Engineering Mechanics and Strength of Materials MCQs 2026

Yield point is where

1. A elastic modulus changes to zero instantly ✓
2. B specimen fractures ✓
3. C material begins large inelastic deformation ✓
4. D creep starts always ✓

Proportional limit is

1. A stress at fracture ✓
2. B ultimate stress ✓
3. C stress below which stress-strain is linear ✓
4. D fatigue limit ✓

Strain is defined as

1. A stress divided by area ✓
2. B force times displacement ✓
3. C moment divided by EI ✓
4. D change in dimension divided by original dimension ✓

A frame differs from truss in that

1. A frames have only pin joints always ✓
2. B trusses carry bending primarily ✓
3. C frames have no moments ✓
4. D frames resist loads by bending in members and joints may be rigid ✓

Centre of gravity of composite body uses

1. A only largest part centroid ✓
2. B only volume without density ✓
3. C only perimeter ✓
4. D moment summation of parts divided by total weight ✓

A cantilever with point load at free end has maximum BM at

1. A the free end ✓
2. B mid-span ✓
3. C the fixed support ✓
4. D point of load only if interior ✓

Deflection of a beam is related to curvature by

1. A dy/dx = M/EI ✓
2. B 1/R ≈ d²y/dx² = M/(EI) ✓
3. C y = M/EI ✓
4. D curvature equals shear ✓

Euler-Bernoulli beam theory assumes

1. A large deflections always ✓
2. B plane sections remain plane and small deformations ✓
3. C shear deformation dominates always ✓
4. D material is rigid-plastic ✓

Moment of inertia of area is used to compute

1. A bending stress and deflection ✓
2. B only axial stress ✓
3. C only torsional shear in all sections ✓
4. D only thermal expansion ✓

Parallel axis theorem states I about any axis equals

1. A I_c − Ad² ✓
2. B I_c only ✓
3. C Ad² only ✓
4. D I_c + Ad² ✓

Section modulus Z is defined as

1. A y_max/I ✓
2. B A/I ✓
3. C I/y_max ✓
4. D I/A ✓

Bending stress in a beam varies

1. A uniformly across depth ✓
2. B linearly with distance from neutral axis ✓
3. C parabolically always ✓
4. D only at supports ✓

Neutral axis in pure bending passes through

1. A top fibre always ✓
2. B centroid of cross-section for homogeneous beams ✓
3. C bottom fibre always ✓
4. D shear centre always ✓

Maximum bending stress occurs at

1. A extreme fibres farthest from neutral axis ✓
2. B neutral axis ✓
3. C shear centre only ✓
4. D centroid only ✓

Shear stress distribution in rectangular beam is

1. A uniform ✓
2. B triangular with max at top ✓
3. C zero at NA ✓
4. D parabolic with maximum at neutral axis ✓

Principal stresses at a point are

1. A always equal to σ_x and σ_y ✓
2. B always zero ✓
3. C normal stresses on planes with zero shear stress ✓
4. D only shear stresses ✓

Mohr circle for plane stress is used to find

1. A principal stresses and maximum shear stress ✓
2. B deflection of beams ✓
3. C buckling load only ✓
4. D reinforcement area ✓

Maximum in-plane shear stress equals

1. A sum of principal stresses ✓
2. B difference of normal stresses without halving ✓
3. C radius of Mohr circle ✓
4. D zero at principal planes ✓

For equal biaxial tension σ_x = σ_y = σ, principal stresses are

1. A σ and −σ ✓
2. B zero and σ ✓
3. C 2σ and 0 ✓
4. D σ and σ (both tensile) ✓

Von Mises yield criterion is important for

1. A ductile materials under combined stress ✓
2. B only brittle fracture ✓
3. C only concrete in tension ✓
4. D only soil consolidation ✓

