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 AugustineSaint 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 Diagrams Simple Beams (Uniformly Distributed Load) Uniform load = 1000 lb/ft L = 20 ft Uniform load = 1200 lb/ft L = 35 ft

5. Reaction Force Formula L w Beam Diagram A B

6. RBRB Reaction Force Formula RARA A B L

7. RARA RBRB A B L w + Since

8. Maximum Moment Formula A B L w Shear Moment

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

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

13. Beam Formula Simple Beam (Concentrated Load at Center) P 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