TYPES OF BEAMS , LOADS AND SUPPORTS

1. UNIT -4
TRANSVERSE LOADING ON BEAMS
AND
STRESSES IN BEAMS

2. BEAM
What is a Beam?
• Beam is defined as the structural member
which is used to bear different loads.
• It resists the vertical loads, shear forces and
bending moments.

3. Types of Beams

4. Cantilever Beam

6. TYPES OF LOADS
• Point or Concentrated Load
• Uniformly Distributed Load (UDL)
• Uniformly Varying Load (UVL)

7. SHEAR FORCE
• It’s the algebraic sum of all the forces acting
on one side of the section or the other
BENDING MOMENT
• It’s the algebraic sum of all the moments
acting on any one side of that section

8. Theory of Simple
Bending
(Pure Bending)

9. Definition
• When a portion of beam is free from shear
force and is subjected to only bending
moment is said to be pure bending (or)
simple bending.

10. Assumptions in theory of simple Bending
• The beam material is homogeneous and isotropic
(isotropic –same elastic properties in all directions)
• Beam is having uniform cross section throughout its
length
• The beam is stressed with in elastic limit.
• The young's modulus is same in both tension and
compression
• The loads are applied before bending

11. Assumptions
• Stress concentrations are neglected
• Radius of curvature ( R ) of bending is very large as
compared to cross sectional dimensions.
• Apart from bending all other deformations are
neglected.
• There is no resultant Thrust on the cross section of
the beam

12. Bending Equation Derivation
Bending theory is also known as flexure theory is defined as the axial
deformation of the beam due to external load that is applied
perpendicularly to a longitudinal axis which finds application in applied
mechanics.
For a material, flexural strength is defined as the stress that is obtained
from the yield just before the flexure test. It represents the highest stress
that is experienced within the material at the moment of its yield. 𝜎 is
used as the symbolic representation of flexural strength.

14. When a beam is subjected to a loading system or by a force couple
acting on a plane passing through the axis, then the beam deforms. In
simple terms, this axial deformation is called as bending of a beam. Due
to the shear force and bending moment, the beam undergoes
deformation. These normal stress due to bending are called flexure
stresses.