# The stresses produced due to constant Bending Moment (with zero Shear Force or pure bending) are know as Bending stresses.

**Assumptions in Theory of Bending :**

**I**

**n deriving the relations between the bending moments and flexure (bending)stresses and between the Shear forces and Sharing stresses the following assumptions are made.**

**1.Transverse sections of the beam that were plane before bending remain so even after bending.**

**2.The material of the beam is isotropic and homogeneous and follows Hooke's law and has the same value of Young's Modulus in tension and compression.**

**3.The beam is subjected to Pure bending and therefore bends in an arc of a circle.**

**4.The radius of curvature is large compared to the dimension of the cross-section.**

**5.Each layer is independent to enlarge or contract.**

**6.The stresses are purely longitudinal and local effects of point loads are neglected.**

#
**Flexure Formula :**

**Stresses caused by the bending moment are known as flexural or bending stresses. Consider a beam to be loaded as shown.**

#### THE BENDING EQUATION:

####
**where ****R is the radius of curvature of the beam in mm, ****M**** is the bending moment in N·mm, ****f****b**** is the flexural stress in MPa., ****I**** is the centroidal moment of inertia in mm**^{4}**, and ***y*** is the distance from the neutral axis to the fiber in mm.**

**M**

**f**

**b**

**I**

*y*

#### THE BENDING EQUATION IS GIVEN BY,

**M/I = f/y = E/R**

**Where**

**M = Bending Moment**

**I = Moment of inertia about Neutral axis (N.A.)**

**f = Bending stress**

**y = Distance of the fiber from N.A.**

**R = Radius of Curvature**

**E = Young's Modulus**

**This equation may be remember as**

**" May I flow you Every Rule "**

**M/I = f/y = E/R**

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