Beam Formula - Long Branch Public Schools...Beam Formulas • Similar loading conditions = similar...
Transcript of Beam Formula - Long Branch Public Schools...Beam Formulas • Similar loading conditions = similar...
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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
![Page 2: Beam Formula - Long Branch Public Schools...Beam Formulas • Similar loading conditions = similar shear and moment diagrams • Standard formula can represent the magnitude of shear](https://reader033.fdocuments.us/reader033/viewer/2022042408/5f24144f7b78d413b10a901b/html5/thumbnails/2.jpg)
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
![Page 3: Beam Formula - Long Branch Public Schools...Beam Formulas • Similar loading conditions = similar shear and moment diagrams • Standard formula can represent the magnitude of shear](https://reader033.fdocuments.us/reader033/viewer/2022042408/5f24144f7b78d413b10a901b/html5/thumbnails/3.jpg)
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
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Shear and Moment DiagramsSimple Beams (Uniformly Distributed Load)
Uniform load = 1000 lb/ft
L = 20 ft
Uniform load = 1200 lb/ft
L = 35 ft
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Reaction Force Formula
L
w
Beam Diagram
A B
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RB
Reaction Force Formula
RA
A B
L
0B
M 0 02
( )A B
LR L wL R
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Reaction Force Formula
RA RB
AB
L
w
+
Since
yF = 0
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Maximum Moment Formula
A B
L
w
Shear
Moment
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Beam FormulaSimple Beam (Uniformly Distributed Load)
L
Beam Diagram
A Bw
(at center)
(at center)
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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
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Your TurnSimple Beam (Concentrate Load at Center)
yF = 0
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Your Turn Simple Beam (Concentrate Load at Center)
![Page 13: Beam Formula - Long Branch Public Schools...Beam Formulas • Similar loading conditions = similar shear and moment diagrams • Standard formula can represent the magnitude of shear](https://reader033.fdocuments.us/reader033/viewer/2022042408/5f24144f7b78d413b10a901b/html5/thumbnails/13.jpg)
Beam FormulaSimple Beam (Concentrated Load at Center)
P
L
(at point of load)
(at point of load)
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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