Strength of Materials and Machine Design MCQs 2026

Coupling used to connect misaligned shafts elastically may be

1. A rigid flange only for large misalignment always ✓
2. B flexible coupling with elastomer element ✓
3. C key only without hub ✓
4. D set screw on glass shaft ✓

Critical speed of shaft occurs when

1. A torque is maximum only ✓
2. B stress is zero ✓
3. C rotational speed equals natural frequency of lateral vibration ✓
4. D bearing friction is zero only ✓

Beam with fixed ends carries less maximum moment than simply supported for same central load because

1. A load disappears ✓
2. B E is higher always ✓
3. C I is zero ✓
4. D negative moments at supports reduce midspan moment ✓

Macaulay's method is used for

1. A torsion of non-circular bars only always analytically simple ✓
2. B beam deflection with discontinuous loading ✓
3. C rankine cycle analysis ✓
4. D radiation view factors only ✓

Principal strain in isotropic material under uniaxial stress includes

1. A only axial strain without lateral ✓
2. B zero strain transverse always ✓
3. C lateral strain from Poisson effect ✓
4. D shear strain equal to normal strain ✓

Thermal stress in restrained bar heated uniformly is

1. A zero always even if restrained ✓
2. B E α ΔT (compressive if heated and restrained) ✓
3. C α ΔT only without E ✓
4. D E/α ΔT ✓

Compound bar of two materials in parallel under load shares strain and

1. A total load according to stiffness EA sum ✓
2. B stress equally always regardless of E ✓
3. C load only by larger area alone always ✓
4. D no load in stiffer material ✓

Strain rosette measures

1. A normal strains at three orientations to find principal strains ✓
2. B temperature only ✓
3. C hardness only ✓
4. D flow rate only ✓

Section modulus for rectangular section bh²/6 uses

1. A b and h as width and depth with bending about horizontal NA ✓
2. B polar diameter only ✓
3. C radius only ✓
4. D thickness of cylinder wall only ✓

Shear flow q in thin-walled section equals

1. A M y / I only always alone for shear flow ✓
2. B T r / J for open section primary bending shear ✓
3. C P/A only ✓
4. D V Q / I ✓

Closed thin-walled tube in torsion resists torque by

1. A only bending of walls without shear flow ✓
2. B axial tension only ✓
3. C internal pressure only ✓
4. D shear flow around perimeter (Bredt-Batho) ✓

Stress in bolt due to external tensile load increases less than external load when

1. A plates have zero stiffness ✓
2. B bolt has zero stiffness ✓
3. C no preload exists always giving full external load on bolt incorrectly stated as always ✓
4. D connected plates are stiff and carry share of load ✓

Gasketed flange joint leakage prevention relies on

1. A zero bolt torque ✓
2. B only paint sealant without load ✓
3. C sufficient gasket compression from bolt preload ✓
4. D shear keys only ✓

Leaf spring is a form of

1. A pure torsion spring only ✓
2. B thin cylinder only ✓
3. C beam bending with multiple leaves ✓
4. D rankine cycle component ✓

Surge in spring occurs when

1. A spring is static only ✓
2. B natural frequency of spring-mass matches forcing frequency ✓
3. C only compression without coils ✓
4. D temperature is constant only ✓

Knuckle joint transmits

1. A pure torsion only always ✓
2. B tensile load in rods with pin connection ✓
3. C hydraulic pressure in pipes only ✓
4. D heat by radiation only ✓

Cotter joint is used for

1. A sealing steam turbine blades only ✓
2. B connecting two rods under axial load with wedge pin ✓
3. C measuring viscosity only ✓
4. D rankine pump only ✓

Riveted joint failure modes include

1. A only buckling of rivet head always alone ✓
2. B only corrosion without mechanics ✓
3. C only torsion of plate ✓
4. D shearing of rivet, bearing, tearing of plate ✓

Efficiency of riveted joint is ratio of

1. A number of rivets to length only ✓
2. B strength of riveted joint to solid plate strength ✓
3. C pitch to diameter only without strength ✓
4. D weight to volume only ✓

Brittle coating method in stress analysis uses

1. A cracking pattern to indicate strain direction/magnitude ✓
2. B thermocouples only ✓
3. C Pitot tube only ✓
4. D orifice meter only ✓

