Question 1 |
A beam of length L is loaded in the xy-plane by a uniformly distributed load,
and by a concentrated tip load parallel to the z-axis, as shown in the figure. The
resulting bending moment distributions about the y and the z axes are denoted by M_y and M_z, respectively.
Which one of the options given depicts qualitatively CORRECT variations of M_y and M_z along the length of the beam?
Which one of the options given depicts qualitatively CORRECT variations of M_y and M_z along the length of the beam?
A | |
B | |
C | |
D |
Question 1 Explanation:
Udl will produced bending moment diagram about z axis \left(M_{2}\right)
Point load will produce bending moment diagram about y-axis \left(M_{y}\right).
Question 2 |
A beam of negligible mass is hinged at support P and has a roller support Q as shown
in the figure.
A point load of 1200 N is applied at point R. The magnitude of the reaction force at support Q is __________ N.
A point load of 1200 N is applied at point R. The magnitude of the reaction force at support Q is __________ N.
3000 | |
1500 | |
300 | |
750 |
Question 2 Explanation:
\begin{aligned} \Sigma \vec{M}_{P} &=0 \\ 1200 \times 5-R_{Q} \times 4 &=0 \\ R_{Q} &=\frac{1200 \times 5}{4}=1500 \mathrm{N} \end{aligned}
Question 3 |
The magnitude of reaction force at joint C of the hinge-beam shown in the figure is
_______ kN (round off to 2 decimal places).
40 | |
10 | |
50 | |
20 |
Question 3 Explanation:
\begin{aligned} \Sigma M_{B_{\text {Right }}} &=0 \\ 4 R_{C} &=10 \times 4 \times 2 \\ R_{C} &=20 \mathrm{kN} \end{aligned}
Question 4 |
The barrier shown between two water tanks of unit width (1 m) into the plane of the screen
is modeled as a cantilever.
Taking the density of water as 1000 kg/m^3, and the acceleration due to gravity as 10 m/s^2, the maximum absolute bending moment developed in the cantilever is ______ kNm (round off to the nearest integer).
Taking the density of water as 1000 kg/m^3, and the acceleration due to gravity as 10 m/s^2, the maximum absolute bending moment developed in the cantilever is ______ kNm (round off to the nearest integer).
85 | |
105 | |
128 | |
146 |
Question 4 Explanation:
\begin{aligned} F_{1} &=\rho g A \cdot \bar{x}_{1} \\ &=1000 \times 10 \times(1 \times 4) \times 2=80 \mathrm{kN}\\ F_{2} &=\rho g A \cdot \bar{x}_{2} \\ &=1000 \times 10 \times(1 \times 1) \times 0.5=5 \mathrm{kN} \\ C P_{1} &=4 \times \frac{1}{3}=\frac{4}{3} \mathrm{m} \\ C P_{2} &=1 \times \frac{1}{3}=\frac{1}{3} \mathrm{m} \\ M_{A} &=80 \times \frac{4}{3}-5 \times \frac{1}{3}=105 \mathrm{kN}-\mathrm{m} \end{aligned}
Question 5 |
A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam is __________ (correct to one decimal place).
25 | |
30 | |
35 | |
50 |
Question 5 Explanation:
\text { Maximum B.M.. } M=\frac{w L^{2}}{8}=\frac{10 \times 16}{8}=20 \mathrm{kNm} \quad (L=4)
Maximum Bending Stress
\begin{aligned} \sigma_{\max } &=\frac{M}{I} y_{\max }=\frac{20 \times 10^{3}}{\left(\frac{0.1 \times 0.2^{3}}{12}\right)} \times 0.1 \\ &=30 \times 10^{6} \mathrm{N} / \mathrm{m}^{2}=30 \mathrm{MPa} \end{aligned}
Maximum Bending Stress
\begin{aligned} \sigma_{\max } &=\frac{M}{I} y_{\max }=\frac{20 \times 10^{3}}{\left(\frac{0.1 \times 0.2^{3}}{12}\right)} \times 0.1 \\ &=30 \times 10^{6} \mathrm{N} / \mathrm{m}^{2}=30 \mathrm{MPa} \end{aligned}
There are 5 questions to complete.