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Rammamrutham, L. Force methods- Originally developed by James Clerk Maxwell in , later developed by Otto Mohr and Heinrich Muller-Breslau, the force method was one of the first methods available for analysis of statically indeterminate structures. As compatibility is the basis for this method, it is sometimes also called as compatibility method or the method of consistent displacements.
In this method, equations are formed that satisfy the compatibility and force- displacement requirements for the given structure in order to determine the redundant forces. Once these forces are determined, the remaining reactive forces on the given structure are found out by satisfying the equilibrium requirements.
Displacement methods- The displacement method works the opposite way. In these methods, we first write load-displacement relations for the members of the structure and then satisfy the equilibrium requirements for the same. In here, the unknowns in the equations are displacements. Unknown displacements are written in terms of the loads i.
As the displacements are determined, the loads are found out from the compatibility and load- displacement equations. Some classical techniques used to apply the displacement method are discussed. Slope deflection method- This method was first devised by Heinrich Manderla and Otto Mohr to study the secondary stresses in trusses and was further developed by G. Maney extend its application to analyze indeterminate beams and framed structures.
The fundamental slope-deflection equation expresses the moment at the end of a member as the superposition of the end moments caused due to the external loads on the member, while the ends being assumed as restrained, and the end moments caused by the displacements and actual end rotations. A structure comprises of several members, slope-deflection equations are applied to each of the member.
Using appropriate equations of equilibrium for the joints along with the slope-deflection equations of each member we can obtain a set of simultaneous equations with unknowns as the displacements. Once we get the values of these unknowns i.
Moment distribution method- This method of analyzing beams and multi-storey frames using moment distribution was introduced by Prof. Hardy Cross in , and is also sometimes referred to as Hardy Cross method. It is an iterative method in which one goes on carrying on the cycle to reach to a desired degree of accuracy.
To start off with this method, initially all the joints are temporarily restrained against rotation and fixed end moments for all the members are written down. Each joint is then released one by one in succession and the unbalanced moment is distributed to the ends of the members, meeting at the same joint, in the ratio of their distribution factors.
These distributed moments are then carried over to the far ends of the joints. Again the joint is temporarily restrained before moving on to the next joint. Same set of operations are performed at each joints till all the joints are completed and the results obtained are up to desired accuracy. The method does not involve solving a number of simultaneous equations, which may get quite complicated while applying large structures, and is therefore preferred over the slope-deflection method.
Gasper Kani of Germany in the year The method is named after him. This is an indirect extension of slope deflection method. This is an efficient method due to simplicity of moment distribution. The method offers an iterative scheme for applying slope deflection method of structural analysis.
This method may be considered as a further simplification of moment distribution method wherein the problems involving sway were attempted in a tabular form thrice for double story frames and two shear coefficients had to be determined which when inserted in end moments gave us the final end moments. All this effort can be cut short very considerably by using this method.
The effects of joint rotations and sway are considered in each cycle of iteration. Henceforth, no need to derive and solve the simultaneous equations. This method thus becomes very effective and easy to use especially in case of multistory building frames.
The method is self correcting, that is, the error, if any, in a cycle is corrected automatically in the subsequent cycles. The checking is easier as only the last cycle is required to be checked.
The convergence is generally fast. It leads to the solutions in just a few cycles of iterations. During recent years, there has been a growing emphasis on using computer aided softwares and tools to analyze the structures. There has also been advancement in finite element analysis of structures using Finite Element Analysis methods or matrix analysis. These developments are most welcome, as they relieve the engineer of the often lengthy calculations and procedures required to be followed while large or complicated structures are analyzed using classical methods.
But not all the time such detailed analysis are necessary to be performed i. It may even happen that sometimes the analysis software or tool is not available at hand?
Or the worst case, the computer itself is not available?? Then in such cases, accurate analysis of such large and complicated structures involving so many calculations is almost impossible. Now-a-days, high rise buildings and multi-bay-multi-storey buildings are very common in metropolitan cities. The analysis of frames of multi- storeyed buildings proves to be rather cumbersome as the frames have a large number of joints which are free to move.
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