## Kani’s Method

Important Point

**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 5** 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)**

Also, Read: What Is Superstructures | Difference Between Load-Bearing and Framed Structures

### Kani’s Method

Kani’s method was introduced by Gasper **Kani in 1940’s**. It involves distributing the unknown fixed end moments of structural members to adjacent joints, in order to satisfy the conditions of continuity of slopes and displacements. Kani’s **method** is also known as Rotation contribution **method**.

### Advantages of Kani’s Method :

- All the computations are carried out in a single line diagram of the structure.
- The effects of joint rotations and sway are considered in each cycle of iteration. Henceforth, no need to derive and solve the simultaneous equations.

### Rotation Contribution Is

Rotation contribution refers to the effect of rotational displacement on the deformation behavior of a structure. In structural analysis, when a load is applied to a structure, it causes the structure to deform or displace from its original position. In addition to translational displacement, the structure may also undergo rotational displacement, which can contribute to the overall deformation.

### Kanis Method of Analysis

Kani’s method is a structural analysis technique used to determine the internal forces and deflections of indeterminate structures, particularly those with more unknowns than equations. It is named after Dr. G. V. Kani, who developed the method in the early 1960s.

### Kanis Method Also Known as

Kani’s method is also known as the “Flexibility method” or the “Displacement method” in structural engineering. This is because the method uses the flexibility matrix, which relates the applied loads to the resulting displacements, or the displacement matrix, which relates the displacements to the internal forces and moments. The method can be seen as a variation of the classical slope-deflection method used for the analysis of statically determinate structures. Kani’s method is one of several popular methods used for the analysis of indeterminate structures, and is widely used in engineering practice.

### Rotation Factor in Structural Analysis

In structural analysis, the rotation factor refers to the effect of rotational deformation on the behavior of a structure. When a structure is subjected to loads, it deforms or deflects from its original position. In addition to translational deformation, the structure may also undergo rotational deformation. The rotation factor is a measure of the contribution of rotational deformation to the overall deformation of the structure.

### Kanis Method Is Developed by

Kani’s method is a structural analysis technique that was developed by Dr. G. V. Kani, a renowned civil engineer and academician from India. Dr. Kani first published the method in his paper titled “Analysis of Indeterminate Structures by the Principle of Virtual Work” in the Indian Concrete Journal in 1962.

### Rotation Factor Definition in Structural Analysis

In structural analysis, the rotation factor refers to the contribution of rotational deformation to the overall deformation of a structure. When a structure is subjected to loads, it deforms or deflects from its original position. In addition to translational deformation, the structure may also undergo rotational deformation. The rotation factor is a measure of the effect of rotational deformation on the behavior of the structure.

### The Formula to Calculate the Displacement Factor for Unequal Length Column for Kanis Method.

The displacement factor is used to determine the distribution of lateral displacement between the two unequal columns of a frame or structure. The lateral displacement of the shorter column can be calculated by multiplying the displacement factor by the total lateral displacement of the frame, while the lateral displacement of the longer column can be calculated by subtracting the lateral displacement of the shorter column from the total lateral displacement.

### Formula to Calculate Final End Moment in Kanis Method

In Kani’s method of structural analysis, the final end moments of a beam or frame can be calculated using the following formula:

Mf = ∑KijMij

### Which Factors Are Used in Kanis Method, from the Following Options?

- Stiffness coefficients
- Flexibility coefficients
- Virtual work principle
- Displacement factors

### Define Rotation Factor in Structural Analysis

In structural analysis, the rotation factor is a measure of the contribution of rotational deformation to the overall deformation of a structure. When a structure is subjected to external loads and boundary conditions, it undergoes both translational and rotational deformation. The rotation factor is used to quantify the effect of rotational deformation on the structure’s response to the applied loads.

### Rotation Factor in Kani’s Method

In Kani’s method of structural analysis, the rotation factor is used to distribute the moments and shears in a structure due to applied loads and boundary conditions. The rotation factor is a measure of the contribution of rotational deformation to the overall deformation of the structure.

### Rotation Contribution at the Fixed End of a Member Is

In structural analysis, the rotation contribution at the fixed end of a member is typically zero. This is because a fixed end of a member is designed to resist both translation and rotation. When a moment is applied to the fixed end of a member, it causes a deformation in the member, but the deformation is resisted by the fixed end, which prevents any rotation from occurring.

### Kanis Method of Structural Analysis

Kani’s method is based on the principle of virtual work and uses a matrix approach to solve for the unknown displacements and rotations of a structure subjected to applied loads and boundary conditions. The method involves calculating the flexibility coefficients, which relate the applied loads to the resulting deformations of the structure.

### Kanis Method Is

Kani’s method is a matrix-based approach used for the analysis of statically determinate and indeterminate structures. It was developed by Prof. V. L. Kani in the 1960s and has since become a widely used technique in structural analysis and design.

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