Gauge length in tensile test standard specimen affects

1. A yield strength fundamentally for same material incorrectly always ✓
2. B modulus E value fundamentally incorrectly always ✓
3. C measured elongation and reported strain ✓
4. D density of specimen ✓

Proportional limit is stress at which

1. A fracture occurs ✓
2. B stress-strain deviates from linearity ✓
3. C necking completes always ✓
4. D hardness equals toughness ✓

Yield point for mild steel shows

1. A perfectly linear behavior to fracture ✓
2. B no plastic region ✓
3. C upper and lower yield phenomenon ✓
4. D negative Poisson ratio always ✓

Necking in tensile test begins at

1. A ultimate tensile strength point ✓
2. B yield point always ✓
3. C proportional limit ✓
4. D elastic limit only for brittle ✓

Hardness test indentation measures

1. A only thermal conductivity ✓
2. B only electrical resistivity ✓
3. C resistance to permanent deformation ✓
4. D only fatigue life directly always accurately ✓

Saint-Venant's principle states localized end effects decay within

1. A entire beam length always ✓
2. B zero distance ✓
3. C infinite distance always ✓
4. D characteristic dimension of cross-section ✓

Normal stress on a plane is defined as

1. A force parallel to area divided by volume ✓
2. B moment divided by area ✓
3. C strain times modulus only ✓
4. D force perpendicular to area divided by area ✓

Shear stress τ is given by

1. A normal force divided by area ✓
2. B force times moment arm ✓
3. C tangential force divided by area ✓
4. D strain divided by time ✓

Hooke's law in elastic range states

1. A stress equals strain always ✓
2. B strain is independent of stress ✓
3. C stress equals modulus only without strain ✓
4. D stress is proportional to strain ✓

Modulus of elasticity E has units of

1. A dimensionless only ✓
2. B m/s ✓
3. C Pa or N/m² ✓
4. D N·m ✓

Poisson's ratio ν is defined as

1. A axial strain divided by lateral strain ✓
2. B shear strain divided by normal strain always ✓
3. C stress divided by strain squared ✓
4. D lateral strain divided by axial strain with opposite sign ✓

For a bar in simple tension, maximum normal stress occurs on

1. A plane at 45° to load always for max ✓
2. B plane parallel to load ✓
3. C any plane equally ✓
4. D plane perpendicular to load ✓

Shear strain γ is approximately

1. A change in right angle between originally perpendicular lines ✓
2. B ratio of normal stresses ✓
3. C change in volume only ✓
4. D stress divided by E only ✓

Modulus of rigidity G relates

1. A normal stress and lateral strain only ✓
2. B bulk modulus and pressure only ✓
3. C shear stress and shear strain ✓
4. D thermal expansion and temperature ✓

Bulk modulus K measures resistance to

1. A uniform volumetric compression ✓
2. B bending only ✓
3. C torsion only ✓
4. D fatigue cracking only ✓

Factor of safety is generally defined as

1. A working stress divided by failure strength ✓
2. B always equal to 1 ✓
3. C load divided by deflection ✓
4. D failure strength divided by allowable or working stress ✓

In bending, neutral axis is the locus of points where

1. A shear stress is maximum always ✓
2. B normal stress is maximum always ✓
3. C deflection is maximum ✓
4. D longitudinal strain is zero ✓

Flexure formula σ = My/I applies to

1. A elastic homogeneous beam in pure bending ✓
2. B plastic collapse always ✓
3. C any shape without NA ✓
4. D torsion of circular shaft ✓

Section modulus Z equals

1. A I divided by distance to extreme fiber c ✓
2. B I times c ✓
3. C I plus c ✓
4. D c divided by I ✓

Maximum shear stress in rectangular beam occurs at

1. A top fiber only ✓
2. B bottom fiber only ✓
3. C quarter depth from NA always for all sections ✓
4. D neutral axis ✓

Deflection of simply supported beam with central point load is proportional to

1. A L³/(E I) ✓
2. B L only ✓
3. C 1/I only without E ✓
4. D E I only without L ✓

Torsion formula τ = T r / J applies to

1. A circular shafts in elastic range ✓
2. B any non-circular section without correction ✓
3. C beams in pure bending ✓
4. D thick cylinders under internal pressure only ✓

