Strength of Materials and Machine Design MCQs 2026

Strain hardening increases

1. Aductility always without limit always✓
2. Byield strength after plastic deformation✓
3. Celastic modulus greatly always✓
4. Ddensity significantly✓

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

1. Aentire beam length always✓
2. Bzero distance✓
3. Cinfinite distance always✓
4. Dcharacteristic dimension of cross-section✓

Beam column combines

1. Apure torsion only✓
2. Bonly heat conduction✓
3. Caxial compression and bending causing instability interaction✓
4. Donly mass diffusion only✓

Hertz contact stress occurs between

1. Aonly fluids at rest✓
2. Bcurved bodies in elastic contact✓
3. Conly ideal gases in piston only without contact mechanics✓
4. Donly radiation surfaces✓

Design against buckling uses critical slenderness to separate

1. Afatigue vs creep only✓
2. Bconduction vs convection only✓
3. CEuler buckling vs yield failure modes✓
4. DOtto vs Diesel only✓

Shock loading factor accounts for

1. Adynamic magnification over static load✓
2. Bonly thermal expansion✓
3. Conly laminar boundary layer✓
4. Donly isentropic flow✓

Stress relaxation in bolt at constant extension over time causes

1. Aincrease in preload always✓
2. Bdecrease in bolt tension✓
3. Cno change ever✓
4. Dincrease in joint separation always immediately✓

Impact toughness is tested by

1. ACharpy or Izod notched bar impact test✓
2. Btensile test only always✓
3. Chardness only always✓
4. Dcreep test at low stress only✓

Splined connection allows

1. Aonly welded joint behavior✓
2. Bno alignment capability✓
3. Conly tensile load never torque✓
4. Dtorque transmission with axial sliding possible✓

Set screw transmits torque primarily by

1. Akeyway shear always required✓
2. Bfriction and indentation at contact✓
3. Csplines only always✓
4. Dwelding only✓

Proof load testing of bolt verifies

1. Aultimate fracture always required✓
2. Bonly torque without tension✓
3. Chardness only✓
4. Dability to sustain specified load without permanent elongation beyond limit✓

Notch sensitivity in fatigue depends on

1. Aonly applied voltage✓
2. Bonly fluid density✓
3. Conly color of surface✓
4. Dmaterial and notch geometry✓

Creep in materials at high temperature is

1. Ainstant elastic recovery only✓
2. Btime-dependent permanent deformation under constant stress✓
3. Cfatigue at one cycle✓
4. Donly buckling✓

Residual stress in welded joint arises from

1. Aonly external tensile load✓
2. Bonly centrifugal force✓
3. Cnon-uniform heating and cooling✓
4. Donly laminar flow✓

Torsional rigidity of shaft is

1. AE I✓
2. BG J✓
3. CP/A✓
4. Dρ g h✓

Relation M = E I d²y/dx² assumes

1. Alarge deflection plasticity always included✓
2. Bshear deformation dominant always✓
3. Cthermal loading absent always required incorrectly✓
4. Dsmall deflections and linear elastic material✓

Deflection curve slope equals

1. Asecond derivative only always✓
2. Bfirst derivative of deflection with respect to x✓
3. Cintegral of M only without relation✓
4. Dshear force directly always✓

Shear center of open thin-walled channel section lies

1. Aat geometric centroid always✓
2. Bat farthest fiber always✓
3. Cat infinity always✓
4. Doutside the cross-section on web side✓

Eccentric loading on column introduces

1. Aonly torsion✓
2. Bonly shear without axial✓
3. Ccombined axial stress and bending stress✓
4. Dzero stress✓

von Mises yield criterion is based on

1. Amaximum principal stress only for all materials always✓
2. Bdistortion energy✓
3. Cvolume change only✓
4. Dthermal stress only✓

Maximum normal stress theory (Rankine) is suitable for

1. Abrittle materials in tension✓
2. Bductile combined loading always better with von Mises✓
3. Cany rubber behavior✓
4. Dfluid flow only✓

Castigliano's theorem relates deflection to

1. Athermal expansion only✓
2. Bpartial derivative of strain energy with respect to load✓
3. Centropy only✓
4. D Reynolds number only✓

