Q: Stress concentration around an elliptical hole in a plate under tension Plate with a central elliptical hole: semi-major axis a is perpendicular to loading; semi-minor axis b is along the loading direction. Let σ be the nominal (no-hole) stress. Fi…

Given • Plate in tension with an elliptical hole (semi-major axis a ⟂ load, semi-minor axis b ∥ load). • Nominal stress (no hole) = σ. Concept The stress concentration factor at the ends of the minor axis for an elliptical hole is K = 1 + 2(a/b)⇒ σmax = K · σ = σ (1 + 2a/b) Step-by-step 1) Identify orientation: a ⟂ load → the high-stress points lie on the ends of b.2) Use the classic elasticity result for an ellipse in an infinite plate.3) Multiply nominal stress by K to obtain σmax. Common pitfall Swapping a and b reverses the factor; ensure correct axes relative to the loading direction. Final Answer σ (1 + 2a/b)

Q: Involute gears: dependence of sliding velocity on contact position Consider a point of contact on the line of action at a distance from the pitch point. State how the sliding velocity varies with the distance from the pitch point.

Concept For involute gears, the rolling (no-slip) point is the pitch point. The sliding velocity at any other contact point on the line of action is proportional to its distance from the pitch point: vslide = (ω1 − ω2) · r′with r′ measured along the line of action from the pitch point. Implication • At the pitch point, distance = 0 → no sliding. • Away from the pitch point, sliding increases linearly. Final Answer Directly proportional to the distance from the pitch point

Question 1

Cams and followers: follower motion direction for a radial (disc) cam  Determine the correct direction of follower motion relative to the cam axis for a radial cam mechanism.  Choose the correct option.

Accepted Answer

Concept A radial (disc) cam has the follower moving in the plane of cam rotation (radially in/out), which is perpendicular to the cam's axis. Elimination (b) and (d) imply axial movement (that is typical for cylindrical/axial cams, not radial cams). (c) is too vague and incorrect. Final Answer In a direction perpendicular to the cam axis

Question 2

Power-transmitting screw threads: best choice when power is transmitted in one direction only  Select the thread form that is mechanically best suited for heavy load transmission predominantly in a single direction.  Choose the correct option.

Accepted Answer

Concept Buttress threads combine the high efficiency of a square thread in the load direction with a stronger tooth form, making them ideal where heavy force acts primarily in one direction (e.g., presses, jacks). Why others are less suitable Square is efficient but weaker at the root; Acme is stronger but less efficient; Knuckle is for rough/rolling engagement, not precision power screws. Final Answer Buttress threads

Question 3

Bolted joints under shock loading: location where resilience must be considered to avoid failure  A bolt under shock/impact may fail at a critical location due to energy absorption limits.  Choose the location where design for resilience is crucial …

Accepted Answer

Concept Resilience is the energy absorbed per unit volume within the elastic range. Under shock/impact, the highest stress concentration in a bolt is typically at the thread root (small net area + notch effect), making it the most likely failure location if not properly designed. Design note To improve resilience and reduce peak stress at the thread, designers often use a reduced shank (to the core diameter) so the shank elastically stretches and load shares with threads, shifting peak stresses away from the root. Final Answer Thread

Question 4

Limits & fits: unilateral system of tolerance — where is the tolerance placed?  Interpret the definition of unilateral tolerance relative to the nominal size.  Choose the correct option.

Accepted Answer

Concept In a unilateral tolerance system, all permissible variation lies on one side of the nominal (basic) size (e.g., +0 / −0.010 or +0.010 / −0). Final Answer On one side of the nominal size

Question 5

Bearings: definition of a hydrodynamic (full-film) lubricated journal bearing  Identify the correct statement describing film formation and pressure generation in hydrodynamic lubrication.  Choose the correct option.

Accepted Answer

Concept Hydrodynamic bearings develop a self-generated pressure in a full fluid film due to relative motion and wedge action, fully separating the surfaces. Option (d) describes hydrostatic lubrication (external pressurisation). Option (b) is boundary/mixed lubrication. Final Answer There is a thick (full) film of lubricant between journal and bearing

Question 6

Stress concentration: primary cause in machine members  Identify the dominant cause that creates localized high stresses relative to nominal stress.  Choose the correct option.

