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A cantilever beam with a rectangular cross-section has a longitudinal hole drilled throughout its length is shown in Fig. 1. The beam supports a load P = 600N The cross-section is 25 mm wide and 50 mm high and the hole has a diameter of 10 mm. Find the bending stresses at the top of the beam, at the top of the hole and at the bottom of the beam.?
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A cantilever beam with a rectangular cross-section has a longitudinal ...
**Given Data:**
- Load (P) = 600N
- Cross-section dimensions: 25 mm (width) x 50 mm (height)
- Hole diameter: 10 mm
**Bending Stresses Calculation:**
**Top of the Beam:**
- Moment of inertia of the beam without the hole, I = (1/12) x width x height^3
- Moment of inertia of the beam with the hole, I_h = I - (π/64) x hole diameter^4
- Bending stress at the top of the beam, σ_top = (M x y) / I
where M = P x L (moment due to load)
y = distance from neutral axis to the top of the beam
**Top of the Hole:**
- Bending stress at the top of the hole, σ_hole = (M x y_h) / I_h
where y_h = (height/2) + (hole diameter/2)
**Bottom of the Beam:**
- Bending stress at the bottom of the beam, σ_bottom = (M x y_bottom) / I
where y_bottom = distance from neutral axis to the bottom of the beam
**Substitute Values and Calculate:**
- Calculate I, I_h, y, y_h, y_bottom using the given dimensions
- Substitute these values into the respective stress formulas to find the bending stresses at the top of the beam, top of the hole, and bottom of the beam.
By following these steps and calculations, you can determine the bending stresses at different points along the cantilever beam with a hole.
- Load (P) = 600N
- Cross-section dimensions: 25 mm (width) x 50 mm (height)
- Hole diameter: 10 mm
**Bending Stresses Calculation:**
**Top of the Beam:**
- Moment of inertia of the beam without the hole, I = (1/12) x width x height^3
- Moment of inertia of the beam with the hole, I_h = I - (π/64) x hole diameter^4
- Bending stress at the top of the beam, σ_top = (M x y) / I
where M = P x L (moment due to load)
y = distance from neutral axis to the top of the beam
**Top of the Hole:**
- Bending stress at the top of the hole, σ_hole = (M x y_h) / I_h
where y_h = (height/2) + (hole diameter/2)
**Bottom of the Beam:**
- Bending stress at the bottom of the beam, σ_bottom = (M x y_bottom) / I
where y_bottom = distance from neutral axis to the bottom of the beam
**Substitute Values and Calculate:**
- Calculate I, I_h, y, y_h, y_bottom using the given dimensions
- Substitute these values into the respective stress formulas to find the bending stresses at the top of the beam, top of the hole, and bottom of the beam.
By following these steps and calculations, you can determine the bending stresses at different points along the cantilever beam with a hole.
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A cantilever beam with a rectangular cross-section has a longitudinal hole drilled throughout its length is shown in Fig. 1. The beam supports a load P = 600N The cross-section is 25 mm wide and 50 mm high and the hole has a diameter of 10 mm. Find the bending stresses at the top of the beam, at the top of the hole and at the bottom of the beam.?
Question Description
A cantilever beam with a rectangular cross-section has a longitudinal hole drilled throughout its length is shown in Fig. 1. The beam supports a load P = 600N The cross-section is 25 mm wide and 50 mm high and the hole has a diameter of 10 mm. Find the bending stresses at the top of the beam, at the top of the hole and at the bottom of the beam.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A cantilever beam with a rectangular cross-section has a longitudinal hole drilled throughout its length is shown in Fig. 1. The beam supports a load P = 600N The cross-section is 25 mm wide and 50 mm high and the hole has a diameter of 10 mm. Find the bending stresses at the top of the beam, at the top of the hole and at the bottom of the beam.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam with a rectangular cross-section has a longitudinal hole drilled throughout its length is shown in Fig. 1. The beam supports a load P = 600N The cross-section is 25 mm wide and 50 mm high and the hole has a diameter of 10 mm. Find the bending stresses at the top of the beam, at the top of the hole and at the bottom of the beam.?.
A cantilever beam with a rectangular cross-section has a longitudinal hole drilled throughout its length is shown in Fig. 1. The beam supports a load P = 600N The cross-section is 25 mm wide and 50 mm high and the hole has a diameter of 10 mm. Find the bending stresses at the top of the beam, at the top of the hole and at the bottom of the beam.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A cantilever beam with a rectangular cross-section has a longitudinal hole drilled throughout its length is shown in Fig. 1. The beam supports a load P = 600N The cross-section is 25 mm wide and 50 mm high and the hole has a diameter of 10 mm. Find the bending stresses at the top of the beam, at the top of the hole and at the bottom of the beam.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam with a rectangular cross-section has a longitudinal hole drilled throughout its length is shown in Fig. 1. The beam supports a load P = 600N The cross-section is 25 mm wide and 50 mm high and the hole has a diameter of 10 mm. Find the bending stresses at the top of the beam, at the top of the hole and at the bottom of the beam.?.
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