Chapter 13 : Analysis of Perfect Frames (Analytical Method) 245
13.2. TYPES OF FRAMES
Though there are many types of frames, yet from the analysis point of view, the frames may be
classified into the following two groups:
- Perfect frame. 2. Imperfect frame.
13.3. PERFECT FRAME
A perfect frame is that, which is made up of members just suf-
ficient to keep it in equilibrium, when loaded, without any change in
its shape.
The simplest perfect frame is a triangle, which contains three
members and three joints as shown in Fig. 13.1. It will be intersting to
know that if such a structure is loaded, its shape will not be distorted.
Thus, for three jointed frame, there should be three members to prevent
any distortion. It will be further noticed that if we want to increase a
joint, to a triangular frame, we require two members as shown by dot-
ted lines in Fig. 13.1. Thus we see that for every additional joint, to a
triangular frame, two members are required.
The no. of members, in a perfect frame, may also be expressed by the relation :
n =(2j – 3)
n = No. of members, and
j = No. of joints.13.4.IMPERFECT FRAME
An imperfect frame is that which does not satisfy the equation :
n = (2j – 3)
Or in other words, it is a frame in which the no. of members are more or less than (2j – 3). The
imperfect frames may be further classified into the following two types :
- Deficient frame. 2. Redundant frame.
13.5.DEFICIENT FRAME
A deficient frame is an imperfect frame, in which the no. of members are less than (2j – 3).13.6.REDUNDANT FRAME
A redundant frame is an imperfect frame, in which the no. of members are more than (2j – 3).
In this chapter, we shall discuss only perfect frames.
13.7.STRESS
When a body is acted upon by a force, the internal force which is transmitted through the body is
known as stress. Following two types of stress are important from the subject point of view :
- Tensile stress. 2. Compressive stress.
13.8. TENSILE STRESS
Fig. 13.2.Fig. 13.1. Perfect Frame.