Accepted Answer

Concept Stress concentration arises primarily from geometric discontinuities such as holes, notches, grooves, fillet corners, and sudden changes in section. These features raise local stresses above the nominal average. Why others are not primary causes Load or property variations affect overall stress but do not, by themselves, create the localized peaks that define stress concentration. Final Answer Abrupt change of cross-section (geometric discontinuity)

Question 7

Levers: identify the second-class lever configuration (Type II)  Recall the relative positions of fulcrum, load, and effort in a second-class lever.  Choose the correct option.

Accepted Answer

Concept In a second-class lever (Type II), the load lies between the fulcrum and the effort (examples: wheelbarrow, nutcracker). First-class has the fulcrum between load and effort; third-class has the effort between fulcrum and load. Final Answer Load is between fulcrum and effort

Question 8

Riveted joints: minimum edge distance to avoid tearing of the plate  Given d = diameter of the rivet hole. Select the minimum required distance from the rivet-hole centreline to the nearest plate edge to prevent edge tearing. Choose the correct valu…

Accepted Answer

Given • Riveted plate; to avoid tearing at the plate edge. • d = rivet-hole diameter. Concept The minimum edge distance (also called margin) commonly adopted in machine design standards is 1.5 d. This ensures adequate net area between the hole and edge to resist tensile tearing. Why not larger or smaller? • If < 1.5 d, the ligament is weak → edge tearing likely. • Values like 2 d or 2.5 d are safe but unnecessarily increase plate size and cost. Final Answer 1.5 d

Question 9

Stress concentration around an elliptical hole in a plate under tension  Plate with a central elliptical hole: semi-major axis a is perpendicular to loading; semi-minor axis b is along the loading direction. Let σ be the nominal (no-hole) stress. Fi…

Accepted Answer

Given • Plate in tension with an elliptical hole (semi-major axis a ⟂ load, semi-minor axis b ∥ load). • Nominal stress (no hole) = σ. Concept The stress concentration factor at the ends of the minor axis for an elliptical hole is K = 1 + 2(a/b)⇒ σmax = K · σ = σ (1 + 2a/b) Step-by-step 1) Identify orientation: a ⟂ load → the high-stress points lie on the ends of b.2) Use the classic elasticity result for an ellipse in an infinite plate.3) Multiply nominal stress by K to obtain σmax. Common pitfall Swapping a and b reverses the factor; ensure correct axes relative to the loading direction. Final Answer σ (1 + 2a/b)

Question 10

Involute gears: dependence of sliding velocity on contact position  Consider a point of contact on the line of action at a distance from the pitch point. State how the sliding velocity varies with the distance from the pitch point.

Accepted Answer

Concept For involute gears, the rolling (no-slip) point is the pitch point. The sliding velocity at any other contact point on the line of action is proportional to its distance from the pitch point: vslide = (ω1 − ω2) · r′with r′ measured along the line of action from the pitch point. Implication • At the pitch point, distance = 0 → no sliding. • Away from the pitch point, sliding increases linearly. Final Answer Directly proportional to the distance from the pitch point

Question 11

Power screw thread forms: friction and strength comparison  Assess the statement: Square threads are not as strong as V-threads, but they offer less frictional resistance than Whitworth threads. Decide whether the statement is correct.

Accepted Answer

Concept • Square threads have zero flank angle → lowest friction among common forms, but less root strength compared to V/Whitworth because of a smaller shear area. • Whitworth (V) threads (55°) have higher friction due to the included angle and normal force components on the flanks. Conclusion The statement matches standard design comparisons. Final Answer True — the statement is correct

Question 12

Pipe joints for low-pressure water service  Identify the joint most commonly used for pipes carrying water at low pressure. Choose the correct option.

Accepted Answer

Concept Cast iron water mains and low-pressure water pipelines commonly use the spigot and socket (bell-and-spigot) joint, which provides alignment and sealing (traditionally with lead/yarn or rubber rings). Elimination Socket, nipple, and union joints are more typical for small-diameter screwed pipes and fittings, not for main low-pressure water lines. Final Answer Spigot and socket joint

Question 13

Column classification by slenderness ratio  Select the threshold slenderness ratio at or above which a column is classified as a long column (Euler-type behavior dominates). Choose the correct value.

Accepted Answer

Concept Columns are often categorized by slenderness ratio (le/k). For typical steels in basic design practice, members with slenderness ≳ 100 are treated as long columns, where elastic buckling dominates the failure mode and Euler-type formulas are applicable. Note Exact limits can vary by code/material; among the given choices, 100 is the appropriate long-column threshold. Final Answer 100

Question 14

Fatigue performance measure of materials  Identify the standard property used to indicate resistance to fatigue failure under cyclic loading. Choose the correct option.