Angle of twist for shaft is φ =

1. A T G / (L J) ✓
2. B T L / (G J) ✓
3. C G J L / T ✓
4. D J / (T L G) ✓

Solid circular shaft polar moment J equals

1. A π d²/4 ✓
2. B π d³/16 ✓
3. C π d⁴/32 ✓
4. D bh³/12 ✓

Hollow shaft is preferred when

1. A weight reduction with similar torsional strength is needed ✓
2. B only bending dominates always ✓
3. C no shear stress exists ✓
4. D material is brittle only ✓

Mohr's circle for plane stress plots

1. A only principal strains without stress ✓
2. B normal and shear stress on various planes ✓
3. C only thermal gradients ✓
4. D only fatigue cycles ✓

Principal stresses are stresses on planes where

1. A normal stress is zero ✓
2. B both stresses are equal always ✓
3. C strain is maximum always ✓
4. D shear stress is zero ✓

Maximum shear stress in plane stress equals

1. A radius of Mohr's circle ✓
2. B sum of principal stresses ✓
3. C difference of principal strains ✓
4. D zero always ✓

Euler column buckling load for pinned-pinned column is

1. A π² E I / L² ✓
2. B E I / L ✓
3. C π E I / L ✓
4. D 4 π² E I / L² always ✓

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

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

Slenderness ratio for column is

1. A diameter divided by length ✓
2. B stress divided by strain ✓
3. C effective length divided by least radius of gyration ✓
4. D load divided by area only ✓

Fatigue failure occurs at stress

1. A below static yield strength under cyclic loading ✓
2. B only above ultimate strength always ✓
3. C only in single static overload ✓
4. D only at zero mean stress always ✓

Endurance limit on S-N curve for ferrous materials in reversed bending often occurs near

1. A 10⁶ cycles ✓
2. B 10³ cycles ✓
3. C 10⁹ cycles always for all materials ✓
4. D one cycle only ✓

Stress concentration factor Kt is ratio of

1. A nominal to maximum stress ✓
2. B fatigue limit to yield ✓
3. C maximum local stress to nominal stress ✓
4. D shear to normal stress always ✓

Goodman line in fatigue relates

1. A thermal stress and strain only ✓
2. B mean and alternating stress for failure ✓
3. C buckling load and length only ✓
4. D torque and power only ✓

Bolt subjected to axial external load shares load with

1. A only nut always ✓
2. B connected members due to joint stiffness ✓
3. C only washer friction without members ✓
4. D air gap only ✓

Initial tightening torque on bolt creates

1. A preload in shank ✓
2. B only shear in plate without axial force ✓
3. C zero stress always ✓
4. D only bending always ✓

Square key transmits torque between shaft and hub by

1. A tension in key only ✓
2. B torsion in key as primary mode always ✓
3. C friction only without bearing ✓
4. D shear and bearing on key sides ✓

Woodruff key is

1. A square parallel key only ✓
2. B splined shaft only ✓
3. C semicircular disk key for tapered hubs ✓
4. D set screw only ✓

Shaft design for combined bending and torsion often uses

1. A only axial stress formula ✓
2. B equivalent bending or torsion theories ✓
3. C only thermal expansion ✓
4. D only Bernoulli equation ✓

Hollow shaft compared to solid of same weight has

1. A lower torsional stiffness always ✓
2. B higher polar moment of inertia ✓
3. C same J always ✓
4. D zero shear stress ✓

Helical compression spring rate k equals

1. A G d⁴ / (8 D³ N) for active coils N ✓
2. B E I / L ✓
3. C P/A only ✓
4. D T/J only ✓

Spring index C is ratio of

1. A wire diameter to coil diameter ✓
2. B free length to solid length always ✓
3. C load to deflection only ✓
4. D mean coil diameter to wire diameter ✓

Wahl factor accounts for

1. A only buckling in columns ✓
2. B only radiation heat transfer ✓
3. C curvature and direct shear in spring wire stress ✓
4. D only entropy generation ✓

Thin cylinder with internal pressure p and radius r has hoop stress

1. A p r / t ✓
2. B p t / r ✓
3. C p r t ✓
4. D p / (r t) only without relation ✓

Longitudinal stress in thin cylinder is

1. A p r / t ✓
2. B 2 p r / t ✓
3. C p r / (2t) ✓
4. D zero always ✓

Thick cylinder analysis uses

1. A only thin wall formula always ✓
2. B only Euler buckling formula ✓
3. C only Fourier law ✓
4. D Lamé equations with radial and hoop stress variation ✓

