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Support Reactions in Beams

The Support Reactions in Beams depends on the type of support on which the beam is supported.
Types of supports
There are 3 types of supports

1. Roller support: 
If a beam is supported on a roller support then it can't in vertical direction but it can move in horizontal direction and can have rotational motion about that support.
Hence total support reactions are 1 i.e in vertical direction.
2. Hinge support / Pinned support 
Similarly hinge support restricts vertical and horizontal motion but beam is free to perform rotational motion.
Hence it has 2 support reactions i.e horizontal and vertical
3. Fixed / Build in support: 
Here the support restricts all kinds of motion. The can't perform horizontal, vertical and rotational motion.
Hence it has 3 support reactions i.e horizontal, vertical and rotational reactions.

Types of Beams
A beam is a structural member designed to support various loading applied at points along the member. 
The forces / loads applied to a beam are counteracted by the supports which are called support reactions 
Based on support conditions the beams are called in the following types.
1.Simply supported Beam :
 a beam supported on the ends which are free to rotate and have no moment resistance.
2.Cantilever Beam :
 a projecting beam fixed only at one end 
3.Over hanging Beam :
 a simple beam extending beyond its support on one end.
4.Double overhanging Beam :
 a simple beam with both ends extending beyond its supports on both ends.
5.Continuous Beam :
 a beam extending over more than two supports.
6.Fixed Beam :
 a beam supported on both ends fixed and restrained from rotation.
7.Propped Cantilever Beam :
 a beam supported on fixed end and other end is supported by a simple support / prop.


Types of Loads
The following are the different types of loads applied to beams.
1. Concentrated or Point Load:
Load is assumed to act at a point.
2.Uniformly Distributed Load (U.D.L.):
Load spread along the length of the Beam uniformly.
3.Uniformly Varying Load:
Load spread along the length of the Beam, Rate of varying loading point to point.
4.Applied couple or pure moment: 
a couple refers to two parallel forces that are equal in magnitude, opposite in direction and its resultant is in the form of a pure moment acting at the connected point.
Support Reactions in Beams
The Support Reactions in Beams will find out by using the three static equilibrium equations. 

The support reactions are less than three we can determine the values by using the three static equilibrium equations. these beams are called Statically determinate beams. 
If the unknown reactions are more than three the beam is considered as Statically indeterminate beam.
Note :
In the simplification of the distributed loading system, the total load is converted to an equivalent point load. The net equivalent point load acts at the centroid of the loading body.
a.If the loading system is in the form of the triangle (distributed uniformly varying load) then the net force of the loading will act at centroid of triangle. The net point load will be the area of the triangular loading.
b. If the loading system is in the form of the rectangular  ( uniformly distributed load) then the net force of the loading will act at centroid of rectangular. The net point load will be the area of the rectangular loading. 
c. If the loading system is in the form of parabola, the net force will act at the centroid of the parabola. Whether it be a parabola or the cubic curve the centroid is the only point at which the net force act. 
Hence whatever be the shape of the loading, the centroid is the point of action of net force. 
The net Force will be the area of the loading diagram and  acted in the direction of the loading. 
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