Agricultural/Bioengineering Strength of Materials 2 — Questions and Answers
Question 1: A steel grain bin support column has a cross-sectional area of 0.005 m² and carries an axial compressive load of 50 kN. What is the compressive stress?
- 5 MPa
- 10 MPa (Correct answer)
- 25 MPa
- 50 MPa
Correct answer: 10 MPa
Stress = Force / Area = 50,000 N / 0.005 m² = 10 MPa.
Question 2: Which of the following materials has the highest modulus of elasticity (stiffness) and is commonly used in agricultural machinery frames?
- Polyethylene
- Aluminum alloy
- Structural steel (Correct answer)
- Douglas fir timber
Correct answer: Structural steel
Structural steel has a modulus of elasticity of approximately 200 GPa, far higher than the other options.
Question 3: A wooden irrigation flume beam spans 4 m and carries a uniformly distributed load. If the maximum bending moment is 8 kN·m and the section modulus is 0.002 m³, what is the bending stress?
- 1 MPa
- 4 MPa (Correct answer)
- 16 MPa
- 4000 MPa
Correct answer: 4 MPa
Bending stress = M / S = 8,000 N·m / 0.002 m³ = 4 MPa.
Question 4: In a thin-walled cylindrical silo storing grain, which stress is approximately twice the longitudinal (axial) stress when internal pressure acts?
- Shear stress
- Hoop (circumferential) stress (Correct answer)
- Bearing stress
- Torsional stress
Correct answer: Hoop (circumferential) stress
For a thin-walled pressure vessel, hoop stress = pd/2t is twice the longitudinal stress = pd/4t.
Question 5: A tractor drawbar pin experiences a shear force of 20 kN across two shear planes (double shear). If the pin diameter is 20 mm, what is the average shear stress?
- 15.9 MPa (Correct answer)
- 31.8 MPa
- 63.7 MPa
- 127.3 MPa
Correct answer: 15.9 MPa
Double shear area = 2 × π(0.01)² = 6.283×10⁻⁴ m²; τ = 20,000 / 6.283×10⁻⁴ ≈ 31.8 MPa — wait, single shear area = π(0.01)² = 3.14×10⁻⁴ m², double shear τ = 20,000 / (2 × 3.14×10⁻⁴) ≈ 31.8 MPa.
Question 6: What does the 'neutral axis' of a beam cross-section represent during bending?
- The axis of maximum shear stress
- The axis where bending stress is zero (Correct answer)
- The axis of maximum deflection
- The centroid of the load distribution
Correct answer: The axis where bending stress is zero
The neutral axis is the line within a beam's cross-section where bending stress transitions from tension to compression and equals zero.
Question 7: A cast iron pump housing in an irrigation system is subjected to a tensile stress of 80 MPa. If the ultimate tensile strength of the cast iron is 200 MPa, what is the factor of safety?
- 0.4
- 1.25
- 2.5 (Correct answer)
- 16,000
Correct answer: 2.5
Factor of safety = Ultimate strength / Applied stress = 200 / 80 = 2.5.
Agricultural/Bioengineering Strength of Materials 2
A steel grain bin support column has a cross-sectional area of 0.005 m² and carries an axial compressive load of 50 kN.
What is the compressive stress?