Q. A beam is subjected to a moment of 50 kNm. If the section modulus is 10 cm^3, what is the bending stress in the beam?
A.
5 MPa
B.
10 MPa
C.
15 MPa
D.
20 MPa
Solution
Bending stress (σ) is calculated using the formula σ = M/Z, where M is the moment and Z is the section modulus. Here, σ = 50 kNm / 10 cm^3 = 50,000 Nm / 0.00001 m^3 = 5 MPa.
Q. A simply supported beam has a length of 8 m and is subjected to a uniformly distributed load of 4 kN/m. What is the deflection at the center of the beam?
A.
0.025 m
B.
0.05 m
C.
0.1 m
D.
0.075 m
Solution
The deflection at the center of a simply supported beam under a uniform load is given by δ = 5wL^4 / (384EI). Substituting w = 4 kN/m, L = 8 m, E = 200 GPa, and I = 0.0001 m^4 gives δ = 0.05 m.
Q. For a truss with a total load of 12 kN applied at joint C, what is the force in member AC if the truss is in equilibrium?
A.
6 kN
B.
12 kN
C.
0 kN
D.
8 kN
Solution
In a statically determinate truss, the force in member AC can be determined using the method of joints. If joint C has a load of 12 kN, member AC will carry the same load in equilibrium.
Q. In a statically indeterminate beam, if the support reactions are not sufficient to maintain equilibrium, what method can be used to analyze the structure?
A.
Method of Joints
B.
Method of Sections
C.
Superposition
D.
Stiffness Method
Solution
The stiffness method is commonly used to analyze statically indeterminate structures by considering the stiffness of members and the compatibility of deformations.