Strain energy per unit volume in elastic uniaxial stress is

1. Aσ E✓
2. BE/σ✓
3. Cσ²/(2E)✓
4. Dσ E²✓

Maximum shear stress in thin cylinder under internal pressure occurs at

1. Ainner surface for thick wall; approximately uniform for thin✓
2. Bouter surface only always✓
3. Cmid-wall only for thin always incorrectly always✓
4. Dzero everywhere✓

Thick cylinder analysis uses

1. Aonly thin wall formula always✓
2. Bonly Euler buckling formula✓
3. Conly Fourier law✓
4. DLamé equations with radial and hoop stress variation✓

Longitudinal stress in thin cylinder is

1. Ap r / t✓
2. B2 p r / t✓
3. Cp r / (2t)✓
4. Dzero always✓

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

1. Ap r / t✓
2. Bp t / r✓
3. Cp r t✓
4. Dp / (r t) only without relation✓

Wahl factor accounts for

1. Aonly buckling in columns✓
2. Bonly radiation heat transfer✓
3. Ccurvature and direct shear in spring wire stress✓
4. Donly entropy generation✓

Spring index C is ratio of

1. Awire diameter to coil diameter✓
2. Bfree length to solid length always✓
3. Cload to deflection only✓
4. Dmean coil diameter to wire diameter✓

Helical compression spring rate k equals

1. AG d⁴ / (8 D³ N) for active coils N✓
2. BE I / L✓
3. CP/A only✓
4. DT/J only✓

Hollow shaft compared to solid of same weight has

1. Alower torsional stiffness always✓
2. Bhigher polar moment of inertia✓
3. Csame J always✓
4. Dzero shear stress✓

Shaft design for combined bending and torsion often uses

1. Aonly axial stress formula✓
2. Bequivalent bending or torsion theories✓
3. Conly thermal expansion✓
4. Donly Bernoulli equation✓

Woodruff key is

1. Asquare parallel key only✓
2. Bsplined shaft only✓
3. Csemicircular disk key for tapered hubs✓
4. Dset screw only✓

Square key transmits torque between shaft and hub by

1. Atension in key only✓
2. Btorsion in key as primary mode always✓
3. Cfriction only without bearing✓
4. Dshear and bearing on key sides✓

Modulus of elasticity E has units of

1. Adimensionless only✓
2. Bm/s✓
3. CPa or N/m²✓
4. DN·m✓

Hooke's law in elastic range states

1. Astress equals strain always✓
2. Bstrain is independent of stress✓
3. Cstress equals modulus only without strain✓
4. Dstress is proportional to strain✓

Shear stress τ is given by

1. Anormal force divided by area✓
2. Bforce times moment arm✓
3. Ctangential force divided by area✓
4. Dstrain divided by time✓

Normal stress on a plane is defined as

1. Aforce parallel to area divided by volume✓
2. Bmoment divided by area✓
3. Cstrain times modulus only✓
4. Dforce perpendicular to area divided by area✓

Goodman line in fatigue relates

1. Athermal stress and strain only✓
2. Bmean and alternating stress for failure✓
3. Cbuckling load and length only✓
4. Dtorque and power only✓

Bolt subjected to axial external load shares load with

1. Aonly nut always✓
2. Bconnected members due to joint stiffness✓
3. Conly washer friction without members✓
4. Dair gap only✓

Poisson's ratio ν is defined as

1. Aaxial strain divided by lateral strain✓
2. Bshear strain divided by normal strain always✓
3. Cstress divided by strain squared✓
4. Dlateral strain divided by axial strain with opposite sign✓

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

1. Aplane at 45° to load always for max✓
2. Bplane parallel to load✓
3. Cany plane equally✓
4. Dplane perpendicular to load✓

Shear strain γ is approximately

1. Achange in right angle between originally perpendicular lines✓
2. Bratio of normal stresses✓
3. Cchange in volume only✓
4. Dstress divided by E only✓

Modulus of rigidity G relates

1. Anormal stress and lateral strain only✓
2. Bbulk modulus and pressure only✓
3. Cshear stress and shear strain✓
4. Dthermal expansion and temperature✓

Bulk modulus K measures resistance to

1. Auniform volumetric compression✓
2. Bbending only✓
3. Ctorsion only✓
4. Dfatigue cracking only✓

Factor of safety is generally defined as

1. Aworking stress divided by failure strength✓
2. Balways equal to 1✓
3. Cload divided by deflection✓
4. Dfailure strength divided by allowable or working stress✓

