Question 1

A copper bar (d = 10 mm, E = 110 GPa) is loaded by tensile load P = 11.5 kN. The maximum shear stress in the bar is approximately: (A) $ 73 \mathrm{MPa} $
(B) $ 87 \mathrm{MPa} $
(C) $ 145 \mathrm{MPa} $
(D) $ 150 \mathrm{MPa} $

Accepted Answer

The answer of A copper bar (d = 10 mm,...

Question 2

A brass bar twisted by torques T acting at the ends has the follow- ing properties: L = 2.1 m, d = 38 mm, and G = 41 GPa. The torsional
Stiffness of the bar is approximately: (A) $ 1200 \mathrm{~N} \cdot \mathrm{m} $
(B) $ 2600 \mathrm{~N} \cdot \mathrm{m} $
(C) $ 4000 \mathrm{~N} \cdot \mathrm{m} $
(D) $ 4800 \mathrm{~N} \cdot \mathrm{m} $

Accepted Answer

The answer of A brass bar twisted by torques T...

Question 3

An aluminum bar of diameter d = 52 mm is twisted by torques $T_{1}$ at the ends. The allowable shear stress is 65 MPa. The maximum permis- sible torque $T_{1}$ is approximately: (A) $ 1450 \mathrm{~N} \cdot \mathrm{m} $
(B) $ 1675 \mathrm{~N} \cdot \mathrm{m} $
(C) $ 1710 \mathrm{~N} \cdot \mathrm{m} $
(D) $ 1800 \mathrm{~N} \cdot \mathrm{m} $

Accepted Answer

The answer of An aluminum bar of diameter d =...

Question 4

A plane stress element on a bar in uniaxial stress has a tensile stress of $\sigma_{\theta}=78 \mathrm{MPa}$ (see fig.). The maximum shear stress in the bar is
Approximately: (A) $ 29 \mathrm{MPa} $
(B) $ 37 \mathrm{MPa} $
(C) $ 50 \mathrm{MPa} $
(D) $ 59 \mathrm{MPa} $

Accepted Answer

The answer of A plane stress element on a bar...

Question 5

The angle of rotation between the ends of a nylon bar is 3.5 °. The bar diameter is 70 mm and the allowable shear strain is 0.014 rad. The
Minimum permissible length of the bar is approximately: (A) $ 0.15 \mathrm{~m} $
(B) $ 0.27 \mathrm{~m} $
(C) $ 0.40 \mathrm{~m} $
(D) $ 0.55 \mathrm{~m} $

Accepted Answer

The answer of The angle of rotation between the ends...

Question 6

A monel shell $\left(E_{m}=170 \mathrm{GPa}, d_{3}=12 \mathrm{~mm}, d_{2}=8 \mathrm{~mm}\right)$ encloses a brass core $\left(E_{b}=96 \mathrm{GPa}, d_{1}=6 \mathrm{~mm}\right)$ . Initially, both shell and core are
A length of 100 mm. A load P is applied to both shell and core through
A cap plate. The load P required to compress both shell and core by
0)10 mm is approximately: (A) $ 10.2 \mathrm{kN} $
(B) $ 13.4 \mathrm{kN} $
(C) $ 18.5 \mathrm{kN} $
(D) $ 21.0 \mathrm{kN} $

Accepted Answer

The answer of A monel shell \(\left(E_{m}=170 \mathrm{GPa}, d_{3}=12 \mathrm{~mm},...

Question 7

A stepped steel shaft (G = 75 GPa) with diameters $d_{1}=36 \mathrm{~mm}$ and $d_{2}=32 \mathrm{~mm}$ is twisted by torques T at each end. Segment lengths are $L_{1}=0.9 \mathrm{~m} \text { and } L_{2}=0.75 \mathrm{~m} \text {. }$ . If the allowable shear stress is 28 MPa and maximum allowable twist is 1.8 °, the maximum permissible torque is
Approximately:
A) 142 N.m
B) 180 N.m
C) 185 N.m
D) 257 N.m

Accepted Answer

The maximum permissible torque is determined by the lesser of the two limits: allowable shear stress and maximum allowable twist. Calculating for both and choosing the smaller torque ensures the shaft's integrity.

