Kani’s Method
- Structural analysis is one of the most important parts of civil engineering. The construction of high rise buildings and multi-storey buildings are increasing day by day.
- The high rise building requires the perfect analysis of frames and different structure of members features has a number of joints.
- Kani’s method was developed by Gasper Kani in the year 1940. The Kani’s method consists of the distribution of the unknown fixed end moments of the different structural members to the adjacent joints in order to satisfy the conditions of continuity of slopes and displacements.
- In this article,you will get to know about the Kani’s method and the Advantages of Kani’s method and how to use kani’s method.
- Kani’s method is also known as the Rotation contribution method. It is a developed method of iteration for the statically indeterminate buildings and structures which is an approximate method that can save a great deal of time compared to the moment distribution method.
- Kani’s method is considered for the further simplification of the moment distribution method for solving various problems.
- This method consists of allotting the an identified within moments of the various structural members to the adjoining joints.
- Kani’s method involves the distribution of the unknown fixed end moments of the different structural members to the adjacent joints in order to satisfy the different conditions of continuity of slopes and displacements.
Advantages of Kani’s Method
There are various advantages of this method in structural analysis of members are as follows
- The main advantage of using Kani’s method for structural analysis is because it is self-corrective.
- The Hardy cross method distributed only the unbalanced moments at the joints, and the Kani’s method distributes the total joints moment at any stage.
- Kani’s method is simple and easy as compared to other methods.
- All the computations of this method are carried out in a single line diagram of the structure.
- The effects of joint rotations are considered in each cycle of iteration.
- The convergence in this method is very fast which leads to the solution in just a few cycles of iterations.
How to Use Kani’s Method for Analysis?:
The junction of the beam with the column consists of rigid joints.
For all beams, I => 2I
For all columns, I => I
Framed structures are rarely symmetric and subjected to side sway that’s why the Kani’s method is best and much simpler as compared to the other types of methods.
Procedure of Kani’s Method
Step 1 :
Rotation stiffness at every end of the members of a structure is determined depending upon the various end conditions. When the Both ends are fixed
Kij= Kji= EI/L
When the near ends are fixed and the far ends are simply supported
Kij= ¾ EI/L; Kji= 0
Step 2 :
Rotational factors which are computed for all the members at each joint it is given are as follows
 Uij= -0.5 (Kij/ ?Kji)
The sum of the rotational factors at the joint is -0.5. The Fixed end moments including transitional moments and the moment releases and carry over moments are computed for the various members. The sum of the FEM at a joint is entered in the central square drawn at the various joints.
Step 3 :
Iterations can be commenced at any joint and the iterations commence from the left end of the structure. It is generally given by the following equations
 M?ij = Uij [(Mfi + M??i) + ? M? ji)]
Step 4 :
Initially the rotational components (which is the sum of the rotational moments at the far ends of the joint) is assumed to be zero. The further various iterations are taken into account of the rotational moments of the previous joints.
Step 5 :
Rotational moments are computed at each joint successively till all the joints are processed. This process completes one cycle of iteration.
Step 6 :
The above steps 4 and 5Â are repeated till the difference in the values of rotation moments will form the successive cycles is neglected.
Step 7 :
Final moments in the various members at each joint are calculated from the rotational members of the final iterations.
 Mij = (Mfij + M??ij) + 2 M?ij + M?jii
Step 8 :
Displacement factors are calculated for each storey given by
Uij = -1.5 (Kij/?Kij)
Frequently asked questions (FAQs) that could be included in your article about Kani’s Method:
What is Kani’s Method in structural analysis?
Kani’s Method, developed by Gasper Kani in 1940, is an iterative technique used for solving statically indeterminate structures. It simplifies the moment distribution method by distributing fixed end moments to adjacent joints, ensuring continuity of slopes and displacements.
What are the advantages of using Kani’s Method?
Kani’s Method offers several advantages, including self-correction during iterations, simplicity in computation (all done in a single line diagram), consideration of joint rotations, and fast convergence to solutions.
How does Kani’s Method differ from the moment distribution method?
Unlike the moment distribution method, which distributes unbalanced moments at joints, Kani’s Method distributes total joint moments at each iteration. It also accounts for joint rotations and is considered simpler and faster for solving complex structural problems.
When should Kani’s Method be used in structural analysis?
Kani’s Method is particularly useful for analyzing framed structures that are asymmetric or subjected to side sway. It simplifies the analysis process compared to other methods, making it ideal for quick iterative solutions.
What are the steps involved in using Kani’s Method for structural analysis?
The steps typically include determining rotational stiffness, computing rotational factors at joints, initiating iterations from one end of the structure, and repeating the process until convergence is achieved. This ensures accurate calculation of member moments and displacements.
How accurate is Kani’s Method compared to other structural analysis techniques?
Kani’s Method provides sufficiently accurate results for many engineering applications, especially for moderately complex structures. Its simplicity and rapid convergence make it a preferred choice in practical engineering scenarios.
Can Kani’s Method handle different types of structural member connections?
Yes, Kani’s Method can handle various types of structural member connections, including fixed ends, simply supported ends, and combinations thereof. Rotational factors are adjusted accordingly based on the specific end conditions of each member.
What are the limitations of Kani’s Method?
While effective for many applications, Kani’s Method may not accurately model highly non-linear behavior or intricate structural configurations. It is best suited for linear elastic analysis and may require adjustments or supplementary methods for more complex scenarios.
Is Kani’s Method widely used in modern structural engineering practices?
Yes, Kani’s Method remains relevant in modern structural engineering, particularly for preliminary design and quick feasibility studies. It provides engineers with a practical tool for analyzing and understanding the behavior of statically indeterminate structures.
Where can I learn more about Kani’s Method and its applications?
Additional resources, including textbooks on structural analysis and civil engineering journals, often provide detailed discussions and case studies showcasing the application of Kani’s Method in real-world projects.
