Engineering Mechanics and Strength of Materials MCQs 2026

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

1. Athe free end✓
2. Bmid-span✓
3. Cthe fixed support✓
4. Dpoint of load only if interior✓

Deflection of a beam is related to curvature by

1. Ady/dx = M/EI✓
2. B1/R ≈ d²y/dx² = M/(EI)✓
3. Cy = M/EI✓
4. Dcurvature equals shear✓

Euler-Bernoulli beam theory assumes

1. Alarge deflections always✓
2. Bplane sections remain plane and small deformations✓
3. Cshear deformation dominates always✓
4. Dmaterial is rigid-plastic✓

Moment of inertia of area is used to compute

1. Abending stress and deflection✓
2. Bonly axial stress✓
3. Conly torsional shear in all sections✓
4. Donly thermal expansion✓

Parallel axis theorem states I about any axis equals

1. AI_c − Ad²✓
2. BI_c only✓
3. CAd² only✓
4. DI_c + Ad²✓

Section modulus Z is defined as

1. Ay_max/I✓
2. BA/I✓
3. CI/y_max✓
4. DI/A✓

Bending stress in a beam varies

1. Auniformly across depth✓
2. Blinearly with distance from neutral axis✓
3. Cparabolically always✓
4. Donly at supports✓

Neutral axis in pure bending passes through

1. Atop fibre always✓
2. Bcentroid of cross-section for homogeneous beams✓
3. Cbottom fibre always✓
4. Dshear centre always✓

Maximum bending stress occurs at

1. Aextreme fibres farthest from neutral axis✓
2. Bneutral axis✓
3. Cshear centre only✓
4. Dcentroid only✓

Shear stress distribution in rectangular beam is

1. Auniform✓
2. Btriangular with max at top✓
3. Czero at NA✓
4. Dparabolic with maximum at neutral axis✓

Principal stresses at a point are

1. Aalways equal to σ_x and σ_y✓
2. Balways zero✓
3. Cnormal stresses on planes with zero shear stress✓
4. Donly shear stresses✓

Mohr circle for plane stress is used to find

1. Aprincipal stresses and maximum shear stress✓
2. Bdeflection of beams✓
3. Cbuckling load only✓
4. Dreinforcement area✓

Maximum in-plane shear stress equals

1. Asum of principal stresses✓
2. Bdifference of normal stresses without halving✓
3. Cradius of Mohr circle✓
4. Dzero at principal planes✓

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

1. Aσ and −σ✓
2. Bzero and σ✓
3. C2σ and 0✓
4. Dσ and σ (both tensile)✓

Von Mises yield criterion is important for

1. Aductile materials under combined stress✓
2. Bonly brittle fracture✓
3. Conly concrete in tension✓
4. Donly soil consolidation✓

Torsional shear stress in circular shaft varies

1. Auniformly across section✓
2. Binversely with radius✓
3. Clinearly with radius✓
4. Donly at surface zero✓

Polar moment of inertia J for solid circle is

1. Aπd⁴/64✓
2. Bπd⁴/32✓
3. Cbh³/12✓
4. Dπr²✓

Power transmitted by shaft is

1. ATω where T is torque and ω angular velocity✓
2. BT/ω✓
3. Cω/T✓
4. DTω² only✓

Strain energy due to axial load is

1. APL/AE✓
2. BP²L/(2AE)✓
3. CAE/L✓
4. Dσ/E only✓

Castigliano theorem states that

1. Astress equals strain energy✓
2. Bmoment equals shear✓
3. Cdeflection equals partial derivative of strain energy with respect to load✓
4. Dload equals stiffness squared✓

A statically determinate structure has

1. Ainfinite solutions✓
2. Bno equilibrium equations✓
3. Conly compatibility needed✓
4. Dunique reactions solvable from equilibrium alone✓

