Torsion & Deflection Twist your brain (and shafts) with this section! Learn how materials behave when twisted or bent — from torque to angle of twist, every question tests your grasp on real-world mechanical behavior. 1 / 20 Deflection in a beam depends on Only load Load, length, E, and I Only material Only span 2 / 20 In a circular shaft under pure torsion, the shape of cross-section remains Circular Elliptical Square Rectangular Cross-section remains circular since torsional deformation preserves the shape but twists the cross-section. 3 / 20 Deflection in beams is inversely proportional to Elastic modulus Load Length³ Moment Higher modulus (E) means stiffer material, resulting in less deflection. 4 / 20 When the slope of deflection curve is zero, the point is Fixed end Free end Inflection point Support At an inflection point, bending moment changes sign and slope becomes zero — beam shape changes curvature direction. 5 / 20 The strain energy stored in a shaft under torque is Tθ/2 Tθ T²θ θ²T Strain energy U=1/2(TθU), representing elastic energy stored due to twisting. 6 / 20 The spring constant defines Flexibility Energy absorbed Length of coil Stiffness Spring constant (k) measures stiffness — the force required per unit extension or compression. 7 / 20 The deflection of a beam is minimum at Supports Free end Any point Mid-span For simply supported beams, deflection is zero at supports and maximum at mid-span. 8 / 20 A shaft is said to fail in torsion when It breaks The material yields in shear It bends permanently It vibrates Failure occurs when shear stress exceeds the shear yield limit of the material. 9 / 20 Modulus of resilience measures Elasticity Ductility Ability to store energy Yield strength It represents the energy per unit volume stored in a material up to elastic limit — important for springs and shock absorbers. 10 / 20 The maximum bending stress occurs at Neutral axis Top and bottom fibers Mid-depth Support Outer fibers experience maximum tensile and compressive stresses during bending, while stress is zero at the neutral axis 11 / 20 The deflection of a cantilever beam carrying a point load W at its free end is WL²/2EI WL³/3EI WL³/6EI WL³/3EI 12 / 20 The bending equation is M/I = E/R = σ/y M/I = σ/R = E/y M/R = σ/I I/M = R/E This relation connects bending moment (M), moment of inertia (I), stress (σ), radius of curvature (R), and distance from neutral axis (y). 13 / 20 In bending, the neutral axis is the line Of maximum stress Of maximum deflection Of zero stress Of zero strain The neutral axis passes through the centroid of the beam’s cross-section, where bending stress is zero. 14 / 20 Deflection in a simply supported beam under central load W is proportional to W/L WL³ W/L² 1/W 15 / 20 A hollow shaft has better strength-to-weight ratio than a solid shaft because It has more mass It has same diameter Outer fibers carry more stress It is easy to manufacture Hollow shafts are lighter and resist torque efficiently since maximum shear stress acts at the outer surface. 16 / 20 The maximum shear stress in a solid circular shaft under torque T is given by T/J T/(πd³/16) T/L TL/J 17 / 20 The polar moment of inertia for a solid circular shaft of diameter d is πd⁴/64 πd³/16 πd⁴/32 πd²/4 J=πd^4/32. It defines the shaft’s capacity to resist torsional shear. 18 / 20 The torsional rigidity of a shaft is given by G/J T/θ GJ J/G Torsional rigidity is the product of modulus of rigidity (G) and polar moment of inertia (J). It represents the shaft’s resistance to twist. 19 / 20 In torsion, the shear stress varies Uniformly across the section Parabolically Linearly from center to surface Exponentially In solid circular shafts, shear stress starts at zero at the center and increases linearly toward the outer surface. 20 / 20 The angle of twist in a circular shaft is directly proportional to Torque applied Length of shaft Modulus of rigidity Polar moment of inertia Angle of twist θ=TL/JG . It increases with torque and length, while higher rigidity or polar moment reduces twist. Your score isThe average score is 0% 0% Restart quiz
