Degree of Freedom for a Pin Jointed Plane Frame

Pin jointed plane frame refers to a structural system consisting of interconnected bars or members that are connected by pin joints. The degree of freedom of this system is the number of independent motions or movements that the system can make. In simple terms, it refers to the number of ways the system can move without violating the constraints imposed by the pin joints.

Formula for Degree of Freedom

The degree of freedom for a pin jointed plane frame can be calculated using the formula:

DF = 2j - r

Where:
DF = Degree of freedom
j = number of joints
r = number of restrained degrees of freedom

Explanation of Formula

The degree of freedom of a structural system is the number of independent parameters required to describe its configuration or motion. In the case of a pin jointed plane frame, the number of joints and the number of restrained degrees of freedom play a crucial role in determining the system's degree of freedom.

Each joint in a pin jointed plane frame can move in two directions, i.e., horizontally and vertically. Therefore, the total number of degrees of freedom for a single joint is two. As such, the degree of freedom for the entire system is calculated by multiplying the number of joints by two.

However, some of these degrees of freedom may not be independent due to the constraints imposed by the pin joints. For instance, a pin joint can restrain the movement of a joint in one or both directions. Therefore, the number of restrained degrees of freedom must be subtracted from the total number of degrees of freedom to obtain the actual degree of freedom of the system.

Example of Calculating Degree of Freedom

Suppose a pin jointed plane frame has 10 joints, and three joints are restrained from moving vertically. The degree of freedom for the system can be calculated as follows:

DF = 2j - r
DF = 2(10) - 3
DF = 17

Therefore, the degree of freedom for the system is 17, which means that the system can make 17 independent movements without violating the constraints imposed by the pin joints.

In conclusion, the degree of freedom for a pin jointed plane frame is determined by the number of joints and the number of restrained degrees of freedom. The formula 2j-r is used to calculate the degree of freedom, where j is the number of joints, and r is the number of restrained degrees of freedom.