Deck 1: Mechanics of Materials

Question 1

A steel plate weighing 27 kN is hoisted by a cable sling that has a clevis at each end. The pins through the clevises are 22 mm in diameter.
Each half of the cable is at an angle of 35⬚ to the vertical. The average
Shear stress in each pin is approximately:

Answer 1

A 

Question 2

A nonprismatic cantilever bar has an internal cylindrical hole of diameter /2 from 0 to x, so the net area of the cross section for Segment 1 . Load P is applied at x, and load is applied at x ⫽ L.
Assume that E is constant. The length of the hollow segment, x, required
To obtain axial displacement at the free end is:

Answer 2

D 

Question 3

Two wires, one copper and the other steel, of equal length stretch the same amount under an applied load P. The moduli of elasticity for
Each is . The ratio of the diameter of
The copper wire to that of the steel wire is approximately:

Answer 3

D 

Question 4

Two flanged shafts are connected by eight 18-mm bolts. The diam- eter of the bolt circle is 240 mm. The allowable shear stress in the bolts is
90 MPa. Ignore friction between the flange plates. The maximum value of
Torque is approximately:

Question 5

A nylon bar (E ⫽ 2.1 GPa) with diameter 12 mm, length 4.5 m, and weight 5.6 N hangs vertically under its own weight. The elongation of
The bar at its free end is approximately:

Question 6

An elastomeric bearing pad is subjected to a shear force V during a static loading test. The pad has dimensions a ⫽ 150 mm and b ⫽ 225 mm,
And thickness t ⫽ 55 mm. The lateral displacement of the top plate with
Respect to the bottom plate is 14 mm under a load P ⫽ 16 kN. The shear
Modulus of elasticity G of the elastomer is approximately:

Question 7

An aluminum bar $(E=72 \mathrm{GPa}, v=0.33)$ of diameter 50 mm cannot exceed a diameter of 50.1 mm when compressed by axial force P.
The maximum acceptable compressive load P is approximately:

A) 190 kN
B) 200 kN
C) 470 kN
D) 860 kN

Question 8

An aluminum bar $(E=70 \mathrm{GPa}, v=0.33)$ of diameter 20 mm is stretched by axial forces P, causing its diameter to decrease by 0.022 mm.
The load P is approximately:

A) 73 kN
B) 100 kN
C) 140 kN
D) 339 kN P d P

Question 9

A copper tube with wall thickness of 8 mm must carry an axial ten- sile force of 175 kN. The allowable tensile stress is 90 MPa. The minimum
Required outer diameter is approximately:

Question 10

A pipe (E = 110 GPa) carries a load $P_{\mathrm{I}}=120 \mathrm{kN}$ at A and a uniformly distributed load $P_{2}=100 \mathrm{kN}$ on the cap plate at B. Initial pipe
Diameters and thicknesses are $d_{A B}=38 \mathrm{~mm}$ , $t_{A B}=12 \mathrm{~mm}$ , $d_{B C}=70 \mathrm{~mm}$ , and $t_{B C}=10 \mathrm{~mm}$ . Under loads $P_{1}$ and $P_{2}$ , wall thickness $t_{B C}$ increases by 0.0036 mm. Poisson's ratio ν for the pipe material is
Approximately:

A) 0.27
B) 0.30
C) 0.31
D) 0.34

Question 11

A plane truss with span length L ⫽ 4.5 m is constructed using cast iron pipes (E ⫽ 170 GPa) with a cross-sectional area of 4500 mm . The
Displacement of joint B cannot exceed 2.7 mm. The maximum value of
Loads P is approximately:

Question 12

An polyethylene bar (E ⫽ 1.4 GPa, v ⫽ 0.4) of diameter 80 mm is inserted in a steel tube of inside diameter 80.2 mm and then compressed
By axial force P. The gap between steel tube and polyethylene bar will
Close when compressive load P is approximately:
(A) 18 kN
(B) 25 kN
(C) 44 kN bar Steeltube
(D) 60 kN Polyethylene d1 d2

Question 13

A brass rod (E ⫽ 110 GPa) with a cross-sectional area of 250 mm2 is loaded by forces . Segment
Lengths of the bar are a ⫽ 2.0 m, b ⫽ 0.75 m, and c ⫽ 1.2 m. The
Change in length of the bar is approximately: D

Question 14

The moment reaction at A in the plane frame below is approximately:

Question 15

A plane truss has downward applied load P at joint 2 and another load P applied leftward at joint 5. The force in member 3-5 is:

Question 16

A bar of diameter d ⫽ 18 mm and length L ⫽ 0.75 m is loaded in tension by forces P. The bar has modulus E ⫽ 45 GPa and allowable
Normal stress of 180 MPa. The elongation of the bar must not exceed
2)7 mm. The allowable value of forces P is approximately:
(A) 41 kN
(B) 46 kN
(C) 56 kN
(D) 63 kN

