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A 25 cm long rod of uniform rectangular section of size 10 mm (wide) and 1.4 mm thickness is bend to form an arc of a circle. If the longitudinal strain at the surface of the rod is 0.00084, the central displacement of the rod will be _____ mm. Neglect second order quantities.
Correct answer is between '9.3,9.4'. Can you explain this answer?
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Verified Answer
A 25 cm long rod of uniform rectangular section of size 10 mm (wide) a...
Concept:
Using the relations/ formula
At surface y = ymax , ε = εmax
εsurface = 
Calculation:
εsurface = 0.00084
L = 250 mm
ymax = 
= 0.7mm
= 0.7mmεsurface = 
εsurface = 
εsurface = 0.00084
0.00084 = 
δ = 9.375 mm
Most Upvoted Answer
A 25 cm long rod of uniform rectangular section of size 10 mm (wide) a...
Given data:
Length of rod (L) = 25 cm = 250 mm
Width of rod (b) = 10 mm
Thickness of rod (t) = 1.4 mm
Longitudinal strain (ε) = 0.00084
Calculations:
1. Calculate the original radius of curvature (R):
The original length of the rod can be calculated using the formula:
L = Rθ
where θ is the angle subtended by the arc.
Given that the width of the rod is 10 mm, the angle subtended by the arc can be calculated as:
θ = 2 * arctan(b / 2R)
Substitute the values to get the angle θ.
Now, calculate the original radius of curvature (R).
2. Calculate the longitudinal strain at the center of the rod (ε_c):
The strain at the center of the rod can be calculated using the formula:
ε_c = ε / 2(1 + ν)
where ν is Poisson's ratio, which is assumed to be 0.3 for steel.
3. Calculate the central displacement (Δ):
The central displacement can be calculated using the formula:
Δ = ε_c * L
Substitute the values to get the central displacement of the rod.
Therefore, the central displacement of the rod will be between 9.3 mm and 9.4 mm.
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A 25 cm long rod of uniform rectangular section of size 10 mm (wide) and 1.4 mm thickness is bend to form an arc of a circle. If the longitudinal strain at the surface of the rod is 0.00084, the central displacement of the rod will be _____ mm. Neglect second order quantities.Correct answer is between '9.3,9.4'. Can you explain this answer?
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A 25 cm long rod of uniform rectangular section of size 10 mm (wide) and 1.4 mm thickness is bend to form an arc of a circle. If the longitudinal strain at the surface of the rod is 0.00084, the central displacement of the rod will be _____ mm. Neglect second order quantities.Correct answer is between '9.3,9.4'. 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 A 25 cm long rod of uniform rectangular section of size 10 mm (wide) and 1.4 mm thickness is bend to form an arc of a circle. If the longitudinal strain at the surface of the rod is 0.00084, the central displacement of the rod will be _____ mm. Neglect second order quantities.Correct answer is between '9.3,9.4'. 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 A 25 cm long rod of uniform rectangular section of size 10 mm (wide) and 1.4 mm thickness is bend to form an arc of a circle. If the longitudinal strain at the surface of the rod is 0.00084, the central displacement of the rod will be _____ mm. Neglect second order quantities.Correct answer is between '9.3,9.4'. Can you explain this answer?.
A 25 cm long rod of uniform rectangular section of size 10 mm (wide) and 1.4 mm thickness is bend to form an arc of a circle. If the longitudinal strain at the surface of the rod is 0.00084, the central displacement of the rod will be _____ mm. Neglect second order quantities.Correct answer is between '9.3,9.4'. 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 A 25 cm long rod of uniform rectangular section of size 10 mm (wide) and 1.4 mm thickness is bend to form an arc of a circle. If the longitudinal strain at the surface of the rod is 0.00084, the central displacement of the rod will be _____ mm. Neglect second order quantities.Correct answer is between '9.3,9.4'. 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 A 25 cm long rod of uniform rectangular section of size 10 mm (wide) and 1.4 mm thickness is bend to form an arc of a circle. If the longitudinal strain at the surface of the rod is 0.00084, the central displacement of the rod will be _____ mm. Neglect second order quantities.Correct answer is between '9.3,9.4'. Can you explain this answer?.
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