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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/ft
L = 20 ft
Uniform load = 1200 lb/ft
L = 35 ft
Reaction Force Formula
L
w
Beam Diagram
A B
RB
Reaction Force Formula
RA
A B
L
0B
M 0 02
( )A B
LR L wL R
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
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