In bending, neutral axis is the locus of points where

1. Ashear stress is maximum always✓
2. Bnormal stress is maximum always✓
3. Cdeflection is maximum✓
4. Dlongitudinal strain is zero✓

Flexure formula σ = My/I applies to

1. Aelastic homogeneous beam in pure bending✓
2. Bplastic collapse always✓
3. Cany shape without NA✓
4. Dtorsion of circular shaft✓

Section modulus Z equals

1. AI divided by distance to extreme fiber c✓
2. BI times c✓
3. CI plus c✓
4. Dc divided by I✓

Maximum shear stress in rectangular beam occurs at

1. Atop fiber only✓
2. Bbottom fiber only✓
3. Cquarter depth from NA always for all sections✓
4. Dneutral axis✓

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

1. AL³/(E I)✓
2. BL only✓
3. C1/I only without E✓
4. DE I only without L✓

Torsion formula τ = T r / J applies to

1. Acircular shafts in elastic range✓
2. Bany non-circular section without correction✓
3. Cbeams in pure bending✓
4. Dthick cylinders under internal pressure only✓

Angle of twist for shaft is φ =

1. AT G / (L J)✓
2. BT L / (G J)✓
3. CG J L / T✓
4. DJ / (T L G)✓

Solid circular shaft polar moment J equals

1. Aπ d²/4✓
2. Bπ d³/16✓
3. Cπ d⁴/32✓
4. Dbh³/12✓

Hollow shaft is preferred when

1. Aweight reduction with similar torsional strength is needed✓
2. Bonly bending dominates always✓
3. Cno shear stress exists✓
4. Dmaterial is brittle only✓

Mohr's circle for plane stress plots

1. Aonly principal strains without stress✓
2. Bnormal and shear stress on various planes✓
3. Conly thermal gradients✓
4. Donly fatigue cycles✓

Principal stresses are stresses on planes where

1. Anormal stress is zero✓
2. Bboth stresses are equal always✓
3. Cstrain is maximum always✓
4. Dshear stress is zero✓

Maximum shear stress in plane stress equals

1. Aradius of Mohr's circle✓
2. Bsum of principal stresses✓
3. Cdifference of principal strains✓
4. Dzero always✓

Euler column buckling load for pinned-pinned column is

1. Aπ² E I / L²✓
2. BE I / L✓
3. Cπ E I / L✓
4. D4 π² E I / L² always✓

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

1. AL/2✓
2. BL✓
3. C2L✓
4. D0.7 L✓

Slenderness ratio for column is

1. Adiameter divided by length✓
2. Bstress divided by strain✓
3. Ceffective length divided by least radius of gyration✓
4. Dload divided by area only✓

Fatigue failure occurs at stress

1. Abelow static yield strength under cyclic loading✓
2. Bonly above ultimate strength always✓
3. Conly in single static overload✓
4. Donly at zero mean stress always✓

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

1. A10⁶ cycles✓
2. B10³ cycles✓
3. C10⁹ cycles always for all materials✓
4. Done cycle only✓

Stress concentration factor Kt is ratio of

1. Anominal to maximum stress✓
2. Bfatigue limit to yield✓
3. Cmaximum local stress to nominal stress✓
4. Dshear to normal stress always✓

Hardness test indentation measures

1. Aonly thermal conductivity✓
2. Bonly electrical resistivity✓
3. Cresistance to permanent deformation✓
4. Donly fatigue life directly always accurately✓

Necking in tensile test begins at

1. Aultimate tensile strength point✓
2. Byield point always✓
3. Cproportional limit✓
4. Delastic limit only for brittle✓

Yield point for mild steel shows

1. Aperfectly linear behavior to fracture✓
2. Bno plastic region✓
3. Cupper and lower yield phenomenon✓
4. Dnegative Poisson ratio always✓

Proportional limit is stress at which

1. Afracture occurs✓
2. Bstress-strain deviates from linearity✓
3. Cnecking completes always✓
4. Dhardness equals toughness✓

Gauge length in tensile test standard specimen affects

1. Ayield strength fundamentally for same material incorrectly always✓
2. Bmodulus E value fundamentally incorrectly always✓
3. Cmeasured elongation and reported strain✓
4. Ddensity of specimen✓

