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SUBSTITUTE FRAME METHOD

Analysis of multi-storey building frames involves lot of complications and tedious calculations by using conventional methods. To carry out exact analysis is a time consuming task. Substitute frame method for analysis of multistory frame can be handy in approximate and quick analysis. This method has been applied only for vertical loading conditions. 

Substitute frame method 

Substitute frame method assumes that the moments in the beams of any floor are influenced by loading on that floor alone. The influence of loading on the lower or upper floors is ignored altogether.
The process involves the division of multi-storied structure into smaller frames. These sub frames are known as Equivalent frames or Substitute frames.
The substitute frames are formed by the beams at the floor level under consideration, together with the columns above and below with their far ends fixed. 

The sub frames are usually analyzed by the moment distribution method, using only Two cycle of distribution. It is only necessary to consider the loads on the two nearest spans on each side of the point .The distributed B.M are not carried over far ends of the columns in this process.
The moments in the columns are computed at each floor level independently and retained at that floor irrespective of further analysis.

Steps for the Analysis 

(1) Select a substitute frame, by taking-floor beam with columns of lower and upper storeys fixed at far ends. 
(2) Cross sectional dimensions of beams and columns may be chosen such that moment of inertia of beam is 1.5 to 2 times that of a column and find distribution factors at a joint considering stiffnesses of beams and columns. 
(3) Calculate the dead load and live load on beam. Live load should be placed in such a way that it causes worst effect at the section considered. (Live loads are placed alternate and adjacent spans as shown below should be adopted)
a) For maximum positive moments at mid point of span : Live loads are on alternate spans 

b) For maximum negative moments at the point of support : Live loads are on adjacent spans.

c) For maximum moments in columns : Live loads are on alternate spans.


(4) Find the initial fixed end moments and analyse this frame by moment distribution method. 
(5) Finally draw shear and moment diagram indicating values at critical section. 
Note: 
1.The Height of all columns should be same in a particular storey.
2. Sway of substitute frame is ignored even during unsymmetrical loading.
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