Agricultural/Bioengineering Strength of Materials 3 — Questions and Answers
Question 1: A steel shaft in a feed mixer has a diameter of 40 mm and transmits a torque of 500 N·m. What is the maximum shear stress in the shaft?
- 19.9 MPa
- 39.8 MPa (Correct answer)
- 79.6 MPa
- 159.2 MPa
Correct answer: 39.8 MPa
τ_max = Tc/J where J = πd⁴/32 = π(0.04)⁴/32 ≈ 2.513×10⁻⁷ m⁴; τ = 500 × 0.02 / 2.513×10⁻⁷ ≈ 39.8 MPa.
Question 2: Which failure mode is most critical for a long, slender steel column supporting a grain dryer platform?
- Shear yielding
- Euler buckling (Correct answer)
- Fatigue fracture
- Creep deformation
Correct answer: Euler buckling
Long slender columns fail by Euler buckling (elastic instability) at loads well below the material's yield strength.
Question 3: If the slenderness ratio (L/r) of a column is increased by doubling its effective length while keeping the cross-section constant, how does the Euler critical buckling load change?
- It doubles
- It halves
- It increases by four times
- It decreases to one-quarter (Correct answer)
Correct answer: It decreases to one-quarter
Euler's formula P_cr = π²EI/L² shows that doubling L reduces P_cr by a factor of four (1/2² = 1/4).
Question 4: A rectangular wooden beam used in a greenhouse structure has width b = 100 mm and depth d = 200 mm. What is its moment of inertia about the horizontal (strong) axis?
- 33.3 × 10⁻⁶ m⁴
- 66.7 × 10⁻⁶ m⁴
- 133.3 × 10⁻⁶ m⁴ (Correct answer)
- 266.7 × 10⁻⁶ m⁴
Correct answer: 133.3 × 10⁻⁶ m⁴
I = bd³/12 = (0.1)(0.2)³/12 = 0.0008/12 ≈ 66.7 × 10⁻⁶ m⁴ — the strong axis (d=200mm) gives I = (0.1)(0.2)³/12 = 6.67×10⁻⁵ m⁴ = 66.7×10⁻⁶ m⁴.
Question 5: A simply supported steel beam of length 6 m carries a central point load of 12 kN. What is the maximum bending moment at midspan?
- 12 kN·m
- 18 kN·m (Correct answer)
- 36 kN·m
- 72 kN·m
Correct answer: 18 kN·m
For a central point load, M_max = PL/4 = 12 × 6 / 4 = 18 kN·m.
Question 6: Poisson's ratio describes the relationship between which two types of strain in a loaded member?
- Shear strain and torsional strain
- Thermal strain and elastic strain
- Lateral strain and axial strain (Correct answer)
- Bending strain and compressive strain
Correct answer: Lateral strain and axial strain
Poisson's ratio ν = –(lateral strain / axial strain) relates the transverse contraction to the longitudinal extension under uniaxial load.
Question 7: In a bioengineering application, a bone scaffold made from a porous polymer has an apparent modulus of elasticity much lower than the bulk material. This is primarily because:
- Polymers are always more flexible than metals
- Porosity reduces the effective cross-sectional area carrying load (Correct answer)
- The scaffold is always loaded in torsion
- Temperature effects dominate polymer stiffness
Correct answer: Porosity reduces the effective cross-sectional area carrying load
Porosity removes load-bearing material, lowering the effective stiffness and apparent modulus of the scaffold structure.
Agricultural/Bioengineering Strength of Materials 3
A steel shaft in a feed mixer has a diameter of 40 mm and transmits a torque of 500 N·m.
What is the maximum shear stress in the shaft?