Subtopic: Measurement of force, stress, torque, speed, displacement and acceleration on machine elements – shafts, couplings, keys, bearings and knuckle joints
Question Statement:
A subsoiler operating at 400 mm depth requires 15 kW peak drawbar power at 3 km h⁻¹ speed. The standard is rigidly fixed vertically on the main frame. The resultant soil resistance acts horizontally at a vertical distance of 450 mm from the main frame. The standard has rectangular cross-section with width to thickness ratio of 4:1, and it fails due to bending. If the allowable bending stress is 90 N mm⁻², the width of the standard in mm will be __________.
Official Answer Key:
128 to 130
Step-by-Step Solution & Explanation
• Soil resistance (draft force), F = Power/Speed = 15,000 W / (3×1000/3600 m/s) = 15,000/0.8333 = 18,000 N.
• Bending moment at the frame due to this horizontal force acting 450 mm below it: M = F × 0.45 m = 18,000 × 0.45 = 8,100 N·m = 8.1×10⁶ N·mm.
• For a rectangular section of width w and thickness t = w/4, bent about the axis resisted by the width dimension, section modulus Z = t w²/6 = (w/4)w²/6 = w³/24.
• σ = M/Z ⇒ Z = M/σ = 8,100,000/90 = 90,000 mm³.
• w³/24 = 90,000 ⇒ w³ = 2,160,000 ⇒ w = (2,160,000)^(1/3) ≈ 129.5 mm, inside the accepted range 128–130.
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