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Calculate total elongation in mm due to axial load of 250kN applied to a flat bar of length 20m and 20mm thick tapering from a width of 150mm to 60mm. Assume E = 205GPa.(round up to 2 decimal places)
Correct answer is between '12,12.8'. Can you explain this answer?
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Calculate total elongation in mm due to axial load of 250kN applied to...
Elongation calculation for a tapered bar under axial load:
Given data:
- Axial load (P) = 250 kN
- Length of the bar (L) = 20 m
- Thickness of the bar (t) = 20 mm
- Width at one end (w1) = 150 mm
- Width at the other end (w2) = 60 mm
- Modulus of elasticity (E) = 205 GPa
Step 1: Calculate the average width of the bar (w_avg):
The average width can be calculated by taking the average of the widths at both ends of the bar.
w_avg = (w1 + w2) / 2
w_avg = (150 + 60) / 2
w_avg = 105 mm
Step 2: Calculate the area of the bar (A):
The area can be calculated by multiplying the average width by the thickness of the bar.
A = w_avg * t
A = 105 mm * 20 mm
A = 2100 mm²
Step 3: Calculate the strain (ε):
The strain can be calculated using the formula:
ε = P / (A * E)
ε = 250 kN / (2100 mm² * 205 GPa)
ε ≈ 0.000570
Step 4: Calculate the elongation (ΔL):
The elongation can be calculated using the formula:
ΔL = ε * L
ΔL = 0.000570 * 20 m
ΔL = 0.0114 m
Step 5: Convert elongation to mm:
To convert the elongation from meters to millimeters, multiply by 1000.
ΔL = 0.0114 m * 1000
ΔL ≈ 11.4 mm
The total elongation of the tapered bar under the axial load of 250 kN is approximately 11.4 mm. Rounding up to 2 decimal places, the answer is between 12 and 12.8 mm.
Given data:
- Axial load (P) = 250 kN
- Length of the bar (L) = 20 m
- Thickness of the bar (t) = 20 mm
- Width at one end (w1) = 150 mm
- Width at the other end (w2) = 60 mm
- Modulus of elasticity (E) = 205 GPa
Step 1: Calculate the average width of the bar (w_avg):
The average width can be calculated by taking the average of the widths at both ends of the bar.
w_avg = (w1 + w2) / 2
w_avg = (150 + 60) / 2
w_avg = 105 mm
Step 2: Calculate the area of the bar (A):
The area can be calculated by multiplying the average width by the thickness of the bar.
A = w_avg * t
A = 105 mm * 20 mm
A = 2100 mm²
Step 3: Calculate the strain (ε):
The strain can be calculated using the formula:
ε = P / (A * E)
ε = 250 kN / (2100 mm² * 205 GPa)
ε ≈ 0.000570
Step 4: Calculate the elongation (ΔL):
The elongation can be calculated using the formula:
ΔL = ε * L
ΔL = 0.000570 * 20 m
ΔL = 0.0114 m
Step 5: Convert elongation to mm:
To convert the elongation from meters to millimeters, multiply by 1000.
ΔL = 0.0114 m * 1000
ΔL ≈ 11.4 mm
The total elongation of the tapered bar under the axial load of 250 kN is approximately 11.4 mm. Rounding up to 2 decimal places, the answer is between 12 and 12.8 mm.
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Calculate total elongation in mm due to axial load of 250kN applied to a flat bar of length 20m and 20mm thick tapering from a width of 150mm to 60mm. Assume E = 205GPa.(round up to 2 decimal places)Correct answer is between '12,12.8'. Can you explain this answer?
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Calculate total elongation in mm due to axial load of 250kN applied to a flat bar of length 20m and 20mm thick tapering from a width of 150mm to 60mm. Assume E = 205GPa.(round up to 2 decimal places)Correct answer is between '12,12.8'. Can you explain this answer? 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 Calculate total elongation in mm due to axial load of 250kN applied to a flat bar of length 20m and 20mm thick tapering from a width of 150mm to 60mm. Assume E = 205GPa.(round up to 2 decimal places)Correct answer is between '12,12.8'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate total elongation in mm due to axial load of 250kN applied to a flat bar of length 20m and 20mm thick tapering from a width of 150mm to 60mm. Assume E = 205GPa.(round up to 2 decimal places)Correct answer is between '12,12.8'. Can you explain this answer?.
Calculate total elongation in mm due to axial load of 250kN applied to a flat bar of length 20m and 20mm thick tapering from a width of 150mm to 60mm. Assume E = 205GPa.(round up to 2 decimal places)Correct answer is between '12,12.8'. Can you explain this answer? 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 Calculate total elongation in mm due to axial load of 250kN applied to a flat bar of length 20m and 20mm thick tapering from a width of 150mm to 60mm. Assume E = 205GPa.(round up to 2 decimal places)Correct answer is between '12,12.8'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate total elongation in mm due to axial load of 250kN applied to a flat bar of length 20m and 20mm thick tapering from a width of 150mm to 60mm. Assume E = 205GPa.(round up to 2 decimal places)Correct answer is between '12,12.8'. Can you explain this answer?.
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