Mechanics of Materials — Quiz 5

Questions in this quiz (10)

1. A rectangular column has dimensions 300 mm × 450 mm. To ensure no tensile stress develops in the section under eccentric loading, what is the maximum eccentricity of the load along the 450 mm dimension?

   • 112.5 mm
   • 75.0 mm
   • 150.0 mm
   • 56.3 mm

2. A bolt group consists of four 18 mm diameter bolts arranged in a square pattern at a radial distance of 90 mm from the centroid. The group is subjected to an eccentric load of 70 kN with an eccentricity of 120 mm. Determine the maximum shear stress in the critical bolt.

   • 95.6 MPa
   • 132.4 MPa
   • 168.3 MPa
   • 210.5 MPa

3. A cantilever beam with a point load at its free end and a simply supported beam with the same load at midspan have identical length and flexural rigidity. What is the ratio of the cantilever's maximum deflection to that of the simply supported beam?

   • 2
   • 4
   • 8
   • 16

4. A fillet weld has a leg size of 12 mm. Determine the effective throat dimension of the weld.

   • 12.0 mm
   • 8.5 mm
   • 6.0 mm
   • 7.07 mm

5. A beam-column is subjected to an axial load of 500 kN and a bending moment of 80 kN-m. If the allowable axial load is 900 kN and the allowable moment is 200 kN-m, determine the interaction ratio using the linear interaction formula:

   • 0.65
   • 0.72
   • 0.80
   • 0.96

6. At a point in a body under plane stress, the principal stresses are $$\sigma_1 = 120\ \text{MPa}$$ and $$\sigma_2 = -40\ \text{MPa}$$. Determine the maximum in-plane shear stress.

   • 40 MPa
   • 60 MPa
   • 80 MPa
   • 100 MPa

7. A hollow circular shaft has an outer diameter of 120 mm and an inner diameter of 80 mm. Compared to a solid shaft with the same outer diameter, what is the percentage weight savings of the hollow shaft?

   • 30%
   • 44%
   • 56%
   • 64%

8. A cantilever beam with a length of 5 m carries a triangular distributed load varying from 40 kN/m at the fixed end to zero at the free end. Determine the bending moment at the fixed support.

   • 200 kN-m
   • 166.7 kN-m
   • 133.3 kN-m
   • 100 kN-m

9. At a point in a stressed body, the stress components are $$\sigma_x=100\ \text{MPa}$$, $$\sigma_y=40\ \text{MPa}$$, and $$\tau_{xy}=20\ \text{MPa}$$. Determine the angle from the x-axis to the plane of maximum shear stress.

   • 22.5°
   • 30°
   • 45°
   • 67.5°

10. A helical spring has a mean coil diameter of 60 mm and a wire diameter of 8 mm. Using the Wahl correction factor, determine the maximum shear stress in the spring when subjected to a load of 500 N.

    • 210 MPa
    • 265 MPa
    • 315 MPa
    • 360 MPa