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

0BM 0 02

( )A BLR 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

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