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Mastering Beam Formulas: Understanding Shear and Moment Diagrams

Learn to analyze shear and moment diagrams for simple beams with uniformly distributed loads and concentrated loads at the center. Discover reaction force formulas and maximum moment formulas applicable in beam analysis. Gain insight into how standard formulas represent shear and bending moment magnitude based on loading conditions.

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Mastering Beam Formulas: Understanding Shear and Moment Diagrams

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  1. Beam Formula If I am given a formula and I am ignorant of its meaning, it cannot teach me anything; but if I already know it, what does the formula teach me? - Saint Aurelius Augustine

  2. Beam Formula • Shear and moment diagrams • Simple beam (uniformly distributed load) • Reaction force formula • Maximum moment formula • Simple beam (concentrated load at center) • Reaction force formula • Maximum moment formula

  3. Beam Formulas • Similar loading conditions = similar shear and moment diagrams • Standard formula can represent the magnitude of shear and moment based on loading condition • Magnitude of shear and bending moment depend on • Span length of beam • Magnitude of applied load • Location of applied load

  4. Shear and Moment DiagramsSimple Beams (Uniformly Distributed Load) Uniform load = 1200 lb/ft L = 35 ft Uniform load = 1000 lb/ft L = 20 ft

  5. Reaction Force Formula w B A L Beam Diagram

  6. Reaction Force Formula B A RA RB L MB = 0 -Ra x L = (wL) x (L/2) + Rb x 0 = 0

  7. Reaction Force Formula w L B + Fy = 0 A RA RB Since

  8. Maximum Moment Formula w L B A Shear Moment

  9. Beam FormulaSimple Beam (Uniformly Distributed Load) w B A L Beam Diagram (at center) (at center)

  10. Your TurnSimple Beam (Concentrate Load at Center) Find a formula for the end reaction forces and for the maximum moment for a simply supported beam with a single concentrated load, P, applied at center span. P L

  11. Your TurnSimple Beam (Concentrate Load at Center) Fy = 0

  12. Your Turn Simple Beam (Concentrate Load at Center)

  13. Beam FormulaSimple Beam (Concentrated Load at Center) P (at point of load) L (at point of load)

  14. Beam Formula • Shear and moment diagrams • Simple beam (uniformly distributed load) • Reaction force formula • Maximum moment formula • Simple beam (concentrated load at center) • Reaction force formula • Maximum moment formula

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