The problem of calculating the theoretical failure load (WF) of a structure with good accuracy compared with its actual failure load value is a very important task of study. Rankine and Merchant suggested aformula for obtaining the failure load of a complete structure by analogy from isolated strut case and this in fact is an approximate method. An isolated strut Of an elastic critical load (Wc), yield load (WL) and failure load (WF) similar to complete structure behaviour.
The application of Merchant equation for porta] and pitched-roof frames Ieads to an overage error equal to + 29% when the failure load calculated compared with its experimental value. Two suggested equations may be estimated after elastic-plastic analysis have been made on three different series of frames tested before till failure in Cambridge University laboratories by Dr. J.C. Heyman. It should be noticed that for frames having the value of (WL/WC) less than 0.3, the failure load of frames may be obtained using suggested equation (1), and for frames having the value of (WL/WC) bigger than 0.3 , the failure load obtained using suggested equation (2). These two suggested equations were estimated after the interpretation of the theoretical and experimental results of the different groups of frames used in that study. Tables and curves were given for the comparison of using these two suggested equations with the experimental failure load. To shows how the calculated value is so better compared with Merchant formula results.