Agricultural/Bioengineering Strength of Materials 5 — Questions and Answers
Question 1: A sprinkler pipe made of PVC has an inner diameter of 50 mm, wall thickness of 4 mm, and internal water pressure of 0.8 MPa. What is the hoop stress?
- 5 MPa (Correct answer)
- 10 MPa
- 12.5 MPa
- 25 MPa
Correct answer: 5 MPa
Hoop stress = pr/t = 0.8 × 0.025 / 0.004 = 5 MPa (r = inner radius = 25 mm).
Question 2: Which of the following best describes 'creep' in a polymer biofilm carrier used in a wastewater treatment bioreactor?
- Sudden brittle fracture under impact load
- Time-dependent plastic deformation under sustained stress below yield strength (Correct answer)
- Elastic recovery after load removal
- Increased stiffness at elevated temperature
Correct answer: Time-dependent plastic deformation under sustained stress below yield strength
Creep is the slow, continuous deformation of a material under constant stress over time, especially significant in polymers at elevated temperatures.
Question 3: In a combined loading scenario, a tractor PTO shaft simultaneously carries a torque of 800 N·m and a bending moment of 400 N·m. The von Mises equivalent stress is used to assess failure against:
- Euler buckling load
- Tensile yield strength of the shaft material (Correct answer)
- Fatigue endurance limit only
- Creep rupture strength
Correct answer: Tensile yield strength of the shaft material
The von Mises criterion predicts yielding when the equivalent stress equals the uniaxial tensile yield strength of the material.
Question 4: A rectangular cross-section timber beam (b=150 mm, d=300 mm) is loaded in bending. The maximum shear stress in the beam occurs:
- At the top and bottom fibers
- At the neutral axis (Correct answer)
- At the quarter-depth points
- At the point of maximum bending moment
Correct answer: At the neutral axis
For a rectangular cross-section, the shear stress distribution is parabolic and reaches its maximum at the neutral axis.
Question 5: A steel wire rope used to lift bales in a hay storage system has a rated breaking strength of 50 kN. If a safety factor of 5 is required, what is the maximum allowable working load?
- 5 kN
- 10 kN (Correct answer)
- 25 kN
- 250 kN
Correct answer: 10 kN
Allowable load = Breaking strength / Safety factor = 50 kN / 5 = 10 kN.
Question 6: During strain gauge testing of an agricultural equipment frame, a gauge reads a strain of 750 microstrain (750 × 10⁻⁶). If E = 200 GPa, what is the corresponding stress?
- 0.15 MPa
- 15 MPa
- 150 MPa (Correct answer)
- 1500 MPa
Correct answer: 150 MPa
Stress = E × ε = 200 × 10⁹ × 750 × 10⁻⁶ = 150 MPa.
Question 7: A biological tissue scaffold in an agricultural bioengineering application exhibits viscoelastic behavior. This means the scaffold:
- Has a perfectly linear stress-strain curve at all strain rates
- Shows both elastic (spring-like) and viscous (dashpot-like) mechanical responses (Correct answer)
- Fails only by brittle fracture with no energy absorption
- Has the same stiffness regardless of loading rate
Correct answer: Shows both elastic (spring-like) and viscous (dashpot-like) mechanical responses
Viscoelastic materials combine elastic energy storage with viscous energy dissipation, making their response time- and rate-dependent.
Agricultural/Bioengineering Strength of Materials 5
A sprinkler pipe made of PVC has an inner diameter of 50 mm, wall thickness of 4 mm, and internal water pressure of 0.8 MPa.
What is the hoop stress?