Three equations of static equilibrium in 2D are

1. Afour moment equations✓
2. BΣFx=0, ΣFy=0, ΣM=0✓
3. Conly ΣF=0✓
4. DΣF and compatibility✓

Method of joints in truss analysis uses

1. Acompatibility of deflections only✓
2. BMohr circle✓
3. Cmoment distribution only✓
4. Dequilibrium of concurrent forces at each joint✓

Method of sections in trusses uses

1. Aonly joint summation✓
2. Bequilibrium of a cut free-body✓
3. Conly energy method✓
4. Donly plastic analysis✓

Zero-force members in trusses occur when

1. Aall members always carry load✓
2. Bonly at supports✓
3. Ctwo non-collinear members at unloaded joint carry no force in third member✓
4. Donly in roof trusses✓

Deflection of cantilever with end load P is

1. APL³/(48EI)✓
2. BPL³/(3EI)✓
3. C5wL⁴/(384EI)✓
4. DPL/4AE✓

Deflection of simply supported beam centre load P is

1. APL³/(3EI)✓
2. BwL⁴/(8EI)✓
3. CPL/2AE✓
4. DPL³/(48EI)✓

Macaulay bracket method helps in

1. Afinding centroid only✓
2. Bsoil bearing capacity✓
3. Cmix design only✓
4. Dwriting deflection equation with discontinuous loading✓

Stress concentration occurs at

1. Auniform prismatic bars only✓
2. Bsudden changes in cross-section✓
3. Ccentroid only✓
4. Dneutral axis only✓

Fatigue failure is caused by

1. Asingle overload only✓
2. Bonly corrosion✓
3. Conly high temperature creep✓
4. Drepeated fluctuating stresses below static strength✓

The SI unit of force is

1. Ajoule✓
2. Bpascal✓
3. Cwatt✓
4. Dnewton✓

A body is in static equilibrium when

1. Aonly forces sum to zero✓
2. Bvelocity is maximum✓
3. Csum of forces and sum of moments are both zero✓
4. Dacceleration is constant✓

The principle of transmissibility of force states that

1. Aforce direction may be changed freely✓
2. Bmoment about any point changes✓
3. Cforce must act only at centroid✓
4. Da force may be moved along its line of action without changing external effects✓

Varignon theorem relates

1. Astress to strain only✓
2. Bwork to power only✓
3. Cmoment of a resultant force to sum of moments of components✓
4. Dmass to weight only✓

The centroid of a uniform semicircular area lies at

1. Ar/2 from the diameter✓
2. Br from the diameter✓
3. Cat the centre of full circle✓
4. D4r/(3π) from the diameter✓

Coefficient of friction is defined as the ratio of

1. Anormal force to weight✓
2. Bshear stress to normal stress✓
3. Celastic modulus to shear modulus✓
4. Dlimiting friction to normal reaction✓

Angle of friction is the angle whose tangent equals

1. Acoefficient of friction✓
2. BPoisson ratio✓
3. Cmodulus of elasticity✓
4. Dfactor of safety✓

Lami theorem applies to

1. Aparallel forces only✓
2. Bfour forces in space✓
3. Cthree coplanar concurrent forces in equilibrium✓
4. Ddistributed loads only✓

A couple produces

1. Apure rotation without translation✓
2. Bpure translation only✓
3. Czero moment everywhere✓
4. Donly normal stress✓

The moment of a couple is independent of

1. Amagnitude of forces✓
2. Bperpendicular distance✓
3. Cplane of action✓
4. Dthe point about which moment is taken✓

Hooke law in elastic range states that

1. Astress equals ultimate strength✓
2. Bstrain is always zero✓
3. Cload is independent of deformation✓
4. Dstress is proportional to strain✓

Young modulus E is defined as

1. Aratio of longitudinal stress to longitudinal strain✓
2. Bshear stress to shear strain✓
3. Clateral strain to longitudinal strain✓
4. Dload to deflection✓

Poisson ratio is defined as

1. Alateral strain divided by longitudinal strain with proper sign✓
2. Blongitudinal to lateral strain without sign✓
3. Cshear to normal strain✓
4. Dstress to strain at failure✓

