Question 1

A nonprismatic cantilever beam of one material is subjected to load P at its free end. Moment of inertia $I_{2}=2 I_{1}$ . The ratio r of the
Deflection $\delta_{B}$ to the deflection $\delta_{1}$ at the free end of a prismatic cantilever
With moment of inertia $I_{1}$ carrying the same load is approximately: (A) $ 0.25 $
(B) $ 0.40 $
(C) $ 0.56 $
(D) $ 0.78 $

Accepted Answer

The answer of A nonprismatic cantilever beam of one material...

Question 2

A steel bracket ABCD $\left(E I=4.2 \times 10^{6} \mathrm{~N} \cdot \mathrm{m}^{2}\right)$ , with span length L = 4.5 m and dimension a = 2m, is subjected to load P = 10 kN at D.
The maximum deflection at B is approximately: (A) $ 10 \mathrm{~mm} $
(B) $ 14 \mathrm{~mm} $
(C) $ 19 \mathrm{~mm} $
(D) $ 24 \mathrm{~mm} $

Accepted Answer

The answer of A steel bracket ABCD \(\left(E I=4.2 \times...

Question 3

A thin-walled cylindrical tank, under internal pressure p, is com- pressed by a force F = 75 kN. Cylinder diameter is d = 90 mm and wall
Thickness t = 5.5 mm. Allowable normal stress is 110 MPa and allowable
Shear stress is 60 MPa. The maximum allowable internal pressure $p_{\max }$ is
Approximately: (A) $ 5 \mathrm{MPa} $
(B) $ 10 \mathrm{MPa} $
(C) $ 13 \mathrm{MPa} $
(D) $ 17 \mathrm{MPa} $

Accepted Answer

The answer of A thin-walled cylindrical tank, under internal pressure...

Question 4

Structure 1 with member BC of length $L / 2$ /2 has force $P_{1}$ applied at joint C. Structure 2 with member BC of length L has force $P_{2}$ applied at C.
Both structures have constant flexural rigidity EI. If the ratio of the
Applied forces $P_{1} / P_{2}=5 / 2$ , the ratio of the joint B rotations $\theta_{B 1} / \theta_{B 2}$ is
Approximately: (A) 1
(B) $ 5 / 4 $
(C) $ 3 / 2 $
(D) 2

Accepted Answer

The answer of Structure 1 with member BC of length...

Question 5

A steel bracket $A B C\left(E I=4.2 \times 10^{6} \mathrm{~N} \cdot \mathrm{m}^{2}\right)$ with span length L = 4.5 m and height H = 2mis subjected to load P = 15 kN at C.
The maximum rotation of joint B is approximately: (A) $ 0.1^{\circ} $
(B) $ 0.3^{\circ} $
(C) $ 0.6^{\circ} $
(D) $ 0.9^{\circ} $

Accepted Answer

The answer of A steel bracket \(A B C\left(E I=4.2...

Question 6

A segment of a drive shaft $\left(d_{2}=200 \mathrm{~mm}, d_{1}=160 \mathrm{~mm}\right)$ is sub- jected to a torque T = 30 kN . m. The allowable shear stress in the shaft
Is 45 MPa. The maximum permissible compressive load P is approxi-
Mately: (A) $ 200 \mathrm{kN} $
(B) $ 286 \mathrm{kN} $
(C) $ 328 \mathrm{kN} $
(D) $ 442 \mathrm{kN} $

Accepted Answer

The answer of A segment of a drive shaft \(\left(d_{2}=200...

Question 7

Propped cantilever beam AB has moment $M_{\mathrm{I}}$ applied at joint B. Framework ABC has moment $M_{2}$ applied at C. Both structures have con-
Stant flexural rigidity EI. If the ratio of the applied moments $M_{1} / M_{2}=3 / 2$ the ratio of the reactive moments $M_{A 1} / M_{A 2}$ at clamped support A is
Approximately: (A) 1
(B) $ 3 / 2 $
(C) 2
(D) $ 5 / 2 $

Accepted Answer

The answer of Propped cantilever beam AB has moment $M_{\mathrm{I}}$...

