Continuous Beams  Moment and Reaction Support Forces
Moments and reaction support forces with distributed or point loads.
Continuous Beam with Distributed Load
For a continuous beam with 3, 4 or 5 supports and distributed load the reaction support forces can be calculated as
R = c_{r} q L (1)
where
R = reaction support force (N, lb_{f})
c_{r} = reaction support force coefficient from the figure above
q = distributed load (N/m, lb_{f}/ft)
L = span length (m, ft)
The moments can be calculated as
M = c_{m} q L^{2} (2)
where
M = beam moment (Nm, lb_{f} ft)
c_{m} = moment coefficient from the figure above
Example  Continuous Beam with Distributed Load
The reaction forces in the end supports for a continuous beam with 3 supports and distributed load 1000 N/m can be calculated as
R_{end} = (0.375) (1000 N/m)
= 375 N
= 0.38 kN
The reaction force in the center support can be calculated as
R_{center} = (1.250) (1000 N/m)
= 1250 N
= 1.25 kN
The beam moments at the middle of spans with span length 1m can be calculated as
M_{end} = (0.070) (1000 N/m) (1 m)^{2}
= 70 Nm
The beam moment at the center support can be calculated as
M_{center} = (0.125) (1000 N/m) (1 m)^{2}
= 125 Nm
Continuous Beam with Point Loads
For a continuous beam with 3, 4 or 5 supports and point loads the reaction support forces can be calculated as
R = c_{r} F (3)
where
c_{r} = reaction support force coefficient from the figure above
F = point load (N, lb_{f})
The moments can be calculated as
M = c_{m} F L (4)
where
c_{m} = moment coefficient from the figure above
Example  Continuous Beam with Point Loads
The reaction forces in the end supports for a continuous beam with 3 supports and 2 point loads 1000 N can be calculated as
R_{end} = (0.313) (1000 N)
= 313 N
= 0.31 kN
The reaction force in the center support can be calculated as
R_{center} = (1.375) (1000 N)
= 1375 N
= 1.4 kN
The beam moments at point loads with span length 1m can be calculated as
M_{end} = (0.156) (1000 N) (1 m)
= 156 Nm
The beam moment at the center support can be calculated as
M_{center} = (0.188) (1000 N) (1 m)
= 188 Nm
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