Agricultural/Bioengineering Strength of Materials 3

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?

Accepted Answer

39.8 MPa

Answer

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?

Accepted Answer

Euler buckling

Answer

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?

Accepted Answer

It decreases to one-quarter

Answer

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?

Accepted Answer

133.3 × 10⁻⁶ m⁴

Answer

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?

Accepted Answer

18 kN·m

Answer

For a central point load, M_max = PL/4 = 12 × 6 / 4 = 18 kN·m.

Agricultural/Bioengineering Practice Test

Agricultural/Bioengineering Practice Test

Agricultural/Bioengineering Strength of Materials 3