For a rectangular cross-section, what is the bending stress at a distance y from the neutral axis when moment M is applied?

For a rectangular cross-section, what is the bending stress at a distance y from the neutral axis when moment M is applied?

• A. σ = M y / I
• B. σ = M / (y I)
• C. σ = I M / y
• D. σ = y / (M I)

Answer: (A)

The bending stress in a beam under a bending moment is described by the flexure formula: the stress at a distance y from the neutral axis is proportional to y and to the applied moment, and inversely proportional to the second moment of area I. This gives σ = M y / I, meaning the neutral axis has zero stress and fibers farther from it experience higher tensile or compressive stress depending on the bend direction. For a rectangular cross-section with width b and height h, I about the centroidal axis is b h^3 / 12, so σ = M y / (b h^3 / 12) = 12 M y / (b h^3). The other expressions would not yield the correct units or relationship between M, y, and I.

The bending stress in a beam under a bending moment is described by the flexure formula: the stress at a distance y from the neutral axis is proportional to y and to the applied moment, and inversely proportional to the second moment of area I. This gives σ = M y / I, meaning the neutral axis has zero stress and fibers farther from it experience higher tensile or compressive stress depending on the bend direction. For a rectangular cross-section with width b and height h, I about the centroidal axis is b h^3 / 12, so σ = M y / (b h^3 / 12) = 12 M y / (b h^3). The other expressions would not yield the correct units or relationship between M, y, and I.