Torsional shear stress in circular shaft varies

1. A uniformly across section ✓
2. B inversely with radius ✓
3. C linearly with radius ✓
4. D only at surface zero ✓

Polar moment of inertia J for solid circle is

1. A πd⁴/64 ✓
2. B πd⁴/32 ✓
3. C bh³/12 ✓
4. D πr² ✓

Power transmitted by shaft is

1. A Tω where T is torque and ω angular velocity ✓
2. B T/ω ✓
3. C ω/T ✓
4. D Tω² only ✓

Strain energy due to axial load is

1. A PL/AE ✓
2. B P²L/(2AE) ✓
3. C AE/L ✓
4. D σ/E only ✓

Castigliano theorem states that

1. A stress equals strain energy ✓
2. B moment equals shear ✓
3. C deflection equals partial derivative of strain energy with respect to load ✓
4. D load equals stiffness squared ✓

A statically determinate structure has

1. A infinite solutions ✓
2. B no equilibrium equations ✓
3. C only compatibility needed ✓
4. D unique reactions solvable from equilibrium alone ✓

Three equations of static equilibrium in 2D are

1. A four moment equations ✓
2. B ΣFx=0, ΣFy=0, ΣM=0 ✓
3. C only ΣF=0 ✓
4. D ΣF and compatibility ✓

Method of joints in truss analysis uses

1. A compatibility of deflections only ✓
2. B Mohr circle ✓
3. C moment distribution only ✓
4. D equilibrium of concurrent forces at each joint ✓

Method of sections in trusses uses

1. A only joint summation ✓
2. B equilibrium of a cut free-body ✓
3. C only energy method ✓
4. D only plastic analysis ✓

Zero-force members in trusses occur when

1. A all members always carry load ✓
2. B only at supports ✓
3. C two non-collinear members at unloaded joint carry no force in third member ✓
4. D only in roof trusses ✓

Deflection of cantilever with end load P is

1. A PL³/(48EI) ✓
2. B PL³/(3EI) ✓
3. C 5wL⁴/(384EI) ✓
4. D PL/4AE ✓

Deflection of simply supported beam centre load P is

1. A PL³/(3EI) ✓
2. B wL⁴/(8EI) ✓
3. C PL/2AE ✓
4. D PL³/(48EI) ✓

Macaulay bracket method helps in

1. A finding centroid only ✓
2. B soil bearing capacity ✓
3. C mix design only ✓
4. D writing deflection equation with discontinuous loading ✓

Wedge friction problem uses

1. A limiting equilibrium on inclined plane ✓
2. B only energy method ✓
3. C only Mohr-Coulomb for soil always ✓
4. D only truss analysis ✓

Resultant of parallel forces equals

1. A algebraic sum of forces ✓
2. B vector sum perpendicular only ✓
3. C product of forces ✓
4. D moment about any point ✓

Complementary shear stresses on perpendicular planes are

1. A equal in magnitude ✓
2. B zero always ✓
3. C double each other ✓
4. D independent ✓

Pure shear stress state has principal stresses

1. A both tensile ✓
2. B equal in magnitude and opposite in sign ✓
3. C both zero ✓
4. D one zero one tensile ✓

Radius of gyration r equals

1. A I/A ✓
2. B A/I ✓
3. C √(I/A) ✓
4. D I×A ✓

Slenderness ratio is defined as

1. A radius over length ✓
2. B effective length divided by radius of gyration ✓
3. C area over I ✓
4. D load over area ✓

Effective length of column fixed at both ends is

1. A 2L ✓
2. B L ✓
3. C 0.7L ✓
4. D 0.5L ✓

Buckling load for pin-ended slender column by Euler is

1. A πEI/L ✓
2. B 4π²EI/L² ✓
3. C π²EI/L² ✓
4. D AE/L ✓

Creep is

1. A instant elastic strain ✓
2. B time-dependent deformation under constant stress at high temperature ✓
3. C only impact loading ✓
4. D only buckling ✓

The SI unit of force is

1. A joule ✓
2. B pascal ✓
3. C watt ✓
4. D newton ✓

Ultimate tensile strength is

1. A stress at elastic limit only ✓
2. B maximum stress on engineering stress-strain curve ✓
3. C minimum stress ✓
4. D shear at NA ✓

Ductility is measured by

1. A only elastic modulus ✓
2. B percentage elongation or reduction in area ✓
3. C only hardness number ✓
4. D only density ✓

