Question 1

Strength of materials: basis for the limit of eccentricity  Evaluate the statement: “The limit of eccentricity is based upon the no-tension condition in the cross-section.” Decide whether the statement is correct.

Accepted Answer

Concept For members that are assumed not to carry tension (e.g., masonry), the limit of eccentricity ensures the resultant compressive stress stays non-negative across the entire section (no-tension condition). Formula note For a rectangular section, a common criterion is e ≤ b/6 (about the relevant axis), keeping the stress distribution fully compressive. Final Answer True

Question 2

Transverse loading vocabulary: name of a load that varies uniformly along a beam  A load is spread over a beam and varies uniformly over its entire length. Choose the correct engineering term for this type of load.

Accepted Answer

Concept Uniformly distributed load has constant intensity (does not vary). A load that varies uniformly (typically linearly) along the span is a uniformly varying load (UVL). Final Answer Uniformly varying load (UVL)

Question 3

Comparing elastic (bending) strength for rectangular beams of different widths  Beam A and Beam B have the same length and depth d; Beam B has double the width b of Beam A. Determine how the elastic bending strength of Beam B compares to Beam A. Cho…

Accepted Answer

Given Rectangular section: width = b, depth = d. Beam B has width 2b, same d. Concept/Approach Elastic bending strength ∝ section modulus Z. For a rectangle: Z = bd²/6. Step-by-step ZA = b d²/6ZB = (2b) d²/6 = 2 × (b d²/6) = 2 ZA Conclusion Strength (at same allowable stress) doubles. Final Answer double

Question 4

Riveted joints: tearing efficiency and rivet pitch–diameter ratio  If the tearing efficiency of a riveted joint is 50%, determine the ratio of the rivet hole diameter to the rivet pitch. Choose the correct value.

Accepted Answer

Given/Formula Tearing efficiency, ηt = (p − d)/p, where p = pitch, d = rivet hole diameter. Calculation ηt = 0.5 ⇒ (p − d)/p = 0.51 − (d/p) = 0.5d/p = 0.5 Final Answer 0.50

Question 5

Material behavior: definition of resilience  Choose the correct definition of resilience in strength of materials. Select the correct option.

Accepted Answer

Definitions Resilience: strain energy stored within the elastic range (per unit volume is modulus of resilience). Proof resilience: maximum strain energy that can be stored within the elastic limit. Hence Option (a) is the correct definition of resilience. Final Answer Energy stored in a body when strained within elastic limits

Question 6

Columns: criterion for classifying a column as long or short  Evaluate the statement: “To know whether a column is long or short, we must know its slenderness ratio.” Mark the statement's correctness.

Accepted Answer

Concept Column classification (short/intermediate/long) is based on slenderness ratio λ = Le/r (effective length over radius of gyration). Buckling susceptibility increases with λ. Final Answer True

Question 7

Bending stresses in a rectangular beam under transverse loading  When a rectangular beam is transversely loaded producing sagging (positive) bending moments, where is the maximum compressive stress developed? Choose the correct location.

Accepted Answer

Concept For sagging (positive) bending moments in a prismatic beam, the top fibers are in compression and the bottom fibers in tension; stress varies linearly from maximum compression at the extreme top to maximum tension at the extreme bottom. Therefore The maximum compressive stress occurs at the top layer. Final Answer top layer

Question 8

Strength of materials: definition of strain energy stored in a loaded member  Consider a ductile or brittle specimen stressed within the elastic limit. Choose the statement that correctly defines strain energy.

Accepted Answer

Given/Concept Strain energy is the elastic energy stored in a member due to deformation under load, provided the loading is within the elastic limit so that unloading would recover the energy. Clarifications • Strain energy (general) ≠ maximum strain energy (that is proof resilience for a body).• Proof resilience per unit volume is a specific quantity (area under the stress–strain curve up to the elastic limit divided by volume), not the general definition. Final Answer Energy stored in a body when strained within elastic limits.

Question 9

Bending stress–section modulus relation in beams  For a prismatic beam subject to bending moment M, use the flexure formula. Choose how bending stress varies with section modulus.

Accepted Answer

Concept/Formula Flexure formula: σ = M y / I. Section modulus Z = I / y. Therefore, σ = M / Z. Implication For a given bending moment M, increasing Z (by choosing a stiffer cross-section) reduces the bending stress linearly. Final Answer Inversely proportional to section modulus.

Question 10

Classification by slenderness ratio: identify the type of column for λ = 100 A column has slenderness ratio λ = 100 (λ = L_e/k). Using standard classification ranges, state the column type.

Accepted Answer

Concept Slenderness ratio λ = Le/k gauges buckling tendency; higher λ means greater susceptibility to Euler-type buckling. Typical ranges (guideline) • Short: small λ (often < 32–40) – crushing governs.• Intermediate: moderate λ (≈ 40–80).• Long: large λ (≈ ≥ 80–100) – buckling dominates; Euler/Rankine applicable. Final Answer Long (slender) column.

Question 11

Loading idealisation on beams: definition of a concentrated (point) load  Choose the statement that best defines a concentrated load in beam theory. Select the correct option.