Maximum shear stress in thin cylinder under internal pressure occurs at

1. A inner surface for thick wall; approximately uniform for thin ✓
2. B outer surface only always ✓
3. C mid-wall only for thin always incorrectly always ✓
4. D zero everywhere ✓

Strain energy per unit volume in elastic uniaxial stress is

1. A σ E ✓
2. B E/σ ✓
3. C σ²/(2E) ✓
4. D σ E² ✓

Castigliano's theorem relates deflection to

1. A thermal expansion only ✓
2. B partial derivative of strain energy with respect to load ✓
3. C entropy only ✓
4. D Reynolds number only ✓

Maximum normal stress theory (Rankine) is suitable for

1. A brittle materials in tension ✓
2. B ductile combined loading always better with von Mises ✓
3. C any rubber behavior ✓
4. D fluid flow only ✓

von Mises yield criterion is based on

1. A maximum principal stress only for all materials always ✓
2. B distortion energy ✓
3. C volume change only ✓
4. D thermal stress only ✓

Eccentric loading on column introduces

1. A only torsion ✓
2. B only shear without axial ✓
3. C combined axial stress and bending stress ✓
4. D zero stress ✓

Shear center of open thin-walled channel section lies

1. A at geometric centroid always ✓
2. B at farthest fiber always ✓
3. C at infinity always ✓
4. D outside the cross-section on web side ✓

Deflection curve slope equals

1. A second derivative only always ✓
2. B first derivative of deflection with respect to x ✓
3. C integral of M only without relation ✓
4. D shear force directly always ✓

Relation M = E I d²y/dx² assumes

1. A large deflection plasticity always included ✓
2. B shear deformation dominant always ✓
3. C thermal loading absent always required incorrectly ✓
4. D small deflections and linear elastic material ✓

Torsional rigidity of shaft is

1. A E I ✓
2. B G J ✓
3. C P/A ✓
4. D ρ g h ✓

Residual stress in welded joint arises from

1. A only external tensile load ✓
2. B only centrifugal force ✓
3. C non-uniform heating and cooling ✓
4. D only laminar flow ✓

Creep in materials at high temperature is

1. A instant elastic recovery only ✓
2. B time-dependent permanent deformation under constant stress ✓
3. C fatigue at one cycle ✓
4. D only buckling ✓

Notch sensitivity in fatigue depends on

1. A only applied voltage ✓
2. B only fluid density ✓
3. C only color of surface ✓
4. D material and notch geometry ✓

Proof load testing of bolt verifies

1. A ultimate fracture always required ✓
2. B only torque without tension ✓
3. C hardness only ✓
4. D ability to sustain specified load without permanent elongation beyond limit ✓

Set screw transmits torque primarily by

1. A keyway shear always required ✓
2. B friction and indentation at contact ✓
3. C splines only always ✓
4. D welding only ✓

Splined connection allows

1. A only welded joint behavior ✓
2. B no alignment capability ✓
3. C only tensile load never torque ✓
4. D torque transmission with axial sliding possible ✓

Impact toughness is tested by

1. A Charpy or Izod notched bar impact test ✓
2. B tensile test only always ✓
3. C hardness only always ✓
4. D creep test at low stress only ✓

Stress relaxation in bolt at constant extension over time causes

1. A increase in preload always ✓
2. B decrease in bolt tension ✓
3. C no change ever ✓
4. D increase in joint separation always immediately ✓

Shock loading factor accounts for

1. A dynamic magnification over static load ✓
2. B only thermal expansion ✓
3. C only laminar boundary layer ✓
4. D only isentropic flow ✓

Design against buckling uses critical slenderness to separate

1. A fatigue vs creep only ✓
2. B conduction vs convection only ✓
3. C Euler buckling vs yield failure modes ✓
4. D Otto vs Diesel only ✓

Hertz contact stress occurs between

1. A only fluids at rest ✓
2. B curved bodies in elastic contact ✓
3. C only ideal gases in piston only without contact mechanics ✓
4. D only radiation surfaces ✓

Beam column combines

1. A pure torsion only ✓
2. B only heat conduction ✓
3. C axial compression and bending causing instability interaction ✓
4. D only mass diffusion only ✓

Strain hardening increases

1. A ductility always without limit always ✓
2. B yield strength after plastic deformation ✓
3. C elastic modulus greatly always ✓
4. D density significantly ✓