Page 1 4.1 SIMPLE BENDING OR PURE BENDING ? When some external force acts on a beam, the shear force and bending moments are set up at all the sections of the beam ? Due to shear force and bending moment, the beam undergoes deformation. The material of the beam offers resistance to deformation ? Stresses introduced by bending moment are known as bending stresses ? Bending stresses are indirect normal stresses Page 2 4.1 SIMPLE BENDING OR PURE BENDING ? When some external force acts on a beam, the shear force and bending moments are set up at all the sections of the beam ? Due to shear force and bending moment, the beam undergoes deformation. The material of the beam offers resistance to deformation ? Stresses introduced by bending moment are known as bending stresses ? Bending stresses are indirect normal stresses 4.1 SIMPLE BENDING OR PURE BENDING ? When a length of a beam is subjected to zero shear force and constant bending moment, then that length of beam is subjected to pure bending or simple pending. ? The stress set up in that length of the beam due to pure bending is called simple bending stresses Page 3 4.1 SIMPLE BENDING OR PURE BENDING ? When some external force acts on a beam, the shear force and bending moments are set up at all the sections of the beam ? Due to shear force and bending moment, the beam undergoes deformation. The material of the beam offers resistance to deformation ? Stresses introduced by bending moment are known as bending stresses ? Bending stresses are indirect normal stresses 4.1 SIMPLE BENDING OR PURE BENDING ? When a length of a beam is subjected to zero shear force and constant bending moment, then that length of beam is subjected to pure bending or simple pending. ? The stress set up in that length of the beam due to pure bending is called simple bending stresses 4.1 SIMPLE BENDING OR PURE BENDING ? Consider a simply supported beam with over hanging portions of equal lengths. Suppose the beam is subjected to equal loads of intensity W at either ends of the over hanging portion ? In the portion of beam of length l, the beam is subjected to constant bending moment of intensity w x a and shear force in this portion is zero ? Hence the portion AB is said to be subjected to pure bending or simple bending Page 4 4.1 SIMPLE BENDING OR PURE BENDING ? When some external force acts on a beam, the shear force and bending moments are set up at all the sections of the beam ? Due to shear force and bending moment, the beam undergoes deformation. The material of the beam offers resistance to deformation ? Stresses introduced by bending moment are known as bending stresses ? Bending stresses are indirect normal stresses 4.1 SIMPLE BENDING OR PURE BENDING ? When a length of a beam is subjected to zero shear force and constant bending moment, then that length of beam is subjected to pure bending or simple pending. ? The stress set up in that length of the beam due to pure bending is called simple bending stresses 4.1 SIMPLE BENDING OR PURE BENDING ? Consider a simply supported beam with over hanging portions of equal lengths. Suppose the beam is subjected to equal loads of intensity W at either ends of the over hanging portion ? In the portion of beam of length l, the beam is subjected to constant bending moment of intensity w x a and shear force in this portion is zero ? Hence the portion AB is said to be subjected to pure bending or simple bending 4.2 ASSUMPTIONS FOR THE THEORY OF PURE BENDING ? The material of the beam is isotropic and homogeneous. Ie of same density and elastic properties throughout ? The beam is initially straight and unstressed and all the longitudinal filaments bend into a circular arc with a common centre of curvature ? The elastic limit is nowhere exceeded during the bending ? Young's modulus for the material is the same in tension and compression Page 5 4.1 SIMPLE BENDING OR PURE BENDING ? When some external force acts on a beam, the shear force and bending moments are set up at all the sections of the beam ? Due to shear force and bending moment, the beam undergoes deformation. The material of the beam offers resistance to deformation ? Stresses introduced by bending moment are known as bending stresses ? Bending stresses are indirect normal stresses 4.1 SIMPLE BENDING OR PURE BENDING ? When a length of a beam is subjected to zero shear force and constant bending moment, then that length of beam is subjected to pure bending or simple pending. ? The stress set up in that length of the beam due to pure bending is called simple bending stresses 4.1 SIMPLE BENDING OR PURE BENDING ? Consider a simply supported beam with over hanging portions of equal lengths. Suppose the beam is subjected to equal loads of intensity W at either ends of the over hanging portion ? In the portion of beam of length l, the beam is subjected to constant bending moment of intensity w x a and shear force in this portion is zero ? Hence the portion AB is said to be subjected to pure bending or simple bending 4.2 ASSUMPTIONS FOR THE THEORY OF PURE BENDING ? The material of the beam is isotropic and homogeneous. Ie of same density and elastic properties throughout ? The beam is initially straight and unstressed and all the longitudinal filaments bend into a circular arc with a common centre of curvature ? The elastic limit is nowhere exceeded during the bending ? Young's modulus for the material is the same in tension and compression 4.2 ASSUMPTIONS FOR THE THEORY OF PURE BENDING ? The transverse sections which were plane before bending remain plane after bending also ? Radius of curvature is large compared to the dimensions of the cross section of the beam ? There is no resultant force perpendicular to any cross section ? All the layers of the beam are free to elongate and contract, independently of the layer, above or below it.Read More

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