Question 8

A hollow aluminum shaft (G = 27 GPa, $d_{2}=96 \mathrm{~mm}$ and $d_{1}=52 \mathrm{~mm}$ has an angle of twist per unit length of 1.8 °/m due to torques T. The resulting maximum tensile stress in the shaft is approx-
Imately: (A) $ 38 \mathrm{MPa} $
(B) $ 41 \mathrm{MPa} $
(C) $ 49 \mathrm{MPa} $
(D) $ 58 \mathrm{MPa} $

Accepted Answer

The answer of A hollow aluminum shaft (G = 27...

Question 9

A motor drives a shaft at $f=10 \mathrm{~Hz} \text { and delivers } P=35 \mathrm{~kW}$ of power. The allowable shear stress in the shaft is 45 MPa. The minimum
Diameter of the shaft is approximately: (A) $ 35 \mathrm{~mm} $
(B) $ 40 \mathrm{~mm} $
(C) $ 47 \mathrm{~mm} $
(D) $ 61 \mathrm{~mm} $

Accepted Answer

The answer of A motor drives a shaft at \(f=10...

Question 10

A brass rod of length L = 0.75 m is twisted by torques T until the angle of rotation between the ends of the rod is 3.5 $3.5^{\circ}$ . The allowable shear
Strain in the copper is 0.0005 rad. The maximum permissible diameter of
The rod is approximately: (A) $ 6.5 \mathrm{~mm} $
(B) $ 8.6 \mathrm{~mm} $
(C) $ 9.7 \mathrm{~mm} $
(D) $ 12.3 \mathrm{~mm} $

Accepted Answer

The answer of A brass rod of length L =...

Question 11

A gear shaft transmits torques $T_{A}=975 \mathrm{~N} \cdot \mathrm{m}, T_{B}=1500 \mathrm{~N} \cdot \mathrm{m}$ , $T_{C}=650 \mathrm{~N} \cdot \mathrm{m}, \text { and } T_{D}=825 \mathrm{~N} \cdot \mathrm{m}$ . If the allowable shear stress is 50 MPa, the required shaft diameter is approximately: (A) $ 38 \mathrm{~mm} $
(B) $ 44 \mathrm{~mm} $
(C) $ 46 \mathrm{~mm} $
(D) $ 48 \mathrm{~mm} $

Accepted Answer

The answer of A gear shaft transmits torques \(T_{A}=975 \mathrm{~N}...

Question 12

A brass pipe is twisted by torques T = 800 N . m acting at the ends causing an angle of twist of 3.5 °. The pipe has the following properties: $L=2.1 \mathrm{~m}, d_{1}=38 \mathrm{~mm}, \text { and } d_{2}=56 \mathrm{~mm}$ . The shear modulus of elas-
Ticity G of the pipe is approximately: (A) $ 36.1 \mathrm{GPa} $
(B) $ 37.3 \mathrm{GPa} $
(C) $ 38.7 \mathrm{GPa} $
(D) $ 40.6 \mathrm{GPa} $

Accepted Answer

The answer of A brass pipe is twisted by torques...

Question 13

A prismatic bar (diameter $d_{0}$ = 18 mm) is loaded by force $P_{\mathrm{1}}$ A stepped bar (diameters $d_{1}$ = 20 mm and $d_{2}$ = 25 mm with radius of fillets R = 2mm) is loaded by force $P_{2}$ . The allowable axial stress in the
Material is 75 MPa. The ratio $P_{1} / P_{2}$ of the maximum permissible loads
That can be applied to the bars, considering stress concentration effects in
The stepped bar, is: (A) $ 0.9 $
(B) $ 1.2 $
(C) $ 1.4 $
(D) $ 2.1 $

FIG. 2-66 Stress-concentration factor K for round bars with shoulder fillets.
The dashed line is for a full quarter-circular fillet.

Accepted Answer

The answer of A prismatic bar (diameter $d_{0}$ = 18...

Question 14

A steel plane truss is loaded at B and C by forces P = 200 kN. The cross-sectional area of each member is $A=3970 \mathrm{~mm}^{2}$ . Truss dimen-
Sions are H = 3mand L = 4m. The maximum shear stress in bar AB is
Approximately: (A) $ 27 \mathrm{MPa} $
(B) $ 33 \mathrm{MPa} $
(C) $ 50 \mathrm{MPa} $
(D) $ 69 \mathrm{MPa} $

Accepted Answer

The answer of A steel plane truss is loaded at...

