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Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 × 107Pa? Assume that each rivet is to carry one quarter of the load.
- a)749 kN
- b)856 kN
- c)652 N
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Two strips of metal are riveted together at their ends by four rivets,...
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Two strips of metal are riveted together at their ends by four rivets,...
To find the maximum tension that can be exerted by the riveted strip, we need to calculate the maximum shearing force that each rivet can withstand.
The shearing stress on the rivet can be calculated using the formula:
shearing stress = force / area
We know that the diameter of each rivet is 6.0 mm, so the radius (r) is 6.0 mm / 2 = 3.0 mm = 0.003 m.
The area of each rivet can be calculated using the formula:
area = π * r^2
Substituting the value of r, we get:
area = π * (0.003 m)^2
Calculating the area, we find:
area = 0.00002827 m^2
The shearing stress on each rivet is given as 6.9 MPa. To convert this to Pascals, we multiply by 10^6:
shearing stress = 6.9 MPa * 10^6
Calculating the shearing stress, we find:
shearing stress = 6,900,000 Pa
Now, we can calculate the maximum force that each rivet can withstand by rearranging the formula:
force = shearing stress * area
Substituting the values we've calculated, we get:
force = 6,900,000 Pa * 0.00002827 m^2
Calculating the force, we find:
force = 194.763 N
Since there are four rivets, the maximum tension that can be exerted by the riveted strip is:
maximum tension = 4 * 194.763 N
Calculating the maximum tension, we find:
maximum tension = 779.052 N
Therefore, the maximum tension that can be exerted by the riveted strip is approximately 779.052 Newtons.
The shearing stress on the rivet can be calculated using the formula:
shearing stress = force / area
We know that the diameter of each rivet is 6.0 mm, so the radius (r) is 6.0 mm / 2 = 3.0 mm = 0.003 m.
The area of each rivet can be calculated using the formula:
area = π * r^2
Substituting the value of r, we get:
area = π * (0.003 m)^2
Calculating the area, we find:
area = 0.00002827 m^2
The shearing stress on each rivet is given as 6.9 MPa. To convert this to Pascals, we multiply by 10^6:
shearing stress = 6.9 MPa * 10^6
Calculating the shearing stress, we find:
shearing stress = 6,900,000 Pa
Now, we can calculate the maximum force that each rivet can withstand by rearranging the formula:
force = shearing stress * area
Substituting the values we've calculated, we get:
force = 6,900,000 Pa * 0.00002827 m^2
Calculating the force, we find:
force = 194.763 N
Since there are four rivets, the maximum tension that can be exerted by the riveted strip is:
maximum tension = 4 * 194.763 N
Calculating the maximum tension, we find:
maximum tension = 779.052 N
Therefore, the maximum tension that can be exerted by the riveted strip is approximately 779.052 Newtons.
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D is correct.
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Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 × 107Pa? Assume that each rivet is to carry one quarter of the load.a)749kNb)856kNc)652 Nd)None of theseCorrect answer is option 'D'. Can you explain this answer?
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