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A Cast ison Cantiliver of length 1.5m helds when a Concentrated load 1920N is applied at the free end Determin the stress at failure if the section of the Cantiliver 40 mma 60 mm?
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A Cast ison Cantiliver of length 1.5m helds when a Concentrated load 1...
Problem:
A cantilever of length 1.5m holds a concentrated load of 1920N at the free end. Determine the stress at failure if the section of the cantilever is 40 mm x 60 mm.
Solution:
Given data:
Length of the cantilever (L) = 1.5 m
Concentrated load (P) = 1920 N
Section dimensions: breadth (b) = 40 mm and depth (d) = 60 mm
Step 1: Calculating the Moment at the Free End
The moment at the free end of a cantilever can be calculated using the formula:
M = P * L
Substituting the given values:
M = 1920 N * 1.5 m
M = 2880 Nm
Step 2: Calculating the Maximum Bending Stress
The maximum bending stress (σ) can be calculated using the formula:
σ = (M * y) / I
Where:
M = moment at the free end (2880 Nm)
y = distance from the neutral axis to the extreme fiber (depth/2 = 30 mm = 0.03 m)
I = moment of inertia of the section
Step 3: Calculating the Moment of Inertia
The moment of inertia (I) for a rectangular section can be calculated using the formula:
I = (b * d^3) / 12
Substituting the given values:
I = (40 mm * (60 mm)^3) / 12
I = (40 mm * 216000 mm^3) / 12
I = 720000 mm^4
Converting the moment of inertia to meter units:
I = 720000 mm^4 * (1 m / 1000 mm)^4
I = 0.000720 m^4
Step 4: Calculating the Maximum Bending Stress
Substituting the values of M, y, and I into the formula:
σ = (2880 Nm * 0.03 m) / 0.000720 m^4
σ = 120000 N/m^2
Step 5: Converting Stress to MPa
To convert the stress from N/m^2 to MPa:
σ = 120000 N/m^2 * (1 MPa / 10^6 N/m^2)
σ = 0.12 MPa
Therefore, the stress at failure for the given cantilever is 0.12 MPa.
A cantilever of length 1.5m holds a concentrated load of 1920N at the free end. Determine the stress at failure if the section of the cantilever is 40 mm x 60 mm.
Solution:
Given data:
Length of the cantilever (L) = 1.5 m
Concentrated load (P) = 1920 N
Section dimensions: breadth (b) = 40 mm and depth (d) = 60 mm
Step 1: Calculating the Moment at the Free End
The moment at the free end of a cantilever can be calculated using the formula:
M = P * L
Substituting the given values:
M = 1920 N * 1.5 m
M = 2880 Nm
Step 2: Calculating the Maximum Bending Stress
The maximum bending stress (σ) can be calculated using the formula:
σ = (M * y) / I
Where:
M = moment at the free end (2880 Nm)
y = distance from the neutral axis to the extreme fiber (depth/2 = 30 mm = 0.03 m)
I = moment of inertia of the section
Step 3: Calculating the Moment of Inertia
The moment of inertia (I) for a rectangular section can be calculated using the formula:
I = (b * d^3) / 12
Substituting the given values:
I = (40 mm * (60 mm)^3) / 12
I = (40 mm * 216000 mm^3) / 12
I = 720000 mm^4
Converting the moment of inertia to meter units:
I = 720000 mm^4 * (1 m / 1000 mm)^4
I = 0.000720 m^4
Step 4: Calculating the Maximum Bending Stress
Substituting the values of M, y, and I into the formula:
σ = (2880 Nm * 0.03 m) / 0.000720 m^4
σ = 120000 N/m^2
Step 5: Converting Stress to MPa
To convert the stress from N/m^2 to MPa:
σ = 120000 N/m^2 * (1 MPa / 10^6 N/m^2)
σ = 0.12 MPa
Therefore, the stress at failure for the given cantilever is 0.12 MPa.
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A Cast ison Cantiliver of length 1.5m helds when a Concentrated load 1...
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A Cast ison Cantiliver of length 1.5m helds when a Concentrated load 1920N is applied at the free end Determin the stress at failure if the section of the Cantiliver 40 mma 60 mm? 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 Cast ison Cantiliver of length 1.5m helds when a Concentrated load 1920N is applied at the free end Determin the stress at failure if the section of the Cantiliver 40 mma 60 mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Cast ison Cantiliver of length 1.5m helds when a Concentrated load 1920N is applied at the free end Determin the stress at failure if the section of the Cantiliver 40 mma 60 mm?.
A Cast ison Cantiliver of length 1.5m helds when a Concentrated load 1920N is applied at the free end Determin the stress at failure if the section of the Cantiliver 40 mma 60 mm? 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 Cast ison Cantiliver of length 1.5m helds when a Concentrated load 1920N is applied at the free end Determin the stress at failure if the section of the Cantiliver 40 mma 60 mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Cast ison Cantiliver of length 1.5m helds when a Concentrated load 1920N is applied at the free end Determin the stress at failure if the section of the Cantiliver 40 mma 60 mm?.
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