Mechanical Engineering: Core Numerical Coverage for UPPSC AE
What the technical paper covers
The UPPSC Assistant Engineer (Mechanical) technical paper is objective and is drawn from the standard B.E. syllabus: engineering mechanics, strength of materials, thermodynamics and IC engines, fluid mechanics and machinery, heat transfer, theory of machines, machine design, manufacturing/production engineering and industrial engineering. Numerical items dominate; theory appears as "which of the following statements is correct" sets.
Formulas worth memorising
- Axial deformation δ = PL/AE, with A = πd²/4 - square the diameter, never the radius by mistake.
- Euler buckling for a hinged–hinged column: P_cr = π²EI/L². Effective lengths: 0.5L fixed–fixed, 0.7L fixed–hinged, L hinged–hinged, 2L fixed–free.
- Thermal stress in a fully restrained bar: σ = αEΔT, compressive on heating.
- Carnot efficiency depends only on source and sink temperatures expressed in kelvin.
- Cutting speed V = πDN/1000 m/min when D is in mm and N in rpm.
Worked example
A 20 mm diameter steel bar, 1 m long, E = 200 GPa, carries a 40 kN axial pull. Find the elongation. A = π(20)²/4 = 314.16 mm². δ = PL/AE = (40,000 N)(1,000 mm)/[(314.16 mm²)(200,000 N/mm²)] = 4×10⁷/6.28×10⁷ ≈ 0.64 mm. Every term is converted to N and mm before substitution - that single habit removes most prefix errors.
Traps that cost marks
- Mixing kN with mm², which shifts the answer by a factor of 1,000.
- Reporting gauge pressure when absolute pressure is asked (absolute = gauge + atmospheric).
- Applying Euler's formula to a short column, where σ = P/A governs instead.
- Sign-convention slips in shear force and bending moment diagrams, especially under point moments.
- Treating degrees and radians loosely in governor, gear and cam problems.