Question 8

A steel beam $(E=210 \mathrm{GPa})$ with $I=119 \times 10^{6} \mathrm{~mm}^{4}$ and span length L = 3.5 m is subjected to uniform load $q=9.5 \mathrm{kN} / \mathrm{m}$ . The maxi-
Mum deflection of the beam is approximately:
A) 10 mm
B) 13 mm
C) 17 mm
D) 19 mm

Accepted Answer

The answer of A steel beam $(E=210 \mathrm{GPa})$ with \(I=119...

Question 9

An aluminum cantilever beam (E = 72 GPa) with a square cross sec- tion and span length L = 2.5 m is subjected to uniform load $q=1.5 \mathrm{kN} / \mathrm{m}$ The allowable bending stress is 55 MPa. The maximum deflection of the
Beam is approximately: (A) $ 10 \mathrm{~mm} $
(B) $ 20 \mathrm{~mm} $
(C) $ 30 \mathrm{~mm} $
(D) $ 40 \mathrm{~mm} $

Accepted Answer

The answer of An aluminum cantilever beam (E = 72...

Question 10

A steel bracket $A B C \quad\left(E I=4.2 \times 10^{6} \mathrm{~N} \cdot \mathrm{m}^{2}\right)$ with span length L = 4.5 m and height H = 2mis subjected to load P = 15 kN
At C. The maximum horizontal displacement of joint C is approximately: (A) $ 22 \mathrm{~mm} $
(B) $ 31 \mathrm{~mm} $
(C) $ 38 \mathrm{~mm} $
(D) $ 40 \mathrm{~mm} $

Accepted Answer

The answer of A steel bracket \(A B C \quad\left(E...

Question 11

Structure 1 with member BC of length $L / 2$ /2 has force $P_{1}$ applied at joint C. Structure 2 with member BC of length L has force $P_{2}$ applied at C.
Both structures have constant flexural rigidity EI. The required ratio of
The applied forces $P_{1} / P_{2}$ so that joint B rotations $\theta_{B 1} \text { and } \theta_{B 2}$ are equal is
Approximately: (A) 1
(B) $ 5 / 4 $
(C) $ 3 / 2 $
(D) 2

Accepted Answer

The answer of Structure 1 with member BC of length...

Question 12

Propped cantilever beam AB has moment $M_{\mathrm{1}}$ applied at joint B. Framework ABC has moment $M_{2}$ applied at C. Both structures have con-
Stant flexural rigidity EI. If the ratio of the applied moments $M_{1} / M_{2}=3 / 2$ the ratio of the joint rotations at B, $\theta_{B 1} / \theta_{B 2}$ , is approximately: (A) 1
(B) $ 3 / 2 $
(C) 2
(D) $ 5 / 2 $

Accepted Answer

The answer of Propped cantilever beam AB has moment $M_{\mathrm{1}}$...

Question 13

Structure 1 with member BC of length $L / 2$ /2 has force $P_{1}$ applied at joint C. Structure 2 with member BC of length L has force $P_{2}$ applied at C.
Both structures have constant flexural rigidity EI. If the ratio of the
Applied forces $P_{1} / P_{2}=5 / 2$ , the ratio of the joint B reactions $R_{B 1} / R_{B 2}$ is
Approximately:
A) 1
B) 5/4
C) 3/2
D) 2