Brittle materials fail

1. A only after large necking ✓
2. B suddenly with little plastic deformation ✓
3. C only in compression always ✓
4. D only under torsion ✓

Modulus of resilience is

1. A total area to fracture ✓
2. B yield stress only ✓
3. C hardness index ✓
4. D area under elastic portion of stress-strain curve ✓

For thin cylinder under internal pressure, hoop stress is

1. A twice longitudinal stress in thin-wall approximation ✓
2. B half longitudinal stress ✓
3. C equal to shear only ✓
4. D zero ✓

Modulus of toughness is

1. A only elastic area ✓
2. B total area under stress-strain curve to fracture ✓
3. C σ_y/E ✓
4. D shear modulus ✓

Bending moment diagram for cantilever with UDL is

1. A linear ✓
2. B constant ✓
3. C parabolic ✓
4. D triangular only at supports ✓

Shear force diagram for beam with UDL is

1. A parabolic ✓
2. B linear ✓
3. C constant non-zero throughout ✓
4. D circular ✓

Combined bending and axial tension shifts neutral axis

1. A to centroid always ✓
2. B to compression side always ✓
3. C toward tension side ✓
4. D outside section always ✓

Eccentric axial load on short column produces

1. A combined axial stress and bending stress ✓
2. B only uniform axial stress ✓
3. C only torsion ✓
4. D only shear ✓

Shear centre is point through which

1. A moment is zero always ✓
2. B BM is maximum ✓
3. C shear load must act to avoid twisting ✓
4. D axial stress is zero ✓

Saint-Venant principle states that

1. A local effects decay away from application region ✓
2. B stress is uniform everywhere ✓
3. C equilibrium is unnecessary ✓
4. D compatibility is zero ✓

Work of a force is

1. A force times time ✓
2. B force times displacement in direction of force ✓
3. C moment times angle only ✓
4. D mass times acceleration ✓

Kinetic energy of particle is

1. A ½mv² ✓
2. B mv ✓
3. C ½mv ✓
4. D mgh always ✓

Potential energy due to gravity is

1. A ½mgh ✓
2. B mv² ✓
3. C mgh ✓
4. D Fh always ✓

Virtual work principle requires

1. A plastic collapse only ✓
2. B equilibrium and virtual displacements compatible ✓
3. C only dynamic loads ✓
4. D only truss zero force ✓

Stress concentration occurs at

1. A uniform prismatic bars only ✓
2. B sudden changes in cross-section ✓
3. C centroid only ✓
4. D neutral axis only ✓

A body is in static equilibrium when

1. A only forces sum to zero ✓
2. B velocity is maximum ✓
3. C sum of forces and sum of moments are both zero ✓
4. D acceleration is constant ✓

Flexural rigidity of beam is

1. A EA ✓
2. B EI ✓
3. C GJ ✓
4. D EI/L only ✓

Compatibility condition in indeterminate structures ensures

1. A only ΣF=0 ✓
2. B only concrete cracks ✓
3. C only steel yields ✓
4. D deformations fit together ✓

A propped cantilever is

1. A statically determinate ✓
2. B unstable ✓
3. C statically indeterminate to first degree ✓
4. D three degrees indeterminate always ✓

Maximum shear in a simply supported beam with central point load occurs

1. A at the supports ✓
2. B at mid-span ✓
3. C at quarter span only ✓
4. D nowhere ✓

Point of contraflexure is where

1. A bending moment is zero and changes sign ✓
2. B shear force is maximum ✓
3. C deflection is maximum ✓
4. D slope is maximum ✓

The relationship between load w, shear force V and bending moment M is

1. A dM/dx = w ✓
2. B dV/dx = M ✓
3. C dM/dx = V and dV/dx = −w ✓
4. D M = V/w always ✓

Bending moment at a section equals

1. A sum of vertical forces only ✓
2. B shear force times span always ✓
3. C algebraic sum of moments of forces on one side about the section ✓
4. D area of SFD ✓

