Beam Formulas

This tool provides formulas for the bending moment, shear, deflection, and rotation of elastic beams


Input:

1xxaaLL

Output:

    Equations
    User Notes:

M(x) - Moment

050.0100-1500-1000-5000x positionMomentx: 0 y: 0x: 6 y: -342x: 12 y: -648x: 18 y: -918x: 24 y: -1152x: 30 y: -1350x: 36 y: -1512x: 42 y: -1638x: 48 y: -1728x: 54 y: -1782x: 60 y: -1800x: 66 y: -1782.0000000000002x: 72 y: -1728x: 78 y: -1638x: 84 y: -1512x: 90 y: -1350x: 96 y: -1152x: 102 y: -918x: 108 y: -648x: 114 y: -342x: 120 y: 0

V(x) - Shear

050.0100-50.0050.0x positionShearx: 0 y: -60x: 6 y: -54x: 12 y: -48x: 18 y: -42x: 24 y: -36x: 30 y: -30x: 36 y: -24x: 42 y: -18x: 48 y: -12x: 54 y: -6x: 60 y: 0x: 66 y: 6x: 72 y: 12x: 78 y: 18x: 84 y: 24x: 90 y: 30x: 96 y: 36x: 102 y: 42x: 108 y: 48x: 114 y: 54x: 120 y: 60

δ(x) - Displacement

050.010000.0200.0400.0600.080x positionDisplacementx: 0 y: 0x: 6 y: 0.014823931034482759x: 12 y: 0.02922703448275862x: 18 y: 0.04282944827586207x: 24 y: 0.055296x: 30 y: 0.06633620689655172x: 36 y: 0.07570427586206896x: 42 y: 0.08319910344827586x: 48 y: 0.08866427586206896x: 54 y: 0.09198806896551724x: 60 y: 0.09310344827586206x: 66 y: 0.09198806896551724x: 72 y: 0.08866427586206896x: 78 y: 0.08319910344827587x: 84 y: 0.07570427586206896x: 90 y: 0.06633620689655173x: 96 y: 0.055296x: 102 y: 0.04282944827586207x: 108 y: 0.02922703448275862x: 114 y: 0.014823931034482759x: 120 y: 0

θ(x) - Rotation

050.0100-0.00200.002x positionRotationx: 0 y: 0.0024827586206896553x: 6 y: 0.0024467586206896553x: 12 y: 0.002343724137931035x: 18 y: 0.0021811034482758624x: 24 y: 0.001966344827586207x: 30 y: 0.001706896551724138x: 36 y: 0.0014102068965517241x: 42 y: 0.0010837241379310345x: 48 y: 0.000734896551724138x: 54 y: 0.0003711724137931035x: 60 y: 0x: 66 y: -0.0003711724137931035x: 72 y: -0.000734896551724138x: 78 y: -0.0010837241379310345x: 84 y: -0.0014102068965517241x: 90 y: -0.001706896551724138x: 96 y: -0.001966344827586207x: 102 y: -0.0021811034482758624x: 108 y: -0.002343724137931035x: 114 y: -0.0024467586206896553x: 120 y: -0.0024827586206896553