Agricultural/Bioengineering Strength of Materials 4

Question 1

A steel tension rod anchoring a guyed tower has a diameter of 25 mm and a length of 3 m. If the applied tensile load is 60 kN and E = 200 GPa, what is the elongation?

Accepted Answer

0.367 mm

Answer

δ = PL/AE = 60,000 × 3 / (π/4 × 0.025² × 200×10⁹) = 180,000 / (9.817×10⁷) ≈ 0.00183 m... recalculating: A=4.909×10⁻⁴ m², AE=9.817×10⁷ N, δ=180,000/9.817×10⁷≈0.00183 m — so 1.83 mm; closest answer shown is 1.834 mm but listed as option C; the correct formula gives ~1.83 mm.

Question 2

Which boundary condition gives the lowest Euler critical buckling load for a column of given length and cross-section?

Accepted Answer

One end fixed, one end free (K=2)

Answer

A fixed-free (cantilever) column has an effective length factor K=2, doubling the effective length and reducing P_cr by a factor of four compared to pinned-pinned.

Question 3

In designing a bolted joint for an agricultural implement attachment, bearing stress is calculated as:

Accepted Answer

Load divided by the projected contact area (diameter × thickness)

Answer

Bearing stress = P / (d × t) where d is bolt diameter and t is plate thickness, representing the average contact pressure between bolt and hole wall.

Question 4

A cantilever beam of length 2 m supports an irrigation pump weighing 5 kN at its free end. What is the maximum bending moment at the fixed support?

Accepted Answer

10 kN·m

Answer

For a cantilever with end point load, M_max = P × L = 5 × 2 = 10 kN·m at the fixed support.

Question 5

A soil bin experiment uses a horizontal steel plate stressed in two principal directions: σ₁ = 100 MPa and σ₂ = 60 MPa. What is the maximum in-plane shear stress?

Accepted Answer

20 MPa

Answer

Maximum in-plane shear stress = (σ₁ – σ₂)/2 = (100 – 60)/2 = 20 MPa.

Agricultural/Bioengineering Practice Test

Agricultural/Bioengineering Practice Test

Agricultural/Bioengineering Strength of Materials 4