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
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
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
Shear and Moment DiagramsSimple Beams (Uniformly Distributed Load)
Uniform load = 1000 lb/ftL = 20 ft
Uniform load = 1200 lb/ftL = 35 ft
Reaction Force Formula
L
w
Beam Diagram
A B
RB
Reaction Force Formula
RA
A B
+
L
Reaction Force Formula
RA RB
AB
L
w
+
Since
yF = 0
Maximum Moment Formula
A B
L
w
Shear
Moment
Beam FormulaSimple Beam (Uniformly Distributed Load)
L
Beam Diagram
A Bw
(at center)
(at center)
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
Your TurnSimple Beam (Concentrate Load at Center)
yF = 0
M = 0 A
Your Turn Simple Beam (Concentrate Load at Center)
Beam FormulaSimple Beam (Concentrated Load at Center)
P
L(at point of load)
(at point of load)
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