PPT: Bending Stresses in Beams | Strength of Materials (SOM) - Mechanical Engineering PDF Download

 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.