## 24 Frames

Frames are statically indeterminate in general; special methods are required for their analysis. The slope deflection and moment distribution methods are two such methods commonly employed. Slope deflection is a method that takes into account the flexural displacements such as rotations and deflections and involves solutions of simultaneous equations. Moment distribution on the other hand involves successive cycles of computation, each cycle drawing closer to the ''exact'' answers. The method is more labor intensive but yields accuracy equivalent to that obtained from the exact methods.

2.4.1 Slope Deflection Method

This method is a special case of the stiffness method of analysis. It is a convenient method for performing hand analysis of small structures.

Let us consider that a prismatic frame member AB with undeformed position along the x axis is deformed into the configuration P as shown in Figure 2.21. Moments at the ends of frame members are expressed in terms of the rotations and deflections of the joints. It is assumed that the joints in a structure may rotate or deflect, but the angles between the members meeting at a joint remain unchanged. The positive axes, along with the positive member end force components and displacement components, are shown in the figure.

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