Mechanics of Materials — Quiz 6

Questions in this quiz (10)

1. An unsymmetrical beam section has a moment of inertia of $$60\times10^6\ \text{mm}^4$$. The distances from the neutral axis to the extreme tension and compression fibers are $$100\ \text{mm}$$ and $$70\ \text{mm}$$, respectively. If the beam is subjected to positive bending moment of $$40\ \text{kN-m}$$, determine the maximum tensile stress.

   • 40.0 MPa
   • 50.0 MPa
   • 66.7 MPa
   • 75.0 MPa

2. Using Castigliano's theorem, determine the deflection at the free end of a cantilever beam carrying a concentrated load of $$12\ \text{kN}$$ at its free end. The beam has a length of $$2.5\ \text{m}$$, $$E=200\ \text{GPa}$$, and $$I=25\times10^6\ \text{mm}^4$$.

   • 8.0 mm
   • 12.5 mm
   • 16.0 mm
   • 20.0 mm

3. A T-beam has a flange $$180\ \text{mm}$$ wide and $$40\ \text{mm}$$ thick, and a web $$60\ \text{mm}$$ wide and $$160\ \text{mm}$$ deep (below the flange). Determine the distance from the bottom of the web to the centroidal axis.

   • 95 mm
   • 123 mm
   • 140 mm
   • 165 mm

4. A simply supported beam with a span of $$6\ \text{m}$$ carries a concentrated load of $$25\ \text{kN}$$ at midspan. If $$E=200\ \text{GPa}$$ and $$I=90\times10^6\ \text{mm}^4$$, determine the slope at the supports.

   • 0.0020 rad
   • 0.0031 rad
   • 0.0045 rad
   • 0.0060 rad

5. A solid circular steel column $$\left(E=200\ \text{GPa}\right)$$ has a diameter of $$50\ \text{mm}$$ and a length of $$3\ \text{m}$$. The column is pinned at both ends. Determine the critical buckling load using Euler's formula.

   • 67.3 kN
   • 120.5 kN
   • 170.7 kN
   • 240.6 kN

6. Two fillet welds, each with a length of 120 mm and a throat thickness of 5 mm, connect two plates. If the joint carries a tensile load of 80 kN, determine the average shear stress in the welds.

   • 40 MPa
   • 50 MPa
   • 67 MPa
   • 80 MPa

7. A beam fixed at both ends with a span of 6 m carries a concentrated load of 40 kN at midspan. Determine the fixed-end moment at each support.

   • 40 kN-m
   • 60 kN-m
   • 80 kN-m
   • 100 kN-m

8. A bolt with a diameter of 20 mm passes through a plate with a thickness of 10 mm. If the bolt carries a tensile load of 50 kN, determine the bearing stress between the bolt and the plate.

   • 125.0 MPa
   • 250.0 MPa
   • 100.0 MPa
   • 200.0 MPa

9. A plate with a circular hole is subjected to an axial tensile load. If the nominal stress away from the hole is 90 MPa and the stress concentration factor is 2.2, determine the maximum stress at the edge of the hole.

   • 198 MPa
   • 180 MPa
   • 220 MPa
   • 240 MPa

10. An I-beam has a moment of inertia of $$180\times10^6\ \text{mm}^4$$ and the distance from the neutral axis to the extreme fiber is 180 mm. If the beam is subjected to a bending moment of 100 kN-m, determine the maximum bending stress.

    • 100 MPa
    • 150 MPa
    • 200 MPa
    • 250 MPa