When external loads act on a beam, bending stresses are introduced. Bending stresses occur due to bending moments in sections of the beam where the shear force is zero, known as pure bending. For rectangular beam sections under pure bending, the stresses are highest at the outer fibers furthest from the neutral axis and reduce towards the center. The distribution of bending stresses over the rectangular cross-section can be calculated using the bending equation.

1. BIBIN CHIDAMBARANATHAN
BENDING STRESSES
IN BEAM
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2. Bending Stresses in Beams
• When some external load acts on a beam, the shear force and bending moments
are set up at all sections of the beam.
• Due to the shear force and bending moment, the beam undergoes certain
deformation.
• The material of the beam will offer resistance or stresses against these
deformations.
• These stresses with certain assumptions can be calculated.
• The stresses introduced by bending moment are known as bending stresses.
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3. PURE BENDING OR SIMPLE BENDING
• If a length of a beam is subjected to a constant bending moment and no shear
force (i.e., zero shear force), then the stresses will be set up in that length of the
beam due to B.M. only and that length of the beam is said to be in pure bending
or simple bending.
• The stresses set up in that length of beam are known as bending stresses.
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4. PURE BENDING OR SIMPLE BENDING
• A beam simply supported at A and B and overhanging by same length at each support is shown
in Fig.
• A point load W is applied at each end of the overhanging portion. The S.F. and B.M. for the beam
are drawn as shown in Fig. (b) and Fig. {c) respectively.
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5. PURE BENDING OR SIMPLE BENDING
• From these diagrams, it is clear that there is no shear force between A and B but
the B.M. between A and B is constant.
• This means that between A and B, the beam is subjected to a constant bending
moment only.
• This condition of the beam between A and B is known as pure bending or simple
bending.
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6. THEORY OF SIMPLE BENDING WITH
ASSUMPTIONS MADE
Let us see the assumptions made in the theory of simple bending. The following are
the important assumptions :
• The material of the beam is homogeneous and isotropic.
• The value of Young's modulus of elasticity is the same in tension and
compression.
• The transverse sections which were plane before bending, remain plane after
bending also.
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7. THEORY OF SIMPLE BENDING WITH
ASSUMPTIONS MADE
• The beam is initially straight and all longitudinal filaments bend into circular
arcs with a common centre of curvature.
• The radius of curvature is large compared with the dimensions of the cross-
section.
• Each layer of the beam is free to expand or contract, independently of the layer,
above or below it.
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9. BIBIN CHIDAMBARANATHAN
DERIVATION OF
BENDING
EQUATION
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19. BIBIN CHIDAMBARANATHAN
DISTRIBUTION OF
BENDING STRESS
OVER
RECTANGULAR SECTION
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30. Thank You
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