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A symmetric I-section (with width of each flange = 50 mm, thickness of web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress (in N/mm2) in the web at its junction with the top flange
Correct answer is between '70,72'. Can you explain this answer?
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To find the magnitude of the shear stress in the web at its junction with the top flange, we need to consider the equilibrium of forces acting on the section.
Given data:
Width of each flange (b) = 50 mm
Thickness of web (t) = 10 mm
Shear force (V) = 100 kN
First, we need to determine the shear area of the web. The shear area is the area through which the shear force is transmitted.
The shear area of the web (A_w) can be calculated using the formula:
A_w = t * d
where t is the thickness of the web and d is the depth of the web.
Since the I-section is symmetric, the depth of the web can be calculated as the difference between the overall height of the section (h) and the sum of the heights of the top and bottom flanges.
Let's assume the overall height of the section (h) is 200 mm.
The height of each flange (h_f) can be calculated as half of the overall height minus half of the thickness of the web:
h_f = (h - t) / 2
The depth of the web (d) can be calculated as:
d = h - 2 * h_f
Substituting the given values:
h_f = (200 - 10) / 2 = 95 mm
d = 200 - 2 * 95 = 10 mm
Now we can calculate the shear area of the web:
A_w = 10 * 10 = 100 mm^2
Next, we can calculate the shear stress (τ) in the web using the formula:
τ = V / A_w
where V is the shear force and A_w is the shear area.
Converting the shear force from kN to N:
V = 100 kN = 100,000 N
Substituting the values:
τ = 100,000 / 100 = 1000 N/mm^2
Therefore, the magnitude of the shear stress in the web at its junction with the top flange is 1000 N/mm^2.
Since the correct answer is between 70 and 72 N/mm^2, it seems there might be an error in the calculations or given data. Please recheck the data and calculations to obtain the correct answer.
Given data:
Width of each flange (b) = 50 mm
Thickness of web (t) = 10 mm
Shear force (V) = 100 kN
First, we need to determine the shear area of the web. The shear area is the area through which the shear force is transmitted.
The shear area of the web (A_w) can be calculated using the formula:
A_w = t * d
where t is the thickness of the web and d is the depth of the web.
Since the I-section is symmetric, the depth of the web can be calculated as the difference between the overall height of the section (h) and the sum of the heights of the top and bottom flanges.
Let's assume the overall height of the section (h) is 200 mm.
The height of each flange (h_f) can be calculated as half of the overall height minus half of the thickness of the web:
h_f = (h - t) / 2
The depth of the web (d) can be calculated as:
d = h - 2 * h_f
Substituting the given values:
h_f = (200 - 10) / 2 = 95 mm
d = 200 - 2 * 95 = 10 mm
Now we can calculate the shear area of the web:
A_w = 10 * 10 = 100 mm^2
Next, we can calculate the shear stress (τ) in the web using the formula:
τ = V / A_w
where V is the shear force and A_w is the shear area.
Converting the shear force from kN to N:
V = 100 kN = 100,000 N
Substituting the values:
τ = 100,000 / 100 = 1000 N/mm^2
Therefore, the magnitude of the shear stress in the web at its junction with the top flange is 1000 N/mm^2.
Since the correct answer is between 70 and 72 N/mm^2, it seems there might be an error in the calculations or given data. Please recheck the data and calculations to obtain the correct answer.
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A symmetric I-section (with width of each flange = 50 mm, thickness of web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress (in N/mm2) in the web at its junction with the top flangeCorrect answer is between '70,72'. Can you explain this answer?
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A symmetric I-section (with width of each flange = 50 mm, thickness of web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress (in N/mm2) in the web at its junction with the top flangeCorrect answer is between '70,72'. 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 symmetric I-section (with width of each flange = 50 mm, thickness of web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress (in N/mm2) in the web at its junction with the top flangeCorrect answer is between '70,72'. 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 symmetric I-section (with width of each flange = 50 mm, thickness of web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress (in N/mm2) in the web at its junction with the top flangeCorrect answer is between '70,72'. Can you explain this answer?.
A symmetric I-section (with width of each flange = 50 mm, thickness of web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress (in N/mm2) in the web at its junction with the top flangeCorrect answer is between '70,72'. 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 symmetric I-section (with width of each flange = 50 mm, thickness of web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress (in N/mm2) in the web at its junction with the top flangeCorrect answer is between '70,72'. 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 symmetric I-section (with width of each flange = 50 mm, thickness of web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress (in N/mm2) in the web at its junction with the top flangeCorrect answer is between '70,72'. Can you explain this answer?.
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