Modulus of rigidity G relates shear stress and shear strain as

1. Aσ = Gε✓
2. Bτ = Eγ✓
3. Cσ = Gγ✓
4. Dτ = Gγ✓

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

1. Aisotropic homogeneous elastic materials✓
2. Bonly plastic materials✓
3. Conly orthotropic timber always✓
4. Donly fluids✓

Normal stress on a plane is defined as

1. Aforce perpendicular to the plane divided by area✓
2. Btangential force divided by area✓
3. Cmoment divided by area✓
4. Ddeflection divided by length✓

Shear stress is defined as

1. Anormal force divided by volume✓
2. Btangential force divided by area✓
3. Cbending moment divided by area✓
4. Dtorque divided by length only✓

Factor of safety is generally

1. Aallowable stress divided by ultimate strength✓
2. Bload divided by deflection✓
3. Cultimate strength divided by allowable stress✓
4. Dstrain divided by stress✓

A prismatic bar under axial tension has constant

1. Anormal stress if load is concentric✓
2. Bshear stress throughout always✓
3. Cbending moment✓
4. Dtorsion✓

Thermal stress in a fully restrained bar is

1. Azero always✓
2. BαΔTE (compressive if temperature rises in restraint)✓
3. Cindependent of E✓
4. Dequal to yield stress always✓

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

1. APL/8✓
2. BPL/2✓
3. Czero at centre✓
4. DPL/4✓

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

1. AwL²/8✓
2. BwL²/2✓
3. CwL²/4✓
4. DwL/8✓

Shear force at any section equals

1. Aalgebraic sum of vertical forces on one side of the section✓
2. Bsum of bending moments✓
3. Cproduct of stress and area only✓
4. Dderivative of moment with respect to time✓

Bending moment at a section equals

1. Asum of vertical forces only✓
2. Bshear force times span always✓
3. Calgebraic sum of moments of forces on one side about the section✓
4. Darea of SFD✓

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

1. AdM/dx = w✓
2. BdV/dx = M✓
3. CdM/dx = V and dV/dx = −w✓
4. DM = V/w always✓

Point of contraflexure is where

1. Abending moment is zero and changes sign✓
2. Bshear force is maximum✓
3. Cdeflection is maximum✓
4. Dslope is maximum✓

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

1. Aat the supports✓
2. Bat mid-span✓
3. Cat quarter span only✓
4. Dnowhere✓

Creep is

1. Ainstant elastic strain✓
2. Btime-dependent deformation under constant stress at high temperature✓
3. Conly impact loading✓
4. Donly buckling✓

Buckling load for pin-ended slender column by Euler is

1. AπEI/L✓
2. B4π²EI/L²✓
3. Cπ²EI/L²✓
4. DAE/L✓

Effective length of column fixed at both ends is

1. A2L✓
2. BL✓
3. C0.7L✓
4. D0.5L✓

Slenderness ratio is defined as

1. Aradius over length✓
2. Beffective length divided by radius of gyration✓
3. Carea over I✓
4. Dload over area✓

Radius of gyration r equals

1. AI/A✓
2. BA/I✓
3. C√(I/A)✓
4. DI×A✓

Pure shear stress state has principal stresses

1. Aboth tensile✓
2. Bequal in magnitude and opposite in sign✓
3. Cboth zero✓
4. Done zero one tensile✓

Complementary shear stresses on perpendicular planes are

1. Aequal in magnitude✓
2. Bzero always✓
3. Cdouble each other✓
4. Dindependent✓

Resultant of parallel forces equals

1. Aalgebraic sum of forces✓
2. Bvector sum perpendicular only✓
3. Cproduct of forces✓
4. Dmoment about any point✓

Wedge friction problem uses

1. Alimiting equilibrium on inclined plane✓
2. Bonly energy method✓
3. Conly Mohr-Coulomb for soil always✓
4. Donly truss analysis✓

Centre of gravity of composite body uses

1. Aonly largest part centroid✓
2. Bonly volume without density✓
3. Conly perimeter✓
4. Dmoment summation of parts divided by total weight✓