Question 17

A steel wire hangs from a high-altitude balloon. The steel has unit weight 77 kN/m3 and yield stress of 280 MPa. The required factor of
Safety against yield is 2.0. The maximum permissible length of the wire is
Approximately:
(A) 1800 m
(B) 2200 m
(C) 2600 m
(D) 3000 m

Question 18

A titanium bar (E ⫽ 100 GPa, v ⫽ 0.33) with square cross sec- tion (b ⫽ 75 mm) and length L ⫽ 3.0 m is subjected to tensile load
P ⫽ 900 kN. The increase in volume of the bar is approximately:

Question 19

The force in member FE of the plane truss below is approximately:

Question 20

A brass bar (E = 110 MPa) of length L = 2.5 m has diameter $d_{1}=18 \mathrm{~mm}$ over one-half of its length and diameter $d_{2}=12 \mathrm{~mm}$ over the other half. Compare this nonprismatic bar to a prismatic bar of the
Same volume of material with constant diameter d and length L. The elon-
Gation of the prismatic bar under the same load P = 25 kN is approxi-
Mately:

A) 3 mm
B) 4 mm
C) 5 mm
D) 6 mm

Question 21

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:

Question 22

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:

Question 23

An aluminum bar of diameter d ⫽ 52 mm is twisted by torques at the ends. The allowable shear stress is 65 MPa. The maximum permis- sible torque is approximately:

Question 24

A plane stress element on a bar in uniaxial stress has a tensile stress of (see fig.). The maximum shear stress in the bar is
Approximately:

Question 25

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:

Question 26

A monel shell encloses a brass core . 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:

Question 27

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

Question 28

A hollow aluminum shaft (G ⫽ 27 GPa, and 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:

Question 29

A motor drives a shaft at of power. The allowable shear stress in the shaft is 45 MPa. The minimum
Diameter of the shaft is approximately:

Question 30

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 . The allowable shear
Strain in the copper is 0.0005 rad. The maximum permissible diameter of
The rod is approximately:

Question 31

A gear shaft transmits torques , . If the allowable shear stress is 50 MPa, the required shaft diameter is approximately:

Question 32

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: . The shear modulus of elas-
Ticity G of the pipe is approximately:

Question 33

A prismatic bar (diameter ⫽ 18 mm) is loaded by force A stepped bar (diameters ⫽ 20 mm and ⫽ 25 mm with radius of fillets R ⫽ 2mm) is loaded by force . The allowable axial stress in the
Material is 75 MPa. The ratio of the maximum permissible loads
That can be applied to the bars, considering stress concentration effects in
The stepped bar, is: FIG. 2-66 Stress-concentration factor K for round bars with shoulder fillets.
The dashed line is for a full quarter-circular fillet.

Question 34

A steel plane truss is loaded at B and C by forces P ⫽ 200 kN. The cross-sectional area of each member is . Truss dimen-
Sions are H ⫽ 3mand L ⫽ 4m. The maximum shear stress in bar AB is
Approximately:

Question 35

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 is
Approximately:

Question 36

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

Question 37

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 . The temperature change at which the wire goes slack is
Approximately:

Question 38

A steel tube with diameters 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:

Question 39

A stepped steel shaft with diameters is twisted by torques and acting in opposite directions. The maximum shear stress is approximately:

Question 40

A motor drives a shaft with diameter and delivers of power. The maximum shear stress in the shaft is approximately:

Question 41

A copper wire (d ⫽ 1.5 mm) is bent around a tube of radius R ⫽ 0.6 m. The maximum normal strain in the wire is approximately:

Question 42

Two thin cables, each having a diameter of and carrying tensile loads P, are bolted to the top of a rectangular steel block with
Cross-sectional dimensions . The ratio of the maximum tensile to
Compressive stress in the block due to loads P is:

Question 43

A drive shaft running at 2500 rpm has outer diameter 60 mm and inner diameter 40 mm. The allowable shear stress in the shaft is 35 MPa.
The maximum power that can be transmitted is approximately:

Question 44

A T-shaped simple beam has a cable with force P anchored at B and passing over a pulley at E, as shown in the figure. The bend-
Ing moment just left of C m. The cable force P is approxi-
Mately:

Question 45

A simple beam AB with an overhang BC is loaded as shown in the figure. The bending moment at the midspan of AB is approximately:

Question 46

A beam with an overhang is loaded by a uniform load of 3 kN/m over its entire length. Moment of inertia and
Distances to top and bottom of the beam cross section are 20 mm and
66)4 mm, respectively. It is known that reactions at A and B are 4.5 kN
And 13.5 kN, respectively. The maximum bending stress in the beam is
Approximately:

