What is the neutral axis for a rectangular beam with depth 'b'?

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In summary, the Engineers Bending Equation, also known as the Euler-Bernoulli beam equation, is a mathematical formula used to determine the internal stresses and deflections of a beam under various loading conditions. It is derived from the principles of mechanics and takes into account the forces, moments, and geometry of a beam. The variables in the equation are P - applied load, L - length of the beam, E - Young's modulus of elasticity, I - area moment of inertia of the cross-section, and y - deflection of the beam. It is commonly used in engineering to design and analyze structural elements, but it may have limitations as it assumes certain properties of the material and does not consider shear stress or warping.
  • #1
Iclaudius
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Hello friends,

a question about the engineers bending equation,

M/I = E/R = (sigma)/y

so take for example a beam with a rectangular cross section with depth 'b'.
Will y then equal b/2 ? As y is measured from the neutral axis?

Thank you in advance for your time,
Claudius
 
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  • #2
Yes, for a rectangular cross-section the neutral axis is centered in the beam. For non-symmetric cross sections such as a T-beam, it will be located at an area-weighted average of the cross-section.
 

1. What is the Engineers Bending Equation?

The Engineers Bending Equation, also known as the Euler-Bernoulli beam equation, is a mathematical formula that describes the relationship between bending stress and the curvature of a beam. It is used to determine the internal stresses and deflections of a beam under various loading conditions.

2. How is the equation derived?

The Engineers Bending Equation is derived from the principles of mechanics, specifically the theory of elasticity. It takes into account the forces, moments, and geometry of a beam to calculate the resulting stress and deflection.

3. What are the variables in the equation?

The variables in the Engineers Bending Equation are: P - applied load, L - length of the beam, E - Young's modulus of elasticity, I - area moment of inertia of the cross-section, and y - deflection of the beam.

4. How is the equation used in engineering?

The Engineers Bending Equation is used in a variety of engineering applications, such as designing and analyzing beams, columns, and other structural elements. It helps engineers determine the maximum stress and deflection of a beam, which is crucial for ensuring the structural integrity and safety of a design.

5. Are there any limitations to the Engineers Bending Equation?

While the Engineers Bending Equation is a useful tool for analyzing beams, it does have limitations. It assumes that the material is homogenous, isotropic, and linearly elastic, which may not be the case in all real-world scenarios. Additionally, it does not take into account the effects of shear stress or warping, which may be significant in certain situations.

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