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A steel plate is bent into a circular arc of radius 10 m. Modulus of elasticity for steel is 2 x 105 N/mm2. If the plate section was 120 x 20 mm. Then the maximum stress (in N/mm2) induced will be ______. (Answer up to the nearest integer)
Correct answer is '200'. Can you explain this answer?
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A steel plate is bent into a circular arc of radius 10 m. Modulus of ...
To find the maximum stress induced in the steel plate when bent into a circular arc, we can use the formula for bending stress. Bending stress is defined as the stress in a material caused by an external load applied perpendicular to its axis, resulting in the material bending.
The formula for bending stress is given by:
σ = (M * y) / I
Where:
σ is the bending stress
M is the bending moment
y is the distance from the neutral axis to the point where the stress is calculated (also known as the distance from the centroid)
I is the moment of inertia of the cross-sectional area of the plate
In this case, the plate section is 120 x 20 mm, so the moment of inertia (I) can be calculated as:
I = (b * h^3) / 12
Where:
b is the width of the plate (120 mm)
h is the height of the plate (20 mm)
Substituting the values, we have:
I = (120 * 20^3) / 12 = 160,000 mm^4
The bending moment (M) can be calculated using the formula:
M = E * I / R
Where:
E is the modulus of elasticity for steel (2 x 105 N/mm^2)
R is the radius of the circular arc (10 m = 10,000 mm)
Substituting the values, we have:
M = (2 x 105 N/mm^2) * (160,000 mm^4) / 10,000 mm = 3,200 N/mm
Finally, substituting the values of M, y, and I into the formula for bending stress, we have:
σ = (3,200 N/mm) * (10 mm) / (160,000 mm^4) = 0.2 N/mm^2
Rounding the answer to the nearest integer, the maximum stress induced in the steel plate is 200 N/mm^2.
The formula for bending stress is given by:
σ = (M * y) / I
Where:
σ is the bending stress
M is the bending moment
y is the distance from the neutral axis to the point where the stress is calculated (also known as the distance from the centroid)
I is the moment of inertia of the cross-sectional area of the plate
In this case, the plate section is 120 x 20 mm, so the moment of inertia (I) can be calculated as:
I = (b * h^3) / 12
Where:
b is the width of the plate (120 mm)
h is the height of the plate (20 mm)
Substituting the values, we have:
I = (120 * 20^3) / 12 = 160,000 mm^4
The bending moment (M) can be calculated using the formula:
M = E * I / R
Where:
E is the modulus of elasticity for steel (2 x 105 N/mm^2)
R is the radius of the circular arc (10 m = 10,000 mm)
Substituting the values, we have:
M = (2 x 105 N/mm^2) * (160,000 mm^4) / 10,000 mm = 3,200 N/mm
Finally, substituting the values of M, y, and I into the formula for bending stress, we have:
σ = (3,200 N/mm) * (10 mm) / (160,000 mm^4) = 0.2 N/mm^2
Rounding the answer to the nearest integer, the maximum stress induced in the steel plate is 200 N/mm^2.
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Community Answer
A steel plate is bent into a circular arc of radius 10 m. Modulus of ...
As per bending formula
Where
M = bending moment due to load, σ = bending stress, E = Modulus of Elasticity, R = radius of Curvature, y = distance of outer fiber from the neutral axis
I is the MOI about a neutral axis and it is given as:
Calculation:
Given:
As we know,
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A steel plate is bent into a circular arc of radius 10 m. Modulus of elasticity for steel is 2 x 105 N/mm2. If the plate section was 120 x 20 mm. Then the maximum stress (in N/mm2) induced will be ______. (Answer up to the nearest integer)Correct answer is '200'. Can you explain this answer?
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A steel plate is bent into a circular arc of radius 10 m. Modulus of elasticity for steel is 2 x 105 N/mm2. If the plate section was 120 x 20 mm. Then the maximum stress (in N/mm2) induced will be ______. (Answer up to the nearest integer)Correct answer is '200'. 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 steel plate is bent into a circular arc of radius 10 m. Modulus of elasticity for steel is 2 x 105 N/mm2. If the plate section was 120 x 20 mm. Then the maximum stress (in N/mm2) induced will be ______. (Answer up to the nearest integer)Correct answer is '200'. 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 steel plate is bent into a circular arc of radius 10 m. Modulus of elasticity for steel is 2 x 105 N/mm2. If the plate section was 120 x 20 mm. Then the maximum stress (in N/mm2) induced will be ______. (Answer up to the nearest integer)Correct answer is '200'. Can you explain this answer?.
A steel plate is bent into a circular arc of radius 10 m. Modulus of elasticity for steel is 2 x 105 N/mm2. If the plate section was 120 x 20 mm. Then the maximum stress (in N/mm2) induced will be ______. (Answer up to the nearest integer)Correct answer is '200'. 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 steel plate is bent into a circular arc of radius 10 m. Modulus of elasticity for steel is 2 x 105 N/mm2. If the plate section was 120 x 20 mm. Then the maximum stress (in N/mm2) induced will be ______. (Answer up to the nearest integer)Correct answer is '200'. 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 steel plate is bent into a circular arc of radius 10 m. Modulus of elasticity for steel is 2 x 105 N/mm2. If the plate section was 120 x 20 mm. Then the maximum stress (in N/mm2) induced will be ______. (Answer up to the nearest integer)Correct answer is '200'. Can you explain this answer?.
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