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Continuous Beam - Moment and Reaction Support Forces

Moment and reaction support forces with distributed or point loads

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Continuous Beam with Distributed Load

continuous beam moment reaction support forces distributed loads

For a continuous beam with 3, 4 or 5 supports and distributed load the reaction support forces can be calculated as

R = cr q L                     (1)

where

R = reaction support force (N, lbf)

cr = reaction support force coefficient from the figure above

q = distributed load (N/m, lbf/ft)

L = span length (m, ft)

The moments can be calculated as 

M = cm q L                     (2)

where

M = beam moment (Nm, lbf ft)

cm = 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 

Rend = (0.375) (1000 N/m)

         = 375 N

         = 0.38 kN

The reaction force in the center support can be calculated as

Rcenter = (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 

Mend = (0.070) (1000 N/m) (1 m)

        = 70 Nm

The beam moment at the center support can be calculated as 

Mcenter = (0.125) (1000 N/m) (1 m)

        = 125 Nm

Continuous Beam with Point Loads

continuous beam moment reaction support forces point loads

For a continuous beam with 3, 4 or 5 supports and point loads the reaction support forces can be calculated as

R = cr F                      (3)

where

cr = reaction support force coefficient from the figure above

F = point load (N, lbf)

The moments can be calculated as 

M = cm F L                     (4)

where

cm = 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 

Rend = (0.313) (1000 N)

         = 313 N

         = 0.31 kN

The reaction force in the center support can be calculated as

Rcenter = (1.375) (1000 N)

         = 1375 N

         = 1.4 kN

The beam moments at point loads with span length 1m can be calculated as 

Mend = (0.156) (1000 N) (1 m)

        = 156 Nm

The beam moment at the center support can be calculated as 

Mcenter = (0.188) (1000 N) (1 m)

        = 188 Nm

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