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A cantilever beam of span 4 m and cross-sectional are 0.3 m wide and 0.4 m deep is subjected to a concentrated load of 10 kN at the free end. Neglecting self-weight, the maximum bending stress at a section 2 m from the free end will be?
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A cantilever beam of span 4 m and cross-sectional are 0.3 m wide and 0...
Problem Statement
A cantilever beam of span 4 m and cross-sectional area 0.3 m wide and 0.4 m deep is subjected to a concentrated load of 10 kN at the free end. Neglecting self-weight, the maximum bending stress at a section 2 m from the free end will be?
Solution
To solve this problem, we need to use the formula for maximum bending stress in a cantilever beam:
σ = Mc / I
- σ is the maximum bending stress
- M is the bending moment at the section
- c is the distance from the neutral axis to the outermost fiber
- I is the moment of inertia of the cross-sectional area
We can first calculate the bending moment at the section 2 m from the free end:
M = Wl - Wx
- W is the concentrated load
- l is the span of the beam
- x is the distance from the free end to the section
Substituting the given values, we get:
M = 10 kN * 4 m - 10 kN * 2 m = 20 kNm
Next, we need to calculate the moment of inertia of the cross-sectional area:
I = (bd^3) / 12
- b is the width of the cross-sectional area
- d is the depth of the cross-sectional area
Substituting the given values, we get:
I = (0.3 m * 0.4 m^3) / 12 = 0.004 m^4
Finally, we can calculate the maximum bending stress at the section:
σ = Mc / I
σ = (20 kNm * 0.2 m) / 0.004 m^4 = 100 MPa
Therefore, the maximum bending stress at the section 2 m from the free end is 100 MPa.
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A cantilever beam of span 4 m and cross-sectional are 0.3 m wide and 0.4 m deep is subjected to a concentrated load of 10 kN at the free end. Neglecting self-weight, the maximum bending stress at a section 2 m from the free end will be?
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A cantilever beam of span 4 m and cross-sectional are 0.3 m wide and 0.4 m deep is subjected to a concentrated load of 10 kN at the free end. Neglecting self-weight, the maximum bending stress at a section 2 m from the free end will be? 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 cantilever beam of span 4 m and cross-sectional are 0.3 m wide and 0.4 m deep is subjected to a concentrated load of 10 kN at the free end. Neglecting self-weight, the maximum bending stress at a section 2 m from the free end will be? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam of span 4 m and cross-sectional are 0.3 m wide and 0.4 m deep is subjected to a concentrated load of 10 kN at the free end. Neglecting self-weight, the maximum bending stress at a section 2 m from the free end will be?.
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