Department of Mecahnical Engineering
MANIT Bhopal
ME 212 Mechanics of Materials
Assignment 1
Due date of submission: August 2, 2024
Q.1: Three wires each of 5 mm diameter are used to lift a load of W = 7500 N. An indicative
diagram is shown (Figure 1). The unstressed lengths of the three wires are 18 m, 17.997 m
and 17.994 m. Find
(i) the stress in the longest wire.
(ii) the stress in the shortest wire if the load is reduced to 2000 N.
Take E = 2.1 × 105 N/mm2.
W
Figure 1
Pytel and Kiusalaas [P2.102], IES [2022]
Q.2: A wall bracket is constructed as shown in Figure 2. All joints may be considered pinconnected. The steel rod AB has a cross-sectional area of 5 mm2. The member BC is a rigid
beam. If a 1 m diameter frictionless drum weighing 4500 N is placed in the position shown,
what will the elogation of the rod AB be?
Take E = 200 GPa.
1.8 m
A
B
2.4 m
4500 N drum
C
1.5
m
Pinned joint
Figure 2
Popov [P2.11]
1
Q.3: The center post B of the assembly has an original length of 124.7 mm, whereas posts A
and C have a length of 125 mm each (as shown in Figure 3). Treating the caps on the top and
bottom as rigid, determine the average normal stress in each post. The posts are made up of
Aluminium and have a cross-sectional area of 400 mm2 each. Take Young’s modulus of the
material, E is 70 GPa.
Figure 3
Hibbeler [P4.64]
Q.4: The soft-ride suspension system of the mountain bike is pinned at C and supported by
the shock absorber BD as shown in Figure 4. If it is designed to support a load of P=1500 N,
determine the factor of safety of pins B and C against failure if they are made of a material
having a shear failure stress of fail = 150 MPa. Pin B has a diameter of 7.5 mm, and pin C has
a diameter of 6.5 mm. Both pins are subjected to double shear.
P
A
300 mm 100 mm
30 mm
B
C
60
D
Figure 4
Hibbeler [P1.91]
2
Q.5: In a uniaxial tensile test, the longitudinal stress is 100 MPa. On which planes, the direct
stress will be 50 MPa?
Q.6: The piece of plastic is originally rectangular as shown in Figure 5. Find
(i) the shear strain at corners A and B if the plastic distorts as shown by the dashed
lines.
(ii) the shear strain at corners D and C if the distorts as shown by the dashed lines.
(iii) the average normal strain occurs along the diagonals AC and DB.
y
5 mm
B
2 mm
C
2 mm
4 mm
B
C
300 mm
A
D
A
2 mm
x
400 mm
Figure 5
Hibbeler [P2.18]
Q.7: The steel column of circular cross section is attached to rigid supports at A and C as
shown in Figure 6. Find the maximum stress in the column caused by the 25 kN load as
indicated in the below figure.
A
15 mm
200 mm
25 kN
B
200 mm
C
25 mm
Figure 6
Pytel and Kiusalaas [P2.61]
3
Q.8: The rigid bar of negligible weight is supported as shown in Figure 7.
Bronze
3m
Steel 1.5 m
1m
2.5 m
1.5 m
W
Figure 7
(i) If W=80 kN, compute the temperature change of the assembly that will cause a
tensile stress of 50 MPa in the steel rod. Use the following data:
Rod
A (mm2)
E (GPa)
 (/C)
materials
Steel
300
11.7×10‒6
200
‒6
Bronze
1400
18.9×10
83
(ii) Considering the assembly initially stress-free then also find the stress in each rod
if the temperature rises 20 C after a load W = 120 kN is applied.
Pytel and Kiusalaas [P2.84, P2.85]
Q.9: The steel bolt of cross-sectional area A0 is placed inside the aluminium tube, also of
cross sectional area A0. The assembly is completed by making the nut “finger tight” The
dimensions of the reduced segment of the bolt (length b and cross-sectional area A) are
designed so that the segment will yield when the temperature of the assembly is increased by
200 C. Write an algorithm that determines the relationship between A/A0 and b/L that
satisfies this design requirement. Plot A/A0 against b/L from b/L = 0 to 1. Use properties of
steel and aluminium shown in Figure 8.
Eal  68.94 GPa
 al  23 10 / C
6
Est  200 GPa
 st  11.7 10 / C
6
   240 MPa
y
st
T  200 C
Figure 8
Pytel and Kiusalaas [C2.6]
4
Q.10: A uniform bar AB of weight W=25 N is supported by two springs, as shown in Figure
9. The spring on the left has stiffness k1=300 N/m and natural length L1=250 mm. The
corresponding quantities for the spring on the right are k2=400 N/m and L2 =200 mm. The
distance between the springs is L=350 mm, and the spring on the right is suspended from a
support that is distance h=80 mm below the point of support for the spring on the left. At
what distance x from the left-hand spring should a load P=18 N be placed in order to bring
the bar to a horizontal position?
Reference line
L1

h
k1
k2
A
x
B
P
L2

W
L 2
L 2
Figure 9
Gere [P2.2-10]
References
1. Pytel, Andrew, and Jaan Kiusalaas. "Mechanics of Materials, Brooks/Cole-Thomson
Learning." Pacific Grove, GA (2003).
2. Popov, E.P., "Mechanics of Materials, 2nd edition, Pearson." Noida, India (2016).
3. Gere, J.M., "Mechanics of Materials, 6th edition, Brooks/Cole-Cengage Learning." Pacific
Grove, GA (2006).
4. Hibbeler, R.C., "Mechanics of Materials, 8th edition, Pearson, Printice Hall, New Delhi
(2001).
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