L13 - Analysis and Design of Beams for Bending Chapter 5...

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Analysis and Design of Beams for Bending • Shear and Bending Moment Diagrams • Relations among Load, Shear, and Bending Moment • Design of Prismatic Beams for Bending Chapter 5
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So far: (in chapter 4) bending
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Beam - structural member that supports loads at various points along the member beam Distributed load Concentrated load
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Loads result in: a shear force (from the shear stress distribution) + a bending couple (from the normal stress distribution)
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Normal stress is often the critical design criteria S M I c M I My m x = = = σ Requires determination of the location and magnitude of largest bending moment
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Classification of Beam Supports
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Shear and Bending Moment Diagrams Why do we need shear and bending moment diagrams? To determine maximum normal and shearing stresses and their respective locations– design safe beams V x M x Shear diagram Moment diagram
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Shear force and bending couple at a point are determined by passing a section through the beam and applying an equilibrium analysis on the beam portions on either side of the section.
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Shear Diagrams: P V L x L P V L x 2 1 2 1 2 1 2 1 0 = < < = < <
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Vw x = −
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L13 - Analysis and Design of Beams for Bending Chapter 5...

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