Accepted Answer

Concept A concentrated (point) load is idealised as acting at one point (mathematically a Dirac-type idealisation). Real loads act over an area/length, but if the loaded length is very small relative to span, the point-load model is valid. Final Answer Acts at a single point on a beam.

Question 12

Beam of uniform strength with constant depth: how should the width vary?  For a rectangular beam of uniform strength with constant depth d, keep maximum bending stress constant along the span. State how the beam width b must vary with bending moment…

Accepted Answer

Derivation For rectangular section: Z = I/y = (b d^2)/6.Flexure formula: σ = M/Z. For uniform strength, σ = constant ⇒ M/Z = constant ⇒ Z ∝ M.With constant depth d, Z ∝ b d^2 ⇒ b ∝ Z ∝ M. Conclusion Width must increase where bending moment is larger. Final Answer Width varies directly with bending moment M.

Question 13

Riveted joints: purpose of caulking operation  In plate joints for boilers/tanks, caulking is done after riveting. Identify the primary objective of caulking.

Accepted Answer

Concept Caulking peens/burrs the plate edges along the riveted seam to close capillary gaps, ensuring fluid tightness of boiler and tank joints. Notes It is not intended to raise tensile capacity nor to remove stresses; it specifically improves tightness against leakage. Final Answer To make the joint leak-proof.

Question 14

Riveted butt joints: identify the double-cover joint with two rows per main plate  Two main plates butt together and are covered by plates on both sides. If there are two rows of rivets per main plate and the rows on each side are opposite each othe…

Accepted Answer

Definitions • Chain riveting: rows are directly opposite each other across the joint.• Zig-zag riveting: rows are staggered. Application With two rows on each main plate and covers on both sides, and rows placed opposite, the joint is termed a chain-riveted double cover butt joint. Final Answer Chain-riveted double cover butt joint.

Question 15

Compression testing of cast iron: fracture orientation  In a compression test on a cast iron specimen (a brittle material), indicate the most likely fracture path. Select the correct description.

Accepted Answer

Concept Brittle materials like cast iron fail in compression by shear along planes where maximum shear stress acts, typically around 45° to the axis of loading. Why not others? Fracture perpendicular to the axis is more typical in tension; axial cracking is not the governing failure mode in brittle compression; brittle specimens can and do fracture in compression. Final Answer Along an oblique plane (≈ 45° to axis).

Question 16

Relation between shear force and bending moment: extremum condition  For a loaded beam, use V = dM/dx. State the value/nature of bending moment at a point where the shear force is zero.

Accepted Answer

Concept/Derivative relation Shear force V = dM/dx. When V = 0, the slope of the bending-moment diagram is zero; therefore, M has an extremum (maximum or minimum) at that location. Engineering usage In most practical positive-moment regions of simply supported beams, the zero-shear point corresponds to the maximum bending moment. Common pitfall Remember it is an extremum in general. With usual loading on simply supported beams, that extremum is the maximum sagging moment. Final Answer Maximum.

Question 17

Dam engineering: identify the possible failure modes of a masonry dam  Consider a gravity or masonry dam resting on soil or rock foundation. Assess the typical structural failure modes that may cause distress or collapse. Choose the correct comprehe…

Accepted Answer

Given/Context Masonry (gravity) dams resist water pressure by their self-weight. Failure may occur if stresses exceed permissible limits or if stability criteria are not met. Concept/Approach Primary structural failure modes include: (i) tension in masonry or at the base (cracking); (ii) overturning when the resultant passes outside the kern; (iii) crushing of masonry at the toe/heel when compressive stress exceeds allowable. Explanation Design checks limit tensile/compressive stresses and ensure the resultant stays within the middle third. If any check fails, a corresponding failure mode can occur. Final Answer Any one of the above mechanisms depending on loading and design inadequacy.

Question 18

Strength of materials terminology: name the energy stored under elastic loading  When a body is loaded within the elastic limit, it stores recoverable energy. Identify the correct term for this stored energy (overall, not per unit volume).

Accepted Answer

Definitions Strain energy: total elastic energy stored by a body under load, recoverable upon unloading (within elastic limit).Resilience: ability to absorb energy elastically; commonly expressed as strain energy per unit volume.Proof resilience: maximum strain energy stored up to the elastic limit.Impact energy: energy absorbed during impact testing (fracture toughness context). Final Answer Strain energy.

Question 19

Axial stress in a tapering bar: where is the maximum stress located?  A bar has a tapering cross-section along its length and carries a constant axial force. State the point along the bar where the axial normal stress is maximum. Choose the correct …

Accepted Answer

Concept Axial stress σ = P / A(x). With constant axial force P, stress varies inversely with local area. Reasoning In a tapering member, A is least at the small end; hence σ is greatest there. Final Answer At the smaller end of the bar.

Question 20

Torsion formula terminology: identify J/R in the torsion equation  Using the torsion relation T/J = τ/R = Gθ/L for circular shafts. State the standard name of the quantity J/R. Choose the correct term.

Accepted Answer

Concept/Formula For circular shafts in torsion: T/J = τ/R = Gθ/L.Here, J is polar moment of inertia and R is outer radius. The ratio J/R is called the polar modulus (or polar section modulus), a geometric property indicating torsional strength. Final Answer Polar modulus (polar section modulus).

Strength of Materials Questions