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Beam Formulas
This tool provides formulas for the bending moment, shear, deflection, and rotation of elastic beams
Input:
Simply-Supported
Cantilever
Beam Type
Uniformly Distributed
Point Load
Load Type
Length
E
I
q
a
x
1
x
x
a
a
L
L
Output:
Equations
User Notes:
User notes
Use Consistent Units. For instance, E=ksi, I=in4, q=kip/in, Forces=kips, Moments=kip*in, and Lengths=in
M(x) - Moment
0
50.0
100
-1500
-1000
-500
0
x position
Moment
x: 0 y: 0
x: 6 y: -342
x: 12 y: -648
x: 18 y: -918
x: 24 y: -1152
x: 30 y: -1350
x: 36 y: -1512
x: 42 y: -1638
x: 48 y: -1728
x: 54 y: -1782
x: 60 y: -1800
x: 66 y: -1782.0000000000002
x: 72 y: -1728
x: 78 y: -1638
x: 84 y: -1512
x: 90 y: -1350
x: 96 y: -1152
x: 102 y: -918
x: 108 y: -648
x: 114 y: -342
x: 120 y: 0
V(x) - Shear
0
50.0
100
-50.0
0
50.0
x position
Shear
x: 0 y: -60
x: 6 y: -54
x: 12 y: -48
x: 18 y: -42
x: 24 y: -36
x: 30 y: -30
x: 36 y: -24
x: 42 y: -18
x: 48 y: -12
x: 54 y: -6
x: 60 y: 0
x: 66 y: 6
x: 72 y: 12
x: 78 y: 18
x: 84 y: 24
x: 90 y: 30
x: 96 y: 36
x: 102 y: 42
x: 108 y: 48
x: 114 y: 54
x: 120 y: 60
δ(x) - Displacement
0
50.0
100
0
0.020
0.040
0.060
0.080
x position
Displacement
x: 0 y: 0
x: 6 y: 0.014823931034482759
x: 12 y: 0.02922703448275862
x: 18 y: 0.04282944827586207
x: 24 y: 0.055296
x: 30 y: 0.06633620689655172
x: 36 y: 0.07570427586206896
x: 42 y: 0.08319910344827586
x: 48 y: 0.08866427586206896
x: 54 y: 0.09198806896551724
x: 60 y: 0.09310344827586206
x: 66 y: 0.09198806896551724
x: 72 y: 0.08866427586206896
x: 78 y: 0.08319910344827587
x: 84 y: 0.07570427586206896
x: 90 y: 0.06633620689655173
x: 96 y: 0.055296
x: 102 y: 0.04282944827586207
x: 108 y: 0.02922703448275862
x: 114 y: 0.014823931034482759
x: 120 y: 0
θ(x) - Rotation
0
50.0
100
-0.002
0
0.002
x position
Rotation
x: 0 y: 0.0024827586206896553
x: 6 y: 0.0024467586206896553
x: 12 y: 0.002343724137931035
x: 18 y: 0.0021811034482758624
x: 24 y: 0.001966344827586207
x: 30 y: 0.001706896551724138
x: 36 y: 0.0014102068965517241
x: 42 y: 0.0010837241379310345
x: 48 y: 0.000734896551724138
x: 54 y: 0.0003711724137931035
x: 60 y: 0
x: 66 y: -0.0003711724137931035
x: 72 y: -0.000734896551724138
x: 78 y: -0.0010837241379310345
x: 84 y: -0.0014102068965517241
x: 90 y: -0.001706896551724138
x: 96 y: -0.001966344827586207
x: 102 y: -0.0021811034482758624
x: 108 y: -0.002343724137931035
x: 114 y: -0.0024467586206896553
x: 120 y: -0.0024827586206896553
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Table of Fixed End Moments
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Wind Load (Envelope Procedure)
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Wind Load (Open Signs and Frames)
Concrete
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Bearing Capacity
Concrete Properties
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Column Axial Capacity
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Rebar Development Length
Rebar Properties
Rebar Quantity Takeoff
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SOG Concentrated Load
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