ICAR AIEEA-PG — Agricultural Engineering & Technology (Major Subject Group 10) · India · National Testing Agency for ICAR
Original practice questions written to the published syllabus · not past papersHow members carry load: stress, strain, bending, torsion, deflection and buckling, used in machine and structure design.
In the exams: NCEES FE 9–14 questions; NCEES PE strength of materials; ICAR AIEEA-PG Unit IV
ICAR AIEEA-PG — Agricultural Engineering & Technology
Unit IV names strength of materials with engineering mechanics and soil mechanics. Expect elastic-constant relations, standard SF/BM and deflection results, section modulus, torsion and power, Euler effective lengths, thin-cylinder stresses, principal stresses and the names and applicability of failure theories, often as one-step numericals. Question papers are not published, so emphasis is inferred from the syllabus.
How our questions for ICAR AIEEA-PG spread across the units of Strength of Materials. Difficulty: 27 easy, 30 medium, 17 hard.
| Elastic constants and their relations | 8 | |
| Strain energy | 8 | |
| Shear force and bending moment diagrams | 7 | |
| Columns: Euler and Rankine formulas | 7 | |
| Combined stresses and Mohr's circle | 7 | |
| Stress, strain and Hooke's law | 6 | |
| Torsion of circular shafts | 6 | |
| Theories of failure | 6 | |
| Bending and shear stresses in beams | 5 | |
| Deflection of beams | 5 | |
| Thin cylinders and spheres | 5 | |
| Thermal stresses | 4 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A material has bulk modulus 150 GPa and modulus of rigidity 75 GPa. Its Young's modulus is closest to:
C. 192.9 GPa
E = 9KG/(3K + G) = 9 × 150 × 75/(450 + 75) = 192.9 GPa. Swapping K and G in the denominator gives 270.0 GPa; assuming ν = 0.3 without checking gives 195 GPa. Dropping the factor 9 to 3 (3KG/(3K + G)) gives 64.3 GPa.
Further reading: Timoshenko and Gere, Mechanics of Materials; Rajput, Strength of Materials
A thin sphere's diameter increases by a strain ε_d under internal pressure. Its volumetric strain is:
B. 3ε_d
Volume varies as d³, so for small strains ΔV/V = 3Δd/d. For a cylinder the answer would be 2ε_d + ε_L.
Further reading: Timoshenko and Gere, Mechanics of Materials; Rajput, Strength of Materials
For the same material, length and weight, a hollow circular shaft compared with a solid circular shaft:
B. Transmits more torque at the same maximum shear stress
Shear stress in torsion is zero at the centre and largest at the surface; moving material outward raises J/r for the same area. The hollow shaft is also stiffer (larger J), so it twists less, not more.
Further reading: Gere and Goodno, Mechanics of Materials, ch. 3
For a column fixed at the base and free at the top, the effective length used in Euler's formula is:
C. 2L
The fixed–free column buckles like half of a pinned–pinned column of length 2L, so L_e = 2L and the critical load is a quarter of the pinned–pinned value. L/2 is fixed–fixed; L/√2 is fixed–pinned.
Further reading: Timoshenko and Gere, Mechanics of Materials; Bansal, Strength of Materials
A mild-steel solid round column, 50 mm in diameter and 2 m long, is pinned at both ends. Using Rankine's formula with σ_c = 320 MPa and a = 1/7500, the crippling load is closest to:
D. 142.4 kN
A = 1963.5 mm², k = d/4 = 12.5 mm, L/k = 160. P = 320 × 1963.5/(1 + 160²/7500) = 142.4 kN. The crushing load σ_cA = 628.3 kN ignores buckling; Euler alone gives 151.4 kN; forgetting to square the slenderness ratio overestimates the load. Forgetting to square L/k gives 615.2 kN.
Further reading: Timoshenko and Gere, Mechanics of Materials; Bansal, Strength of Materials
A slender column is pinned at one end and fixed at the other. Compared with the same column pinned at both ends, its Euler load is about:
B. Two times
Fixed–pinned L_e = L/√2, so P_cr ∝ 1/L_e² = 2/L². 1.41 = √2 is the ratio of lengths, not loads.
Further reading: Timoshenko and Gere, Mechanics of Materials; Bansal, Strength of Materials
For the same internal pressure, diameter and allowable stress, the wall thickness needed for a thin sphere compared with a thin cylinder is:
D. Half
Sphere: σ = pD/(4t); cylinder hoop: σ = pD/(2t). For equal σ, t_sphere = t_cylinder/2.
Further reading: Beer and Johnston, Mechanics of Materials, ch. 7
A steel shear block (G = 80 GPa) is uniformly stressed in shear to 60 MPa. The strain energy stored per unit volume is:
B. 22.5 kJ/m³
u = τ²/(2G) = 60²/(2 × 80,000) = 0.0225 N·mm/mm³ = 22.5 kJ/m³. Using E instead of G gives 9.0 kJ/m³. Omitting the ½ gives 45.0 kJ/m³, and the solid-shaft factor τ²/(4G) gives 11.25 kJ/m³.
Further reading: Timoshenko and Gere, Mechanics of Materials; Rajput, Strength of Materials
For ductile metals, the failure theory that agrees best with experimental yield data under combined stress is the:
C. Distortion energy theory (von Mises)
Tests on ductile steels and aluminium lie close to the von Mises ellipse. Tresca is close and slightly conservative; Rankine and Saint-Venant fit ductile yielding poorly.
Further reading: Popov, Engineering Mechanics of Solids; Shigley-type machine design texts
Guest's theory of failure is another name for the:
B. Maximum shear stress theory
Guest's (Tresca's) theory: yield when τ_max = σ_y/2. Saint-Venant's is the maximum principal strain theory; Rankine's is maximum principal stress; von Mises–Hencky is distortion energy.
Further reading: Popov, Engineering Mechanics of Solids; Shigley-type machine design texts
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