Shear force at any section equals

1. A algebraic sum of vertical forces on one side of the section ✓
2. B sum of bending moments ✓
3. C product of stress and area only ✓
4. D derivative of moment with respect to time ✓

In a simply supported beam with UDL w over span L, maximum bending moment is

1. A wL²/8 ✓
2. B wL²/2 ✓
3. C wL²/4 ✓
4. D wL/8 ✓

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

1. A PL/8 ✓
2. B PL/2 ✓
3. C zero at centre ✓
4. D PL/4 ✓

Thermal stress in a fully restrained bar is

1. A zero always ✓
2. B αΔTE (compressive if temperature rises in restraint) ✓
3. C independent of E ✓
4. D equal to yield stress always ✓

A prismatic bar under axial tension has constant

1. A normal stress if load is concentric ✓
2. B shear stress throughout always ✓
3. C bending moment ✓
4. D torsion ✓

Factor of safety is generally

1. A allowable stress divided by ultimate strength ✓
2. B load divided by deflection ✓
3. C ultimate strength divided by allowable stress ✓
4. D strain divided by stress ✓

Shear stress is defined as

1. A normal force divided by volume ✓
2. B tangential force divided by area ✓
3. C bending moment divided by area ✓
4. D torque divided by length only ✓

Normal stress on a plane is defined as

1. A force perpendicular to the plane divided by area ✓
2. B tangential force divided by area ✓
3. C moment divided by area ✓
4. D deflection divided by length ✓

The relationship E = 2G(1+ν) is valid for

1. A isotropic homogeneous elastic materials ✓
2. B only plastic materials ✓
3. C only orthotropic timber always ✓
4. D only fluids ✓

Modulus of rigidity G relates shear stress and shear strain as

1. A σ = Gε ✓
2. B τ = Eγ ✓
3. C σ = Gγ ✓
4. D τ = Gγ ✓

Poisson ratio is defined as

1. A lateral strain divided by longitudinal strain with proper sign ✓
2. B longitudinal to lateral strain without sign ✓
3. C shear to normal strain ✓
4. D stress to strain at failure ✓

Young modulus E is defined as

1. A ratio of longitudinal stress to longitudinal strain ✓
2. B shear stress to shear strain ✓
3. C lateral strain to longitudinal strain ✓
4. D load to deflection ✓

Hooke law in elastic range states that

1. A stress equals ultimate strength ✓
2. B strain is always zero ✓
3. C load is independent of deformation ✓
4. D stress is proportional to strain ✓

The moment of a couple is independent of

1. A magnitude of forces ✓
2. B perpendicular distance ✓
3. C plane of action ✓
4. D the point about which moment is taken ✓

A couple produces

1. A pure rotation without translation ✓
2. B pure translation only ✓
3. C zero moment everywhere ✓
4. D only normal stress ✓

Lami theorem applies to

1. A parallel forces only ✓
2. B four forces in space ✓
3. C three coplanar concurrent forces in equilibrium ✓
4. D distributed loads only ✓

Fatigue failure is caused by

1. A single overload only ✓
2. B only corrosion ✓
3. C only high temperature creep ✓
4. D repeated fluctuating stresses below static strength ✓

Angle of friction is the angle whose tangent equals

1. A coefficient of friction ✓
2. B Poisson ratio ✓
3. C modulus of elasticity ✓
4. D factor of safety ✓

Coefficient of friction is defined as the ratio of

1. A normal force to weight ✓
2. B shear stress to normal stress ✓
3. C elastic modulus to shear modulus ✓
4. D limiting friction to normal reaction ✓

The centroid of a uniform semicircular area lies at

1. A r/2 from the diameter ✓
2. B r from the diameter ✓
3. C at the centre of full circle ✓
4. D 4r/(3π) from the diameter ✓

Varignon theorem relates

1. A stress to strain only ✓
2. B work to power only ✓
3. C moment of a resultant force to sum of moments of components ✓
4. D mass to weight only ✓

The principle of transmissibility of force states that

1. A force direction may be changed freely ✓
2. B moment about any point changes ✓
3. C force must act only at centroid ✓
4. D a force may be moved along its line of action without changing external effects ✓