# Boundary Conditions in Structural Analysis

Some standard idealization and assumptions are followed for material properties, boundary conditions and support conditions of the structure in order to perform structural analysis.

### Material Properties of Structures in Structural Analysis

The assumptions regarding material properties are:

1. Materials are homogeneous and isotropic.
2. The stress-strain curve is linear
Note* A homogeneous material means a material with identical particles. An isotropic material means, the physical properties of materials are identical in all directions.

A linear stress-strain relation that is within the limit of proportionality of materials are followed. In case of concrete, the stress-strain relation is approximated to a linear relation.

### Boundary Conditions for Structural Analysis

The following boundary conditions are assumed for different structures:

#### 1. Free End

The free end of any structural element can be subjected to linear to rotational displacement due to action of load. But, there is no sort of reaction happening at this end.

#### 2. Roller Support

At a roller support end, the member is free to move along the support and to rotate freely. It resist the movement of the member at the support in the direction perpendicular to the support.

Hence, as the movement in perpendicular direction is restricted, there is a reaction produced in the direction perpendicular to the support. As, it lets rotation and movement along the supports, no reaction arises along these direction i.e ( reaction and resisting moment = 0).

 Fig. Roller Support Boundary Conditions

#### 3. Hinged Supports

At a hinged support as shown in figure below, the support restricts linear motion i.e.Â  along X and Y direction. But it allows to rotate freely about the support i.e. about the point that is pinned.

This provision to rotation helps the member to develop requiredÂ resisting force in any direction and do not create any resisting moment. As linear motion is restricted, reactions Rx and Ry are created at the hinged support of the member as shown in figure below.

 Fig. Hinged Support

#### 4. Fixed Ends

A fixed end do not permit any linear or rotational movement. Hence, at the fixed end, the support develop both resisting force or reaction in X and Y direction and also resisting moment.Â

 Fig. Fixed End

### Deflection in Structural Analysis

Deflections in structural analysis is considered to be small and hence the changes that is happening due to loading are consideredÂ negligible. So, during the analysis, the changes in the length of a member and the angle between the two members are neglected.