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# 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 = 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 L2                     (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)2

= 70 Nm

The beam moment at the center support can be calculated as

Mcenter = (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 = 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

## Related Topics

• Beams and Columns - Deflection and stress, moment of inertia, section modulus and technical information of beams and columns.

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