PPT: Bending Stresses in Beams

# 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.
```

## Strength of Materials (SOM)

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## FAQs on PPT: Bending Stresses in Beams - Strength of Materials (SOM) - Mechanical Engineering

 1. What is the definition of bending stresses in beams?
Ans. Bending stresses in beams refer to the internal forces that develop within a beam when subjected to a bending moment. These stresses cause the beam to bend or deform, and they are highest at the point farthest from the neutral axis.
 2. How do bending stresses affect the design of beams?
Ans. Bending stresses play a crucial role in the design of beams as they determine the beam's strength and structural integrity. Engineers need to ensure that the maximum bending stress does not exceed the material's allowable stress to prevent failure or excessive deformation.
 3. What factors influence the magnitude of bending stresses in beams?
Ans. The magnitude of bending stresses in beams is influenced by several factors, including the magnitude of the applied bending moment, the shape and size of the cross-section, and the material properties of the beam. Additionally, the distance from the neutral axis also affects the magnitude of bending stresses.
 4. How are bending stresses calculated in beams?
Ans. Bending stresses can be calculated using the formula σ = (M * c) / I, where σ is the bending stress, M is the bending moment, c is the distance from the neutral axis to the point of interest, and I is the moment of inertia of the beam's cross-section. This formula applies to beams with simple cross-sections.
 5. What are the different types of beam failures related to bending stresses?
Ans. Bending stresses can lead to different types of beam failures, such as elastic failure, plastic failure, and ultimate failure. Elastic failure occurs when the bending stress exceeds the elastic limit of the material, causing permanent deformation. Plastic failure occurs when the bending stress exceeds the yield strength, resulting in permanent deformation without any further increase in load. Ultimate failure occurs when the bending stress exceeds the ultimate strength of the material, leading to complete fracture or collapse of the beam.

## Strength of Materials (SOM)

37 videos|39 docs|45 tests

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