# 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*