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A rectangular beam 100 mm deep and 75 mm wide in simply supported over a span of 6 m. It carries a uniformly distributed load of 4000 N/m over the whole span. Calculate the maximum bending stress developed in the section at: (i) supports, (ii) 1.5 m from the support, (iii) mid span of the beam?
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A rectangular beam 100 mm deep and 75 mm wide in simply supported over...
Problem Statement
A rectangular beam 100 mm deep and 75 mm wide is simply supported over a span of 6 m. It carries a uniformly distributed load of 4000 N/m over the whole span. Calculate the maximum bending stress developed in the section at:
- Supports
- 1.5 m from the support
- Mid-span of the beam
Solution
Given data:
- Depth of beam, d = 100 mm
- Width of beam, b = 75 mm
- Span of beam, L = 6 m
- Uniformly distributed load, w = 4000 N/m
Step 1: Calculation of Maximum Bending Moment (M)
The maximum bending moment occurs at the mid-span of the beam and is given by the formula:
M = wL^2/8
Substituting the given values, we get:
M = (4000 x 6^2)/8 = 135000 N-mm
Step 2: Calculation of Maximum Bending Stress (σ)
The maximum bending stress occurs at the top and bottom fibers of the beam and is given by the formula:
σ = My/I
- M = Maximum bending moment
- y = Distance of fiber from the neutral axis
- I = Moment of inertia of the beam section
The moment of inertia of a rectangular beam section about its neutral axis is given by:
I = bd^3/12
Substituting the given values, we get:
I = (75 x 100^3)/12 = 62500000 mm^4
Now, let's calculate the maximum bending stress at different points:
(i) At supports
At the supports, the bending moment is zero. Therefore, the bending stress is also zero.
(ii) 1.5 m from the support
At a distance of 1.5 m from the support, the bending moment is:
M = w (L/2 - 1.5)^2/2
Substituting the given values, we get:
M = (4000 x 2.25)/2 = 4500 N-mm
The distance of the top and bottom fibers from the neutral axis is half the depth of the beam, i.e., y = d/2 = 50 mm. Therefore, the maximum bending stress is:
σ = My/I = (4500 x 50)/62500000 = 0.036 N/mm^2
(iii) At mid-span of the beam
At mid-span, the bending moment is maximum and is equal to M = 135000 N-mm. The distance of the top and bottom fibers from the neutral axis is half the depth of
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A rectangular beam 100 mm deep and 75 mm wide in simply supported over a span of 6 m. It carries a uniformly distributed load of 4000 N/m over the whole span. Calculate the maximum bending stress developed in the section at: (i) supports, (ii) 1.5 m from the support, (iii) mid span of the beam?
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A rectangular beam 100 mm deep and 75 mm wide in simply supported over a span of 6 m. It carries a uniformly distributed load of 4000 N/m over the whole span. Calculate the maximum bending stress developed in the section at: (i) supports, (ii) 1.5 m from the support, (iii) mid span of the beam? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A rectangular beam 100 mm deep and 75 mm wide in simply supported over a span of 6 m. It carries a uniformly distributed load of 4000 N/m over the whole span. Calculate the maximum bending stress developed in the section at: (i) supports, (ii) 1.5 m from the support, (iii) mid span of the beam? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular beam 100 mm deep and 75 mm wide in simply supported over a span of 6 m. It carries a uniformly distributed load of 4000 N/m over the whole span. Calculate the maximum bending stress developed in the section at: (i) supports, (ii) 1.5 m from the support, (iii) mid span of the beam?.
A rectangular beam 100 mm deep and 75 mm wide in simply supported over a span of 6 m. It carries a uniformly distributed load of 4000 N/m over the whole span. Calculate the maximum bending stress developed in the section at: (i) supports, (ii) 1.5 m from the support, (iii) mid span of the beam? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A rectangular beam 100 mm deep and 75 mm wide in simply supported over a span of 6 m. It carries a uniformly distributed load of 4000 N/m over the whole span. Calculate the maximum bending stress developed in the section at: (i) supports, (ii) 1.5 m from the support, (iii) mid span of the beam? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular beam 100 mm deep and 75 mm wide in simply supported over a span of 6 m. It carries a uniformly distributed load of 4000 N/m over the whole span. Calculate the maximum bending stress developed in the section at: (i) supports, (ii) 1.5 m from the support, (iii) mid span of the beam?.
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