The flexure formula σ=My/I gives stress distribution in a beam.
σ=-My/I for pure bending: zero at the neutral axis, tension on one side and compression on the other. The extreme fibre stress is Mc/I. Assumes plane sections remain plane and linear elasticity.
A 100×200 mm beam under 20 kN·m has σmax=15 MPa.
The flexure formula gives the bending stress at any point across a section, so it is central to beam design.
The flexure formula σ=My/I gives stress distribution in a beam.
The flexure formula gives the bending stress at any point across a section, so it is central to beam design.
The stress is proportional to distance from the neutral axis, so it is zero at the neutral axis and largest at the outer fibres.
The neutral axis passes through the centroid, and you must measure the distance to the outer fibres from it, which may differ top and bottom.
Typical applications include checking the stress at the top fibre of a steel joist, sizing a beam to keep stress within the allowable limit and finding the stress in a wooden floor joist under occupancy load.
Study "Shear force and bending moment diagrams" first (topic 54 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Neutral axis passes through the centroid. Deeper beams are stronger. Asymmetric sections have different tensile and compressive maxima.
A 100×200 mm beam under 20 kN·m has σmax=15 MPa.
The next topic is "Section modulus", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 55 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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