Question 47

A simply supported steel beam of length L ⫽ 1.5 m and rectangu- lar cross section carries a uniform load of
Q ⫽ 48 kN/m that includes its own weight. The maximum transverse
Shear stress on the cross section at 0.25 m from the left support is approx-
Imately:

Question 48

A simply supported beam is loaded as shown in the figure. The bending moment at point C is approximately:

Question 49

An aluminum light pole weighs 4300 N and supports an arm of weight 700 N, with the arm center of gravity at 1.2 m left of the centroidal
Axis of the pole. A wind force of 1500 N acts to the right at 7.5 m above
The base. The pole cross section at the base has an outside diameter of
235 mm and thickness of 20 mm. The maximum compressive stress at the
Base is approximately:

Question 50

A simply supported laminated beam of length L ⫽ 0.5 m and square cross section weighs 4.8 N. Three strips are glued together to form
The beam, with the allowable shear stress in the glued joint equal to
0)3 MPa. Considering also the weight of the beam, the maximum load P
That can be applied at L/3 from the left support is approximately:

Question 51

A steel hanger with solid cross section has horizontal force P ⫽ 5.5 kN applied at free end D. Dimension variable b ⫽ 175 mm and
Allowable normal stress is 150 MPa. Neglect self-weight of the hanger.
The required diameter of the hanger is approximately:
(A) 5 cm
(B) 7 cm
(C) 10 cm
(D) 13 cm

Question 52

An L-shaped beam is loaded as shown in the figure. The bending moment at the midpoint of span AB is approximately:

Question 53

A simply supported wood beam (L ⫽ 5m)with rectangular cross section (b ⫽ 200 mm, h ⫽ 280 mm) carries uniform load includes the weight of the beam. The maximum flexural stress is
Approximately:

Question 54

A cast iron pipe is lifted by a hoist. The lift points are 6 m apart. The maximum bending stress in the pipe is approximately:

Question 55

A simple beam (L ⫽ 9m) with attached bracket BDE has force P ⫽ 5kNapplied downward at E. The bending moment just right of B is
Approximately:

Question 56

A cantilever beam is loaded as shown in the figure. The bending moment at 0.5 m from the support is approximately:

Question 57

A prismatic shaft (diameter $d_{0}=19 \mathrm{~mm}$ ) is loaded by torque $T_{1}$ A stepped shaft (diameters $d_{1}=20 \mathrm{~mm} \text { and } d_{2}=25$ mm with radius of fillets R = 2mm) is loaded by torque $T_{2}$ . The allowable shear stress in the
Material is 42 MPa. The ratio $T_{1} / T_{2}$ of the maximum permissible torques
That can be applied to the shafts, considering stress concentration effects
In the stepped shaft is:

A) 0.9
B) 1.2
C) 1.4
D) 2.1

Question 58

A cantilever wood pole carries force P = 300 N applied at its free end, as well as its own weight $\text { (weight density }=6 \mathrm{kN} / \mathrm{m}^{3} \text { ) }$ . The length of
The pole is L = 0.75 m and the allowable bending stress is 14 MPa. The
Required diameter of the pole is approximately:

A) 4.2 cm
B) 5.5 cm
C) 6.1 cm
D) 8.5 cm

Question 59

A simply supported beam with proportional loading (P ⫽ 4.1 kN) has span length L ⫽ 5m. Load P is 1.2 m from support A and load 2P is
1)5 m from support B. The bending moment just left of load 2P is approx-
Imately:

Question 60

An aluminum cantilever beam of length L ⫽ 0.65 m carries a distributed load, which includes its own weight, of intensity /2 at A and
Q at B. The beam cross section has a width of 50 mm and height of
170 mm. Allowable bending stress is 95 MPa and allowable shear stress is
12 MPa. The permissible value of load intensity q is approximately:

Question 61

A rectangular plate in plane stress is subjected to normal stresses , and shear stress . The ratio of the magnitudes of the principal stresses is approximately:

Question 62

A drive shaft resists torsional shear stress of 45 MPa and axial com- pressive stress of 100 MPa. The ratio of the magnitudes of the principal $\left(\sigma_{1} / \sigma_{2}\right)$ approximately:

A) 0.15
B) 0.55
C) 1.2
D) 1.9

Question 63

A rectangular plate (a = 120 mm, b = 160 mm) is subjected to compressive stress $\sigma_{x}=-4.5 \mathrm{MPa} \text { and tensile stress } \sigma_{y}=15 \mathrm{MPa}$ . The
Ratio of the normal stress acting perpendicular to the weld to the shear
Stress acting along the weld is approximately:

A) 0.27
B) 0.54
C) 0.85
D) 1.22

Question 64

A cylindrical tank is assembled by welding steel sections circumfer- entially. Tank diameter is 1.5 m, thickness is 20 mm, and internal pressure
Is 2.0 MPa. The maximum tensile stress in the cylindrical part of the tank
Is approximately:

