In mechanics of materials, the flexural (bending) equation relates bending stress at any point in a beam's cross-section to the bending moment, the distance from the neutral axis, and the section's moment of inertia, under the assumptions that plane cross-sections remain plane and perpendicular to the deformed beam axis, and that the neutral axis (where stress and strain are zero) must pass through the centroid of the cross-section to satisfy zero net axial force. For cross-sections symmetrical about the vertical (loading) axis but unsymmetrical about the horizontal axis, the distances from the neutral axis to the extreme fibers differ, producing unequal magnitudes of compressive and tensile bending stress for a given moment, whereas doubly symmetrical sections yield equal magnitudes; this motivates the concept of an economical section, in which cross-sectional area is concentrated away from the neutral axis to maximize section modulus (moment of inertia divided by extreme-fiber distance) and thereby minimize bending stress for a given moment and area.
In mechanics of materials, the flexural (bending) equation relates bending stress at any point in a beam's cross-section to the bending moment, the distance from the neutral axis, and the section's m…