Mechanical Engineering 2023 Paper I 50 marks Solve

Q3

(a) The coefficient of friction for all contacting surfaces in Figure 3(a) is 0·2. Does the 25 kg force move the block A up, hold it in equilibrium, or is it too small to prevent A from coming down and B from moving out ? The 25 kg force is exerted at the mid-plane of the block so that we can consider this a coplanar problem. (20 marks) (b) A plane stress condition exists at a point in a loaded structure. The stresses have the magnitude and directions shown on the stress element of Figure 3(b). Calculate the stress acting on the planes obtained by rotating the element clockwise through an angle of 15°. (20 marks) (c) Discuss microstructure and mechanical properties of pearlite, bainite and martensite. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) चित्र 3(a) में सभी संपर्कीय सतहों का घर्षण गुणांक 0·2 है । क्या 25 kg का बल, गुटका A को ऊपर की तरफ अग्रसर करेगा, संतुलन में रखेगा, या यह इतना छोटा है कि A को नीचे आने से तथा B को बाहर जाने से नहीं रोक पाएगा ? 25 kg का बल गुटके के मध्य-तल पर लग रहा है जिससे कि हम इस समस्या को समतलीय मान सकते हैं । (20 अंक) (b) तलीय प्रतिबल की दशा एक भारित संरचना के एक बिंदु पर मौजूद है । प्रतिबलों का परिमाण तथा दिशाएँ चित्र 3(b) में एक प्रतिबल अंश पर दर्शाया गया है । उस तल पर प्रतिबल को परिकलित कीजिए जो कि इस अंश को 15° के कोण द्वारा घड़ी की दिशा में घुमाकर प्राप्त किया गया हो । (20 अंक) (c) पर्लाइट, बेनाइट तथा मार्टेंसाइट की सूक्ष्म-संरचना तथा यांत्रिक गुणों की विवेचना कीजिए । (10 अंक)

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How this answer will be evaluated

Approach

Solve the friction equilibrium problem in (a) by drawing FBDs of blocks A and B, applying equilibrium equations and checking against limiting friction; for (b) apply stress transformation equations (or Mohr's circle) to find rotated stresses; for (c) discuss microstructures with TTT diagram context and property comparisons. Allocate ~40% time to (a) due to multi-body friction analysis, ~35% to (b) for careful computation, and ~25% to (c) for structured comparison.

Key points expected

  • Part (a): FBDs showing normal forces, friction forces (μN = 0.2N) on all contacting surfaces; equilibrium equations for block A (vertical) and block B (horizontal); comparison of applied 25 kg force with minimum holding force and maximum lifting force to determine equilibrium state
  • Part (a): Correct identification that 25 kg force is insufficient to move A up but sufficient to prevent downward motion of A and outward motion of B (or correct alternative conclusion with proper justification)
  • Part (b): Application of stress transformation formulas σ_θ = (σx+σy)/2 + (σx-σy)/2 cos2θ + τxy sin2θ and τ_θ = -(σx-σy)/2 sin2θ + τxy cos2θ with θ = -15° (clockwise rotation)
  • Part (b): Correct substitution of given stress values (σx, σy, τxy from Figure 3b) and computation of transformed normal and shear stresses on the rotated plane
  • Part (c): Pearlite: lamellar ferrite-cementite structure, moderate strength/ductility, formed by eutectoid transformation; Bainite: non-lamellar aggregate of ferrite and carbide, finer than pearlite, higher strength with good toughness
  • Part (c): Martensite: body-centered tetragonal structure, supersaturated carbon, very hard and brittle, diffusionless shear transformation; comparison of hardness, toughness, and applications (e.g., rail steels, automotive components)
  • Part (c): Reference to TTT diagram showing transformation temperature ranges and resulting microstructures; effect of cooling rate on final microstructure and mechanical properties

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies Coulomb friction model with proper direction of friction forces opposing impending motion in (a); uses correct stress transformation equations with proper sign convention for clockwise rotation in (b); accurately describes crystal structures and transformation mechanisms for all three microstructures in (c)Correct friction concept but minor error in force direction assumption; stress transformation formula correct but sign error on θ; basic microstructure descriptions correct but incomplete transformation mechanismFundamental error in friction direction (static vs kinetic confusion); uses wrong transformation equations or Mohr's circle rotation direction; confuses microstructures or describes only one correctly
Numerical accuracy20%10Precise calculation of normal forces, friction limits, and equilibrium check in (a) with correct conclusion; accurate computation of transformed stresses to 2 decimal places in (b); quantitative property comparisons (e.g., hardness values, approximate carbon content) in (c)Correct numerical approach but minor arithmetic slip leading to slightly wrong threshold values; stress values mostly correct but one component wrong; qualitative rather than quantitative property discussionMajor calculation errors in friction analysis leading to wrong conclusion; completely wrong stress values; no numerical data in microstructure discussion
Diagram quality20%10Clear FBDs for both blocks in (a) with all forces labelled and angles shown; original and rotated stress elements in (b) with principal stresses indicated; schematic microstructure sketches for pearlite (lamellar), bainite (acicular), martensite (lath/martensitic) in (c)FBDs present but missing some force labels; stress element drawn but rotated plane not clearly marked; only one or two microstructure sketches or verbal descriptions onlyNo FBDs or incomprehensible sketches; no stress element diagram; no microstructure illustrations
Step-by-step derivation20%10Systematic equilibrium equations for both blocks in (a) with explicit inequality checks; full derivation of stress transformation with substitution steps shown; logical progression from iron-carbon diagram to TTT to microstructure-property links in (c)Some equilibrium steps skipped but key equations present; jumps to final stress values without showing intermediate steps; descriptive rather than logically structured microstructure discussionNo derivation, only final answers stated; incorrect or missing transformation derivation; random facts about microstructures without connecting logic
Practical interpretation20%10Physical interpretation of why block remains in equilibrium with safety margin discussion in (a); significance of rotated stresses in failure analysis (e.g., critical plane for ductile failure) in (b); industrial relevance—pearlite in rails (Indian Railways), bainite in high-strength automotive steels, martensite in tools and hardenable components in (c)Brief mention of equilibrium state without margin discussion; states stress values without physical meaning; generic application mentions without Indian contextNo interpretation of results; purely mathematical treatment; no applications or relevance discussed

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