## Unit 5: Pin Jointed Frames

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Types of Frames:

The different types of frames are:

1. Perfect frame    and

2.  Imperfect frame

Imperfect frame may be a deficient frame or a redundant frame.

Perfect frame:

The frame which is composed of such members, which are just sufficient to keep the frame in equilibrium, when the frame is supporting an external load, is known a perfect  frame is a  triangle as shown in figure 1 which consists three members and three joints. The three members are: AB, BC, and CA whereas the three joints are A, B, C. This frame can be easily analysed by the condition of equilibrium.

Figure 1

Let the two members CD and BD and a joint D are added to the triangular frame ABC. Now we get a frame ABCD as shown in figure 2. This frame can also be analysed by the conditions of equilibrium. This frame is also known as perfect frame.

Suppose we add a set of two members and a joint again, we get a perfect frame as shown in figure 3. Hence for a perfect frame the number of joints and number of members are given by, n=2j-3
Where,      n= number of members   and      j=number of joints

Figure 2                                                                    Figure 3

Imperfect frame:

A frame that number of members and number of joints are not given by n=2j-3  is known, an imperfect frame. This means that number of members in an imperfect frame will be either more or less than (2j-3)

1. If the number of members in a frame is less than (2j-3), then the frame is known as deficient frame.

2. If the number of members in a frame is more than (2j-3), then the frame is known as redundant frame.

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