Unit 4 transverse loading on beams and stresses in beams
- 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.
- 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.