Question 65

A bimetallic beam of aluminum and copper strips has a width of b ⫽ 25 mm; each strip has a thick- ness t ⫽ 1.5 mm. A bending moment of 1.75 N m is applied about
The z axis. The ratio of the maximum stress in the aluminum to that in the
Copper is approximately:

Question 66

A cylindrical tank is assembled by welding steel sections in a heli- cal pattern with angle . Tank diameter is 1.6 m, thickness is
20 mm, and internal pressure is 2.75 MPa. Modulus E ⫽ 210 GPa and
Poisson's ratio . The normal stress acting perpendicular to the
Weld is approximately:

Question 67

A cylindrical tank is assembled by welding steel sections circumfer- entially. Tank diameter is 1.5 m, thickness is 20 mm, and internal pressure
Is 2.0 MPa. The maximum shear stress in the heads is approximately:

Question 68

A drive shaft resists torsional shear stress of 45 MPa and axial com- pressive stress of 100 MPa. The maximum shear stress is approximately:

Question 69

A cylindrical tank is assembled by welding steel sections circum- ferentially. Tank diameter is 1.5 m, thickness is 20 mm, and internal pres-
Sure is 2.0 MPa. The maximum shear stress in the cylindrical part of the
Tank is approximately:

Question 70

A steel pipe has a plastic liner with inner diameter . The modulus of elasticity of the steel is 75
Times that of the modulus of the plastic. Allowable stresses in steel and
Plastic are 40 MPa and 550 kPa, respectively. The allowable bending
Moment for the composite pipe is approximately:

Question 71

A cylindrical tank is assembled by welding steel sections circumfer- entially. Tank diameter is 1.5 m, thickness is 20 mm, and internal pressure
Is 2.0 MPa. The maximum stress in the heads of the tank is approximately:

Question 72

A drive shaft resists torsional shear stress of and axial compressive stress . One principal normal stress is
Known to be 38 MPa (tensile). The stress is approximately:

Question 73

A rectangular plate in plane stress is subjected to normal stresses and and shear stress . Stress is known to be 15 MPa, but and are unknown. However, the normal stress is known to be 33 MPa at counterclockwise angles of 35⬚ and 75⬚ from the x axis. Based on this, the
Normal stress on the element in the figure is approximately:

Question 74

A composite beam is made up of a 200 mm ⫻ 300 mm core and an exterior cover sheet (300 mm ⫻ 12 mm, on each side. Allowable stresses in core and exterior sheets are 9.5 MPa and 140 MPa, respectively. The ratio of the maximum
Permissible bending moment about the z axis to that about the y axis is
Most nearly:

Question 75

A composite beam is made up of a 90 mm ⫻ 160 mm wood beam . Allowable stresses in wood and steel are 6.5 MPa and and a steel bottom cover plate (90 mm ⫻ 8 mm,
110 MPa, respectively. The allowable bending moment about the z axis of
The composite beam is most nearly:

Question 76

A cylindrical tank is assembled by welding steel sections in a heli- cal pattern with angle . Tank diameter is 1.6 m, thickness is
20 mm, and internal pressure is 2.75 MPa. Modulus and
Poisson's ratio . The longitudinal strain in the the wall of the
Tank is approximately:

Question 77

A rectangular beam with semicircular notches has dimen- sions . The maximum allowable bending
Stress in the plastic beam is , and the bending moment
Is . The minimum permissible width of the beam is: FIG. 5-50 Stress-concentration factor K for a notched beam of rectangular
Cross section in pure bending (h ⫽ height of beam; b ⫽ thickness of beam,
Perpendicular to the plane of the figure). The dashed line is for semicircular

Question 78

A cylindrical tank is assembled by welding steel sections in a heli- cal pattern with angle 20 mm, and internal pressure is 2.75 MPa. Modulus E ⫽ 210 GPa and
Tank is approximately:
Poisson's ratio . The circumferential strain in the wall of the

Question 79

A cylindrical tank is assembled by welding steel sections circumfer- entially. Tank diameter is 1.5 m, thickness is 20 mm, and internal pressure
Is 2.0 MPa. The maximum tensile stress perpendicular to the welds is
Approximately:

Question 80

A composite beam of aluminum $\left(E_{a}=72 \mathrm{GPa}\right)$ and steel $\left(E_{s}=190 \mathrm{GPa}\right)$ has a width b = 25 mm and heights $h_{a}=42 \mathrm{~mm}$ and $h_{s}=68 \mathrm{~mm}$ , respectively. A bending moment is applied about the z axis resulting in a maximum stress in the aluminum of 55 MPa. The maximum
Stress in the steel is approximately:

A) 86 MPa
B) 90 MPa
C) 94 MPa
D) 98 MPa