: Shape factor measures reserve moment capacity beyond first yield.

  44. 44
    Strength of Materials and Structural AnalysisEASY

    In a simply supported beam with central point load W, maximum bending moment is:

    AWL/2
    BWL/4
    CWL/8
    DWL

    Answer: B. WL/4

    Explanation: Reactions are W/2 each and maximum moment occurs at midspan.

  45. 45
    Strength of Materials and Structural AnalysisHARD

    Euler buckling load of a column is inversely proportional to:

    AModulus of elasticity only
    BSquare of effective length
    CEffective length only
    DRadius of gyration only

    Answer: B. Square of effective length

    Explanation: Euler's critical buckling load: Pcr = π²EI / Le², where E is Young's modulus, I is moment of inertia, and Le is effective length of the column. Pcr is inversely proportional to Le² (square of effective length). Answer: Square of effective length. Effective length Le depends on end conditions: Le = L (pinned-pinned), Le = 0.5L (fixed-fixed), Le = 0.7L (fixed-pinned), Le = 2L (fixed-free/cantilever).

  46. 46
    Strength of Materials and Structural AnalysisHARD

    In pure bending, shear force is:

    AMaximum
    BInfinite
    CEqual to bending moment
    DZero

    Answer: D. Zero

    Explanation: Pure bending means constant bending moment and zero shear force.

  47. 47
    Strength of MaterialsMEDIUM

    A rectangular beam is to be cut from a circular log of wood of diameter D. The depth of the strongest section is

    AD/3
    BD/sqrt(3)
    C2D/3
    DD sqrt(2/3)

    Answer: D. D sqrt(2/3)

    Explanation: For maximum section modulus of a rectangle inscribed in a circle, depth = D sqrt(2/3)

  48. 48
    Geotechnical EngineeringMEDIUM

    The quantity of seepage of water through soil is proportional to: (I) coefficient of permeability of the soil; (II) total head loss through the soil.

    AOnly I
    BOnly II
    CBoth I and II
    DNeither I nor II

    Answer: C. Both I and II

    Explanation: q = k i A = k (h/L) A, so the seepage is proportional to both the permeability and the total head loss.

  49. 49
    RCC DesignMEDIUM

    A slab supported along two opposite sides is called a

    AOverhanging slab
    BTwo way slab
    COne way slab
    DCantilever slab

    Answer: C. One way slab

    Explanation: A slab spanning between two opposite supports bends in one direction and is a one-way slab.

  50. 50
    Irrigation & Water ResourcesMEDIUM

    Which of the following methods of irrigation does NOT use open ditches for water delivery?

    ASub-irrigation
    BTrickle irrigation
    CFurrow irrigation
    DCheck irrigation

    Answer: B. Trickle irrigation

    Explanation: Trickle (drip) irrigation delivers water through a closed network of pipes and emitters, not open ditches. [Self-solved — please verify.]

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