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Volume Strain thumbs-up A solid circu. Question A solid circular shaft tapers uniformly from 100 m m to 20 m m over a length of 500 m m is hanged vertically as shown: If the self weight of shaft is 78.5 k N / m 3 and modulus of elasticity, E = 2.1 × 10 5 M P a then the elongation of shaft due to its own weight is × 10 - 5 mm . (Answer correct upto two decimal places).?
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Volume Strain thumbs-up A solid circu. Question A solid circular shaft...
Given:
- Shaft tapers uniformly from 100 mm to 20 mm over a length of 500 mm
- Self weight of shaft = 78.5 kN/m^3
- Modulus of elasticity (E) = 2.1 × 10^5 MPa
Calculation:
Step 1: Calculate the volume of the shaft
The volume of the shaft can be calculated using the formula for the volume of a frustum of a cone:
V = (1/3)πh(r1^2 + r2^2 + r1r2)
where V is the volume, h is the height of the frustum, r1 is the radius at the top, and r2 is the radius at the bottom.
In this case, the height of the frustum is 500 mm, r1 is 50 mm (half of the top diameter), and r2 is 10 mm (half of the bottom diameter).
Therefore, V = (1/3)π(500)(2500 + 100 + 500) = 1,047,200 mm^3
Step 2: Calculate the weight of the shaft
The weight of the shaft can be calculated using the formula:
Weight = Volume × Density
Given that the density of the shaft is 78.5 kN/m^3, we need to convert it to N/mm^3:
Density = 78.5 × 10^6 N/m^3 = 78.5 N/mm^3
Therefore, Weight = 1,047,200 mm^3 × 78.5 N/mm^3 = 82,238,400 N
Step 3: Calculate the elongation of the shaft
The elongation of the shaft due to its own weight can be calculated using the formula:
Elongation = (Weight × Length) / (π × Average cross-sectional area × Modulus of elasticity)
The average cross-sectional area can be calculated as the average of the cross-sectional areas at the top and bottom of the shaft:
Average cross-sectional area = (π × r1^2 + π × r2^2) / 2
Substituting the values, we get:
Elongation = (82,238,400 N × 500 mm) / (π × ((2500 + 100) mm^2 + (1000 + 400) mm^2)/2) × (2.1 × 10^5 MPa)
Simplifying the equation, we find that the elongation of the shaft is approximately 0.0007 mm.
Answer:
The elongation of the shaft due to its own weight is approximately 0.0007 mm.
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Volume Strain thumbs-up A solid circu. Question A solid circular shaft tapers uniformly from 100 m m to 20 m m over a length of 500 m m is hanged vertically as shown: If the self weight of shaft is 78.5 k N / m 3 and modulus of elasticity, E = 2.1 × 10 5 M P a then the elongation of shaft due to its own weight is × 10 - 5 mm . (Answer correct upto two decimal places).?
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Volume Strain thumbs-up A solid circu. Question A solid circular shaft tapers uniformly from 100 m m to 20 m m over a length of 500 m m is hanged vertically as shown: If the self weight of shaft is 78.5 k N / m 3 and modulus of elasticity, E = 2.1 × 10 5 M P a then the elongation of shaft due to its own weight is × 10 - 5 mm . (Answer correct upto two decimal places).? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Volume Strain thumbs-up A solid circu. Question A solid circular shaft tapers uniformly from 100 m m to 20 m m over a length of 500 m m is hanged vertically as shown: If the self weight of shaft is 78.5 k N / m 3 and modulus of elasticity, E = 2.1 × 10 5 M P a then the elongation of shaft due to its own weight is × 10 - 5 mm . (Answer correct upto two decimal places).? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Volume Strain thumbs-up A solid circu. Question A solid circular shaft tapers uniformly from 100 m m to 20 m m over a length of 500 m m is hanged vertically as shown: If the self weight of shaft is 78.5 k N / m 3 and modulus of elasticity, E = 2.1 × 10 5 M P a then the elongation of shaft due to its own weight is × 10 - 5 mm . (Answer correct upto two decimal places).?.
Volume Strain thumbs-up A solid circu. Question A solid circular shaft tapers uniformly from 100 m m to 20 m m over a length of 500 m m is hanged vertically as shown: If the self weight of shaft is 78.5 k N / m 3 and modulus of elasticity, E = 2.1 × 10 5 M P a then the elongation of shaft due to its own weight is × 10 - 5 mm . (Answer correct upto two decimal places).? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Volume Strain thumbs-up A solid circu. Question A solid circular shaft tapers uniformly from 100 m m to 20 m m over a length of 500 m m is hanged vertically as shown: If the self weight of shaft is 78.5 k N / m 3 and modulus of elasticity, E = 2.1 × 10 5 M P a then the elongation of shaft due to its own weight is × 10 - 5 mm . (Answer correct upto two decimal places).? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Volume Strain thumbs-up A solid circu. Question A solid circular shaft tapers uniformly from 100 m m to 20 m m over a length of 500 m m is hanged vertically as shown: If the self weight of shaft is 78.5 k N / m 3 and modulus of elasticity, E = 2.1 × 10 5 M P a then the elongation of shaft due to its own weight is × 10 - 5 mm . (Answer correct upto two decimal places).?.
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