bending stresses, shear stress, for I SECTION, CHANNEL SECTION, HOLLOW RECTANGULAR SECTION, RECTANGULAR SECTION, CIRCULAR SECTION

1. A
Presentation on
Stresses in Beam
By
Prof. V N Nikam
(LECTURER)
Email- vilas5151@gmail.com
Sandip Institute of Polytechnic
Sandip Foundation
Nashik

2. Concept of pure bending
● Bending Stress – when the beam is subjected to external loading applied
vertically, then the resistance offered by the internal stresses to bending is
called as bending stress

3. Assumption in the theory of pure bending
1. Beam is initially straight , and has a constant cross-section.
2. Beam is made of homogeneous material and the beam has a
longitudinal plane of symmetry.
3. Resultant of the applied loads across the transverse section is zero.
4. The geometry of the overall member is such that bending not buckling is
the primary cause of failure.
5. Value of ‘E' is same in tension and compression.
6. Plane cross - sections remains plane before and after bending.
7. Elastic limit is not exceeded.
8. Deformation due to shear force is neglected.

4. Some definition
1. Neutral axis (N.A) – When beam subjected to pure bending, one layer
which is not subjected to tension or compression
2. Section modulus : the ratio of moment of inertia about the neutral axis to
the distance 'y' from N.A to extreme layer of section
Z = I/ymax

5. Flexural formula of Bending Equation
M = Maximum bending moment 'kN-m'
IXX = Moment of inertia about N.A 'mm3'
Ϭ = Bending Stress in N/ mm2
Ymax = Distance of extreme layer of the section from N.A
E = Modulus of elasticity of Material in N/ mm2
R = Radius of curvature in 'm'

6. BENDING STRESS DISTRIBUTION
1. Rectangular
Section
2. Circular
Section
3. Hollow
circular
section

7. Bending Stress Distribution for
unsymmetrical section in case of
Simply Supported Beam
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8. Bending Stress Distribution for
unsymmetrical section in case of
Cantilever Beam

9. Bending Stress Distribution for
Symmetrical section in case of
Cantilever Beam

11. Shear stress Distribution for 'Rectangular' Section

12. Shear stress Distribution for 'Circular' Section

13. Shear stress Distribution for 'Rectangular' SectionShear stress Distribution for 'I' Section

14. Shear stress Distribution for 'Hollow
Rectangular' Section

15. Shear stress Distribution for 'Hollow 'T'
Section

16. Shear stress Distribution for 'Hollow
'Angle' Section

17. Shear stress Distribution for 'Hollow
'Channel' Section