Strength of Materials Questions

• Torsional rigidity identification:\nFor a prismatic circular shaft, which expression represents torsional rigidity (torque per radian of twist over the full length)?
• Composite shaft twist distribution:\nA circular shaft is fixed at A. Segment AB (first half of length) has diameter D; segment BC (second half) has diameter D/2. If the rotation of B relative to A is 0.1 rad, what is the rotation of C relative to B (assume same torque along the shaft)?
• Eccentric loading on a column:\nIf the magnitudes of direct (uniform) stress and bending stress are equal, what happens to the stress at one extreme fibre of the column cross-section?
• Units check in mechanics of materials:\nWhat is the unit of (engineering) strain for axial loading or bending?
• Volumetric stiffness definition:\nA body is subjected to equal direct stresses in three mutually perpendicular directions (hydrostatic state). The ratio of direct stress to the corresponding volumetric strain is called:
• Helical spring geometry:\nA closely coiled helical spring has mean coil diameter D and wire diameter d. The spring index is defined as which of the following ratios?
• Design of riveted joints – Tearing of plate across a pitch length\nWhat is the pull required to tear off the plate per pitch length?\n(Use: p = pitch of rivets, t = plate thickness, σt, τ, σc = permissible tensile, shear, and crushing stresses respectively.)
• Thin cylindrical shell under internal pressure\nThe volumetric strain of a thin cylinder is expressed in terms of hoop strain ε1 and longitudinal strain ε2 as:
• Beam types – identification by support conditions\nA beam that is fixed at one end and free at the other is called:
• Fixed–fixed beam under uniformly distributed load\nFor a fixed beam of length l carrying a total load W uniformly distributed over the whole span, what is the maximum deflection?
• Cantilever with a point load at the free end\nFor a cantilever beam of length l carrying a point load W at the free end, what is the maximum deflection?
• Simple bending theory – meaning of “plane sections remain plane”\nIn the assumptions of Euler–Bernoulli beam theory, the statement “plane sections before bending remain plane after bending” implies that:
• Thick cylinder under internal pressure – Minimum hoop (tangential) stress at outer surface\nA thick cylindrical shell with inner radius r_i and outer radius r_o is subjected to internal pressure p only. What is the tangential (hoop) stress at the outer surface?
• Simply supported beam with symmetric, zero-end, maximum-at-centre triangular load\nFor a simply supported beam carrying a distributed load that varies from zero at both ends to w per metre at the centre (symmetric triangular), the location of maximum bending moment is:
• Riveted joints – basic terminology and correct statements\nWhich of the following statements is correct?
• Riveted joints in manufacturing and structural design:\nRivets are generally used for which type of fastenings in permanent assemblies and structural connections?
• Engineering design basics – factor of safety:\nState whether the following statement is correct: “The factor of safety (FOS) used in design is always greater than unity.”
• Mohr’s circle for combined stress:\nFor a body under normal stresses σx and σy (mutually perpendicular) and shear stress τxy, what is the radius of Mohr’s circle?
• Assumptions of simple (Euler–Bernoulli) bending theory:\nWhich of the following standard assumptions are made for a straight prismatic beam under pure bending?
• Cantilever fundamentals:\nWhat is the bending moment at the free end of a cantilever beam (no overhang beyond the free end)?