Brittle coating method in stress analysis uses

1. Acracking pattern to indicate strain direction/magnitude✓
2. Bthermocouples only✓
3. CPitot tube only✓
4. Dorifice meter only✓

Efficiency of riveted joint is ratio of

1. Anumber of rivets to length only✓
2. Bstrength of riveted joint to solid plate strength✓
3. Cpitch to diameter only without strength✓
4. Dweight to volume only✓

Riveted joint failure modes include

1. Aonly buckling of rivet head always alone✓
2. Bonly corrosion without mechanics✓
3. Conly torsion of plate✓
4. Dshearing of rivet, bearing, tearing of plate✓

Cotter joint is used for

1. Asealing steam turbine blades only✓
2. Bconnecting two rods under axial load with wedge pin✓
3. Cmeasuring viscosity only✓
4. Drankine pump only✓

Knuckle joint transmits

1. Apure torsion only always✓
2. Btensile load in rods with pin connection✓
3. Chydraulic pressure in pipes only✓
4. Dheat by radiation only✓

Surge in spring occurs when

1. Aspring is static only✓
2. Bnatural frequency of spring-mass matches forcing frequency✓
3. Conly compression without coils✓
4. Dtemperature is constant only✓

Leaf spring is a form of

1. Apure torsion spring only✓
2. Bthin cylinder only✓
3. Cbeam bending with multiple leaves✓
4. Drankine cycle component✓

Gasketed flange joint leakage prevention relies on

1. Azero bolt torque✓
2. Bonly paint sealant without load✓
3. Csufficient gasket compression from bolt preload✓
4. Dshear keys only✓

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

1. Aplates have zero stiffness✓
2. Bbolt has zero stiffness✓
3. Cno preload exists always giving full external load on bolt incorrectly stated as always✓
4. Dconnected plates are stiff and carry share of load✓

Closed thin-walled tube in torsion resists torque by

1. Aonly bending of walls without shear flow✓
2. Baxial tension only✓
3. Cinternal pressure only✓
4. Dshear flow around perimeter (Bredt-Batho)✓

Shear flow q in thin-walled section equals

1. AM y / I only always alone for shear flow✓
2. BT r / J for open section primary bending shear✓
3. CP/A only✓
4. DV Q / I✓

Section modulus for rectangular section bh²/6 uses

1. Ab and h as width and depth with bending about horizontal NA✓
2. Bpolar diameter only✓
3. Cradius only✓
4. Dthickness of cylinder wall only✓

Strain rosette measures

1. Anormal strains at three orientations to find principal strains✓
2. Btemperature only✓
3. Chardness only✓
4. Dflow rate only✓

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

1. Atotal load according to stiffness EA sum✓
2. Bstress equally always regardless of E✓
3. Cload only by larger area alone always✓
4. Dno load in stiffer material✓

Thermal stress in restrained bar heated uniformly is

1. Azero always even if restrained✓
2. BE α ΔT (compressive if heated and restrained)✓
3. Cα ΔT only without E✓
4. DE/α ΔT✓

Principal strain in isotropic material under uniaxial stress includes

1. Aonly axial strain without lateral✓
2. Bzero strain transverse always✓
3. Clateral strain from Poisson effect✓
4. Dshear strain equal to normal strain✓

Macaulay's method is used for

1. Atorsion of non-circular bars only always analytically simple✓
2. Bbeam deflection with discontinuous loading✓
3. Crankine cycle analysis✓
4. Dradiation view factors only✓

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

1. Aload disappears✓
2. BE is higher always✓
3. CI is zero✓
4. Dnegative moments at supports reduce midspan moment✓

Critical speed of shaft occurs when

1. Atorque is maximum only✓
2. Bstress is zero✓
3. Crotational speed equals natural frequency of lateral vibration✓
4. Dbearing friction is zero only✓

Coupling used to connect misaligned shafts elastically may be

1. Arigid flange only for large misalignment always✓
2. Bflexible coupling with elastomer element✓
3. Ckey only without hub✓
4. Dset screw on glass shaft✓

Initial tightening torque on bolt creates

1. Apreload in shank✓
2. Bonly shear in plate without axial force✓
3. Czero stress always✓
4. Donly bending always✓