1. Three long parallel wires equal in length are supporting a rigid bar connected at their bottoms as shown in Fig. 4.15. If the cross-sectional area of each wire is 100 mm, calculate the stresses in each wire. Take E, = 100 GPa and E, 200 GPa. (Ans. O, = 25 MPa ; o, = 50 MPa] %3D

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EXERCISE 4.2
1. Three long parallel wires equal in length are supporting a rigid bar connected at their bottoms as
shown in Fig. 4.15. If the cross-sectional area of each wire is 100 mm“, calculate the stresses in
each wire. Take E, = 100 GPa and E, = 200 GPa.
[Ans. O, = 25 MPa ; o, = 50 MPa]
10 kN
220 kN
Fig. 4.15
Fig. 4.16
2. Three wires made of copper, zinc and aluminium are of equal lengths and have cross-sectional
areas of 100, 150 and 200 square mm respectively. They are rigidly connected at their ends as
shown in Fig. 4.16. If this compound member is subjected to a longitudinal pull of 220 kN,
estimate the load carried on each wire. Take E = 130 GPa, E, = 100 GPa and E, = 80 GPa.
[Ans. Pe= 65 kN, P,= 75 kN, P= 80 kN]
3. Two steel rods and one copper rod each of 20 mm diameter together support a load of 50 kN as
shown in Fig.4.17. Find the stresses in each rod. Take E for steel and copper as 200 GPa and
[Ans. o. = 39.8 MPa ; o, = 59.7 MPa]
100 GPa respectively.
60 I Strength of Materials
50 kN
Copper wire
1.6 mm o
Steel wire
0.9 mm o
4.5 m
1.5 m
500 mm
2 m
200 N
Fig. 4.17
Fig. 4.18
4. Two vertical wires are suspended at a distance of 500 mm apart as shown in Fig. 4.18. Their
upper ends are firmly secured and their lower ends support a rigid horizontal bar, which carries
a load of 200 N. The left hand wire has a diameter of 1.6 mm and is made of copper, and the
right hand wire has a diameter of 0.9 mm and is made of steel. Both wires, initially, are 4.5
metres long. Determine :
(a) Position of the line of action of the load, if both the wires extend by the same amount.
(b) Slope of the rigid wire, if the load is hung at the centre of the bar. Neglect weight of the bar.
[Ans. 170 mm ; 0.15°]
Take E for copper as 100 GPa and E for steel as 200 GPa.
Copper
Steel
Transcribed Image Text:EXERCISE 4.2 1. Three long parallel wires equal in length are supporting a rigid bar connected at their bottoms as shown in Fig. 4.15. If the cross-sectional area of each wire is 100 mm“, calculate the stresses in each wire. Take E, = 100 GPa and E, = 200 GPa. [Ans. O, = 25 MPa ; o, = 50 MPa] 10 kN 220 kN Fig. 4.15 Fig. 4.16 2. Three wires made of copper, zinc and aluminium are of equal lengths and have cross-sectional areas of 100, 150 and 200 square mm respectively. They are rigidly connected at their ends as shown in Fig. 4.16. If this compound member is subjected to a longitudinal pull of 220 kN, estimate the load carried on each wire. Take E = 130 GPa, E, = 100 GPa and E, = 80 GPa. [Ans. Pe= 65 kN, P,= 75 kN, P= 80 kN] 3. Two steel rods and one copper rod each of 20 mm diameter together support a load of 50 kN as shown in Fig.4.17. Find the stresses in each rod. Take E for steel and copper as 200 GPa and [Ans. o. = 39.8 MPa ; o, = 59.7 MPa] 100 GPa respectively. 60 I Strength of Materials 50 kN Copper wire 1.6 mm o Steel wire 0.9 mm o 4.5 m 1.5 m 500 mm 2 m 200 N Fig. 4.17 Fig. 4.18 4. Two vertical wires are suspended at a distance of 500 mm apart as shown in Fig. 4.18. Their upper ends are firmly secured and their lower ends support a rigid horizontal bar, which carries a load of 200 N. The left hand wire has a diameter of 1.6 mm and is made of copper, and the right hand wire has a diameter of 0.9 mm and is made of steel. Both wires, initially, are 4.5 metres long. Determine : (a) Position of the line of action of the load, if both the wires extend by the same amount. (b) Slope of the rigid wire, if the load is hung at the centre of the bar. Neglect weight of the bar. [Ans. 170 mm ; 0.15°] Take E for copper as 100 GPa and E for steel as 200 GPa. Copper Steel
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