Chapter 4 Pure Bending Eng. Mahmoud AlQazzaz

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 bending moment 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 normal stress at any distance y from the neutral axis

The deformation of the member caused by the bending moment M 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

Elastic section modulus (S) depends only upon the geometry of the cross section

Reinforced Concrete beam :-

Example

ECCENTRIC AXIAL LOADING IN A PLANE OF SYMMETRY

Example

HW 4.3 , 4.19 , 4.20 , 4.33 , 4.34 , 4.51 , 4.100 , 4.102 , 4.105 , 4.117