Shear-force and Bending Moment Diagrams

 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?

 A A B B C C D D
GATE ME 2023   Strength of Materials
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 3000 B 1500 C 300 D 750
GATE ME 2020 SET-2   Strength of Materials
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).
 A 40 B 10 C 50 D 20
GATE ME 2020 SET-1   Strength of Materials
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).
 A 85 B 105 C 128 D 146
GATE ME 2020 SET-1   Strength of Materials
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).
 A 25 B 30 C 35 D 50
GATE ME 2018 SET-1   Strength of Materials
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}

There are 5 questions to complete.