Which expression relates the bending stress sigma to bending moment M, distance c, and second moment of area I?

Which expression relates the bending stress sigma to bending moment M, distance c, and second moment of area I?

• A. sigma = M*c/I
• B. sigma = M/(I*c)
• C. sigma = I*M/c
• D. sigma = c*M^2/I

Answer: (D)

In bending, the stress at a point in a beam varies linearly with distance from the neutral axis and is set by how the moment is carried by the section. The bending stress at a distance y from the neutral axis is given by sigma = M*y/I. If you’re looking at the outermost fiber, that distance is c, so the maximum bending stress becomes sigma_max = M*c/I. This shows why the expression that directly uses M, c, and I is the correct one: stress grows with the moment and with how far you are from the neutral axis, and it’s inversely proportional to the section’s second moment of area. The other forms would mix up the factors or involve M squared, which does not match how bending stress behaves physically.

In bending, the stress at a point in a beam varies linearly with distance from the neutral axis and is set by how the moment is carried by the section. The bending stress at a distance y from the neutral axis is given by sigma = My/I. If you’re looking at the outermost fiber, that distance is c, so the maximum bending stress becomes sigma_max = Mc/I. This shows why the expression that directly uses M, c, and I is the correct one: stress grows with the moment and with how far you are from the neutral axis, and it’s inversely proportional to the section’s second moment of area. The other forms would mix up the factors or involve M squared, which does not match how bending stress behaves physically.