Question 15

A steel bar of rectangular cross section (a = 38 mm, b = 50 mm) carries a tensile load P. The allowable stresses in tension and shear are
100 MPa and 48 MPa, respectively. The maximum permissible load $P_{\max }$ is
Approximately: (A) $ 56 \mathrm{kN} $
(B) $ 62 \mathrm{kN} $
(C) $ 74 \mathrm{kN} $
(D) $ 91 \mathrm{kN} $

Accepted Answer

The answer of A steel bar of rectangular cross section...

Question 16

Torques T = 5.7 kN . m are applied to a hollow aluminum shaft (G = 27 GPa and $d_{1}=52 \mathrm{~mm}$ . The allowable shear stress is 45 MPa
And the allowable normal strain is $8.0 \times 10^{-4}$ . The required outside
Diameter $d_{2}$ of the shaft is approximately:
A) 38 mm
B) 56 mm
C) 87 mm
D) 91 mm

Accepted Answer

To find the required outside diameter $d_2$, we use the torsion formula $\tau = \frac{T \cdot c}{J}$, where $\tau$ is the shear stress, $T$ is the torque, $c$ is the outer radius, and $J$ is the polar moment of inertia for a hollow shaft. Given the allowable shear stress and the torque, we solve for $d_2$ ensuring it does not exceed the allowable stress. Calculations show that $d_2 \approx 91 \, \text{mm}$ satisfies the conditions.

Question 17

A brass wire (d = 2.0 mm, E = 110 GPa) is pretensioned to T = 85 N. The coefficient of thermal expansion for the wire is $19.5 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ . The temperature change at which the wire goes slack is
Approximately: (A) $ +5.7^{\circ} \mathrm{C} $
(B) $ -12.6^{\circ} \mathrm{C} $
(C) $ +12.6^{\circ} \mathrm{C} $
(D) $ -18.2^{\circ} \mathrm{C} $

Accepted Answer

The answer of A brass wire (d = 2.0 mm,...

Question 18

A steel tube with diameters $d_{2}=86 \mathrm{~mm} \text { and } d_{1}=52 \mathrm{~mm}$ is twisted by torques at the ends. The diameter of a solid steel shaft that
Resists the same torque at the same maximum shear stress is approxi-
Mately: (A) $ 56 \mathrm{~mm} $
(B) $ 62 \mathrm{~mm} $
(C) $ 75 \mathrm{~mm} $
(D) $ 82 \mathrm{~mm} $

Accepted Answer

The answer of A steel tube with diameters \(d_{2}=86 \mathrm{~mm}...

Question 19

A stepped steel shaft with diameters $d_{1}=56 \mathrm{~mm} \text { and } d_{2}=52 \mathrm{~mm}$ is twisted by torques $T_{1}=3.5 \mathrm{kN} \cdot \mathrm{m}$ and $T_{2}=1.5 \mathrm{kN} \cdot \mathrm{m}$ acting in opposite directions. The maximum shear stress is approximately: (A) $ 54 \mathrm{MPa} $
(B) $ 58 \mathrm{MPa} $
(C) $ 62 \mathrm{MPa} $
(D) $ 79 \mathrm{MPa} $

Accepted Answer

The answer of A stepped steel shaft with diameters \(d_{1}=56...

Question 20

A motor drives a shaft with diameter $d=46 \mathrm{~mm} \text { at } f=5.25 \mathrm{~Hz}$ and delivers $P=25 \mathrm{~kW}$ of power. The maximum shear stress in the shaft is approximately: (A) $ 32 \mathrm{MPa} $
(B) $ 40 \mathrm{MPa} $
(C) $ 83 \mathrm{MPa} $
(D) $ 91 \mathrm{MPa} $

Accepted Answer

The answer of A motor drives a shaft with diameter...

Quiz 1: Mechanics of Materials

A copper bar (d = 10 mm, E = 110 GPa) is loaded by tensile load P = 11.5 kN. The maximum shear stress in the bar is approximately: (A) 73MPa 73 \mathrm{MPa} 73MPa (B) 87MPa 87 \mathrm{MPa} 87MPa (C) 145MPa 145 \mathrm{MPa} 145MPa (D) 150MPa 150 \mathrm{MPa} 150MPa