beam formula
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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) - PowerPoint PPT PresentationTRANSCRIPT
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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](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/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](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/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
![Page 4: Beam Formula](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/html5/thumbnails/4.jpg)
Shear and Moment DiagramsSimple Beams (Uniformly Distributed Load)
Uniform load = 1000 lb/ftL = 20 ft
Uniform load = 1200 lb/ftL = 35 ft
![Page 5: Beam Formula](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/html5/thumbnails/5.jpg)
Reaction Force Formula
L
w
Beam Diagram
A B
![Page 6: Beam Formula](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/html5/thumbnails/6.jpg)
RB
Reaction Force Formula
RA
A B
L
0BM 0 02
( )A BLR L wL R
![Page 7: Beam Formula](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/html5/thumbnails/7.jpg)
Reaction Force Formula
RA RB
AB
L
w
+
Since
yF = 0
![Page 8: Beam Formula](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/html5/thumbnails/8.jpg)
Maximum Moment Formula
A B
L
w
Shear
Moment
![Page 9: Beam Formula](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/html5/thumbnails/9.jpg)
Beam FormulaSimple Beam (Uniformly Distributed Load)
L
Beam Diagram
A Bw
(at center)
(at center)
![Page 10: Beam Formula](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/html5/thumbnails/10.jpg)
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
M = 0 A
![Page 12: Beam Formula](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/html5/thumbnails/12.jpg)
Your Turn Simple Beam (Concentrate Load at Center)
![Page 13: Beam Formula](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/html5/thumbnails/13.jpg)
Beam FormulaSimple Beam (Concentrated Load at Center)
P
L(at point of load)
(at point of load)
![Page 14: Beam Formula](https://reader036.vdocuments.us/reader036/viewer/2022062517/568134d6550346895d9c005c/html5/thumbnails/14.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