Accepted Answer

Concept The endurance limit (or fatigue limit) is the stress amplitude below which a material can theoretically endure an infinite number of cycles without failure (for some ferrous alloys). It is the standard measure of fatigue resistance. Why others are incorrect Elastic limit and E relate to elastic behavior; UTS measures monotonic strength, not endurance under cyclic loads. Final Answer Endurance limit

Question 15

Stress concentration factor (K_t): dependence on part characteristics Determine what K_t primarily depends on for an elastic member with a notch/hole/fillet. Choose the correct option.

Accepted Answer

Concept The theoretical stress concentration factor Kt is a geometric amplification factor (ratio of maximum local stress to nominal stress) dictated by shape features: holes, notches, grooves, and fillet radii. In linear elasticity, Kt is independent of material; material enters through notch sensitivity in fatigue, not in Kt itself. Final Answer Geometry of the part

Question 16

Riveted boiler joints: thickness of unequal double-cover butt straps  For unequal-width double-cover butt straps on a plate of thickness t: Identify the standard strap thicknesses (inside wide strap vs. outside narrow strap). Choose the correct opti…

Accepted Answer

Concept For unequal double-cover butt joints (as used in boiler work), a common rule is: • Inside/wide strap thickness = 0.75 t• Outside/narrow strap thickness = 0.625 twhere t is the main plate thickness. Final Answer 0.75 t (inside wide) and 0.625 t (outside narrow)

Question 17

IBR boiler riveting: shearing resistance per pitch length in double shear  Let d = rivet diameter, τ = allowable shear stress, and n = number of rivets per pitch length. According to I.B.R., determine the shearing resistance required to shear off th…

Accepted Answer

Given • Boiler joint design per I.B.R. (Indian Boiler Regulations). • Double-shear condition; n rivets per pitch length. Concept/Approach Per I.B.R. empirical provisions, the shearing resistance in single shear is taken as 0.9375 · d^2 · τ · n (using an effective shear area factor). For double shear, multiply by 2: Shearing resistance (double shear) = 2 × 0.9375 · d^2 · τ · n = 1.875 · d^2 · τ · n Common pitfall Do not confuse with the theoretical area πd^2/4; I.B.R. uses codified effective factors for boiler riveting. Final Answer 1.875 · d^2 · τ · n

Question 18

Gears: identify the correct statements about fundamental gear terms.  Evaluate each statement about standard involute gears and choose the single best option that encompasses all true statements. • Addendum vs. dedendum magnitude • Relation between …

Accepted Answer

Given concepts Addendum ≈ 1×module; dedendum ≈ 1.25×module in standard gears. Pitch circle diameter: D = m × Z where m = module and Z = number of teeth. Base circle diameter: Db = D × cos φ (φ = pressure angle), so D > Db. Reasoning Since dedendum > addendum (standard proportions), statement (a) is true.Since D = mZ, statement (b) is true.Since cos φ < 1, base circle < pitch circle, so (c) is true. Common pitfall Confusing base circle with addendum circle; base circle is smaller than pitch circle for involute gears. Final Answer All of the above

Question 19

Columns: define slenderness ratio precisely.  Use the standard mechanical design definition relating effective length and cross-section property.  Choose the correct option.

Accepted Answer

Definition The slenderness ratio quantifies column propensity to buckle and is defined as λ = Le / kmin where Le is the effective length and kmin is the least radius of gyration of the cross section. Why option (c) Euler buckling and design formulas employ λ = Le/k; using the least radius of gyration is conservative because buckling occurs about the weakest axis. Final Answer Effective length of column ÷ least radius of gyration of the column

Question 20

Power screws (motion/power transmission): target property for thread selection.  For screws used to transmit power/motion (e.g., screw jacks, presses, lead screws), identify the desired efficiency characteristic.  Choose the correct option.

Accepted Answer

Concept Power-transmission screws (square/Acme threads) aim to minimize friction losses so that a larger fraction of input work becomes useful output. Thus a high efficiency is desirable. (Some applications may also require self-locking, but the general design goal for power transmission is higher efficiency than, say, fastening.) Why not others Low efficiency wastes power and increases heating. Very fine threads are for precise adjustment, not necessarily for efficient power transmission. Strong teeth (wording fits gears; threads need strength, but efficiency is the key differentiator for this question). Final Answer High efficiency

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