vilas nikam- mechanics of structure-stress in beam presentation
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APresentation onStresses in BeamBy Prof. V N Nikam
(LECTURER)
Email- [email protected]
Sandip Institute of PolytechnicSandip FoundationNashik
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 compression2. Section modulus : the ratio of moment of inertia about the neutral axis to the distance 'y' from N.A to extreme layer of sectionZ = I/ymax
Flexural formula of Bending Equation
M = Maximum bending moment 'kN-m'IXX = Moment of inertia about N.A 'mm3'
= 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 DISTRIBUTION
1. Rectangular Section2. Circular Section3. 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' Section
Shear 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