Mechanics of Beams
This chapter covers the mechanics of beams, discussing how they resist bending and shear under various types of loads. It examines shear force and bending moment diagrams, types of beam supports, and the principles of static determinacy and indeterminacy. The theory of bending is introduced, including key concepts such as the neutral plane and shear stress distribution, along with related mathematical formulations for understanding beam behavior under load.
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What we have learnt
- Beams are designed to resist bending and shear from transverse loads.
- Different types of loads (point, uniformly distributed, and varying) affect beams differently.
- Understanding shear force and bending moment diagrams is crucial for analyzing beams.
Key Concepts
- -- Shear Force (SF)
- The internal force acting perpendicular to the beam’s longitudinal axis.
- -- Bending Moment (BM)
- The internal moment that causes bending in the beam.
- -- Simply Supported Beam
- A beam that is hinged at one end and roller-supported at the other.
- -- Statically Determinate Beam
- A beam with a number of reactions equal to the number of equilibrium equations available.
- -- Bending Equation
- Describes the relationship between moment, stress, and curvature in bending beams, formulated as MI=σy=ER.
- -- Second Moment of Area
- A measure of a beam's resistance to bending, calculated over the beam's cross-section.
- -- Shear Stress
- The internal stress distributed within a beam, maximum at the neutral axis and varies across the beam's height.
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