Accepted Answer

The deflection of a beam (δ) due to a point load P at any point is given by the formula $δ = \frac{P \cdot L^3}{3EI}$ for a simply supported beam, where L is the length of the beam, E is the modulus of elasticity, I is the moment of inertia, and P is the applied force. The reaction at the support B for both structures can be considered proportional to the deflection caused by the applied forces $P_1$ and $P_2$, since both structures have constant flexural rigidity EI.Given that $P_1 / P_2 = 5 / 2$ and the length of member BC in structure 1 is $L/2$, the deflection caused by $P_1$ in structure 1 can be compared to the deflection caused by $P_2$ in structure 2 by adjusting for the length difference. The deflection formula adjusted for length gives us $\delta \proportional P \cdot L^3$, so when the length is halved, the effect on deflection (and thus on the reaction at B) is reduced by a factor of $1/2^3 = 1/8$.Therefore, for structure 1 with force $P_1$ and length $L/2$, the reaction at B compared to structure 2 with force $P_2$ and length L, taking into account the force ratio of $5/2$ and the length effect, gives us a combined factor of $(5/2) \cdot (1/8) = 5/16$. However, since the length effect significantly reduces the deflection and thus the reaction force at B for structure 1, we need to adjust our understanding based on the direct comparison of forces and the structural response, which is more straightforwardly related to the force applied rather than the deflection formula directly.Given the complexity of directly applying the deflection formula to determine the reaction at B without considering the specific structural setup and load distribution, the correct approach involves understanding how the force and length differences affect the reactions at the supports. The force ratio of $5/2$ suggests that for equal lengths, the reaction would directly scale with the force. However, the difference in lengths (and thus the leverage effect) between the two structures complicates this direct comparison.Considering the principles of static equilibrium and beam deflection without overcomplicating the analysis with the detailed deflection formula leads to recognizing that the reaction at B for both structures will indeed be influenced by both the applied force and the length of the beam, but the exact ratio of $R_{B1} / R_{B2}$ requires a more nuanced understanding of structural behavior than provided by a straightforward application of the deflection formula. The correct answer, based on the information given and typical structural analysis principles, would focus on the proportional relationship between the forces and the structural responses, leading to the selection of choice B) 5/4 as an approximation of how the reactions at B compare, acknowledging the simplification in the explanation.

Question 14

An aluminum beam $(E=72 \mathrm{GPa})$ with a square cross section and span length L = 2.5 m is subjected to uniform load $q=1.5 \mathrm{kN} / \mathrm{m}$ . The
Allowable bending stress is 60 MPa. The maximum deflection of the beam
Is approximately: (A) $ 10 \mathrm{~mm} $
(B) $ 16 \mathrm{~mm} $
(C) $ 22 \mathrm{~mm} $
(D) $ 26 \mathrm{~mm} $

Accepted Answer

The answer of An aluminum beam $(E=72 \mathrm{GPa})$ with a...

Quiz 1: Mechanics of Materials

A steel bracket $A B C\left(E I=4.2 \times 10^{6} \mathrm{~N} \cdot \mathrm{m}^{2}\right)$ with span length L = 4.5 m and height H = 2mis subjected to load P = 15 kN at C. The maximum rotation of joint B is approximately: (A) $0.1^{\circ}$ (B) $0.3^{\circ}$ (C) $0.6^{\circ}$ (D) $0.9^{\circ}$

A steel beam $(E=210 \mathrm{GPa})$ with $I=119 \times 10^{6} \mathrm{~mm}^{4}$ and span length L = 3.5 m is subjected to uniform load $q=9.5 \mathrm{kN} / \mathrm{m}$ . The maxi- Mum deflection of the beam is approximately:

Quiz 1: Mechanics of Materials

A steel beam (E=210GPa) (E=210 \mathrm{GPa}) (E=210GPa) with I=119×106 mm4I=119 \times 10^{6} \mathrm{~mm}^{4}I=119×106 mm4 and span length L = 3.5 m is subjected to uniform load q=9.5kN/mq=9.5 \mathrm{kN} / \mathrm{m}q=9.5kN/m . The maxi- Mum deflection of the beam is approximately:

A steel beam $(E=210 \mathrm{GPa})$ with $I=119 \times 10^{6} \mathrm{~mm}^{4}$ and span length L = 3.5 m is subjected to uniform load $q=9.5 \mathrm{kN} / \mathrm{m}$ . The maxi- Mum deflection of the beam is approximately: