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Section modulus or shape factor z for rectangle type beam is bd²/6?
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Section modulus or shape factor z for rectangle type beam is bd²/6?
Section Modulus or Shape Factor for Rectangle Beam
The section modulus or shape factor (z) for a rectangular beam is given by the formula:
z = bd²/6
Explanation
- b: Width or breadth of the rectangle beam
- d: Depth or height of the rectangle beam
The section modulus, also known as the shape factor, is a geometric property of a beam cross-section that represents its ability to resist bending. It is a measure of the distribution of material around the neutral axis of the beam.
The formula for the section modulus of a rectangle beam is derived based on the moment of inertia (I) and the maximum bending stress (σ).
Moment of Inertia (I)
The moment of inertia (I) of a rectangle beam is given by the formula:
I = bd³/12
The moment of inertia represents the resistance of a beam to bending. It depends on the shape and size of the beam's cross-section. For a rectangle beam, the moment of inertia is directly proportional to the cube of the depth (d) and the product of the width (b).
Maximum Bending Stress (σ)
The maximum bending stress (σ) in a beam is given by the formula:
σ = M / (I / c)
- M: Bending moment acting on the beam
- c: Distance from the neutral axis to the outermost fiber
The maximum bending stress occurs at the outermost fiber of the beam cross-section. It is directly proportional to the bending moment (M) and inversely proportional to the moment of inertia (I) divided by the distance (c) from the neutral axis to the outermost fiber. The distance (c) is half of the depth (d) for a rectangle beam.
Section Modulus (z)
The section modulus (z) is defined as the ratio of the moment of inertia (I) to the distance (c) from the neutral axis to the outermost fiber:
z = I / c
For a rectangle beam, the distance (c) is half of the depth (d). Substituting the moment of inertia formula into the section modulus formula, we get:
z = (bd³/12) / (d/2)
Simplifying the formula, we have:
z = bd²/6
Therefore, the section modulus or shape factor (z) for a rectangle beam is given by the formula bd²/6.
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Section modulus or shape factor z for rectangle type beam is bd²/6?
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Section modulus or shape factor z for rectangle type beam is bd²/6? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Section modulus or shape factor z for rectangle type beam is bd²/6? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Section modulus or shape factor z for rectangle type beam is bd²/6?.
Section modulus or shape factor z for rectangle type beam is bd²/6? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Section modulus or shape factor z for rectangle type beam is bd²/6? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Section modulus or shape factor z for rectangle type beam is bd²/6?.
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