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Presentation onStresses in Beam

By

Prof. V N Nikam

(LECTURER)

Email- vilas5151@gmail.com

Sandip Institute of PolytechnicSandip Foundation

Nashik

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

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.

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

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'

BENDING STRESS DISTRIBUTION1. Rectangular Section

2. Circular Section

3. Hollow circular section

Bending Stress Distribution for unsymmetrical section in case of

Simply Supported Beam

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Bending Stress Distribution for unsymmetrical section in case of

Cantilever Beam

Bending Stress Distribution for Symmetrical section in case of

Cantilever Beam

Shear stress Distribution for 'Rectangular' Section

Shear stress Distribution for 'Circular' Section

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

Shear stress Distribution for 'Hollow Rectangular' Section

Shear stress Distribution for 'Hollow 'T' Section

Shear stress Distribution for 'Hollow 'Angle' Section

Shear stress Distribution for 'Hollow 'Channel' Section