Chapter 4 Pure Bending

Engr. Othman A. Tayeh

DEFORMATIONS IN A SYMMETRIC MEMBER IN PURE BENDING

The line AB, which was originally a straight line, will be transformed into a circle of center C, and so will the line A’B’ (not shown in the figure) along which the lower face of the member intersects the plane of symmetry. We also note that the line AB will decrease in length when the member is bent as shown in the figure, i.e., when M >0, while A’B’ will become longer.

there must exist a surface parallel to the upper and lower faces of the member, where the stress and strain are zero.This surface is called the neutral surface.

The minus sign is due to the fact that we have assumed the bendingmoment to be positive and, thus, the beam to be concave upward.

the maximum absolute value of the strain

STRESSES AND DEFORMATIONS IN THE ELASTIC RANGE (flexural stress)

the normalstress at any distance y from the neutral axis

Elastic section modulus (S)

depends onlyupon the geometry of the cross section

The deformation of the member caused by the bending momentM is measured by the curvature of the neutral surface. The curvature is defined as the reciprocal of the radius of curvature ρ, and can be

Exam 2012