A frame differs from truss in that

1. Aframes have only pin joints always✓
2. Btrusses carry bending primarily✓
3. Cframes have no moments✓
4. Dframes resist loads by bending in members and joints may be rigid✓

Strain is defined as

1. Astress divided by area✓
2. Bforce times displacement✓
3. Cmoment divided by EI✓
4. Dchange in dimension divided by original dimension✓

Proportional limit is

1. Astress at fracture✓
2. Bultimate stress✓
3. Cstress below which stress-strain is linear✓
4. Dfatigue limit✓

Yield point is where

1. Aelastic modulus changes to zero instantly✓
2. Bspecimen fractures✓
3. Cmaterial begins large inelastic deformation✓
4. Dcreep starts always✓

Ultimate tensile strength is

1. Astress at elastic limit only✓
2. Bmaximum stress on engineering stress-strain curve✓
3. Cminimum stress✓
4. Dshear at NA✓

Ductility is measured by

1. Aonly elastic modulus✓
2. Bpercentage elongation or reduction in area✓
3. Conly hardness number✓
4. Donly density✓

Brittle materials fail

1. Aonly after large necking✓
2. Bsuddenly with little plastic deformation✓
3. Conly in compression always✓
4. Donly under torsion✓

Modulus of resilience is

1. Atotal area to fracture✓
2. Byield stress only✓
3. Chardness index✓
4. Darea under elastic portion of stress-strain curve✓

Modulus of toughness is

1. Aonly elastic area✓
2. Btotal area under stress-strain curve to fracture✓
3. Cσ_y/E✓
4. Dshear modulus✓

For thin cylinder under internal pressure, hoop stress is

1. Atwice longitudinal stress in thin-wall approximation✓
2. Bhalf longitudinal stress✓
3. Cequal to shear only✓
4. Dzero✓

Bending moment diagram for cantilever with UDL is

1. Alinear✓
2. Bconstant✓
3. Cparabolic✓
4. Dtriangular only at supports✓

Shear force diagram for beam with UDL is

1. Aparabolic✓
2. Blinear✓
3. Cconstant non-zero throughout✓
4. Dcircular✓

Combined bending and axial tension shifts neutral axis

1. Ato centroid always✓
2. Bto compression side always✓
3. Ctoward tension side✓
4. Doutside section always✓

Eccentric axial load on short column produces

1. Acombined axial stress and bending stress✓
2. Bonly uniform axial stress✓
3. Conly torsion✓
4. Donly shear✓

Shear centre is point through which

1. Amoment is zero always✓
2. BBM is maximum✓
3. Cshear load must act to avoid twisting✓
4. Daxial stress is zero✓

Saint-Venant principle states that

1. Alocal effects decay away from application region✓
2. Bstress is uniform everywhere✓
3. Cequilibrium is unnecessary✓
4. Dcompatibility is zero✓

Work of a force is

1. Aforce times time✓
2. Bforce times displacement in direction of force✓
3. Cmoment times angle only✓
4. Dmass times acceleration✓

Kinetic energy of particle is

1. A½mv²✓
2. Bmv✓
3. C½mv✓
4. Dmgh always✓

Potential energy due to gravity is

1. A½mgh✓
2. Bmv²✓
3. Cmgh✓
4. DFh always✓

Virtual work principle requires

1. Aplastic collapse only✓
2. Bequilibrium and virtual displacements compatible✓
3. Conly dynamic loads✓
4. Donly truss zero force✓

A propped cantilever is

1. Astatically determinate✓
2. Bunstable✓
3. Cstatically indeterminate to first degree✓
4. Dthree degrees indeterminate always✓

Compatibility condition in indeterminate structures ensures

1. Aonly ΣF=0✓
2. Bonly concrete cracks✓
3. Conly steel yields✓
4. Ddeformations fit together✓

Flexural rigidity of beam is

1. AEA✓
2. BEI✓
3. CGJ✓
4. DEI/L only✓