Analysis of Frames - 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 :

1. Hardy Cross method distributed only the unbalanced moments at joints, whereas Kani’s method distributes the total joint moment at any stage of iteration.

2. The more significant feature of Kani’s method is that the process is self corrective. Any error at any stage of iteration is corrected in subsequent steps.

Framed structures are rarely symmetric and subjected to side sway, hence Kani’s method is best and much simpler than other methods like moment distribution method and slope displacement method.

Procedure 

1. Rotation stiffness at each end of all members of a structure is determined depending upon the end conditions.

The stiffness factors 

a) If Both ends are fixed

Kab= Kba = I/L

b) If Near end fixed and far end simply supported

Kab = ¾ I/L and Kba = 0

2. The Rotational factors are computed for all the members at each joint it is given by

rab= - 0.5 (Kab/ Sum of Kab)

Note: 

The sum of rotational factors at a joint is 0.5 

3.Fixed end moments (FEM) including transitional moments, moment releases and carry over moments are computed for members. 

The sum of the FEM at a joint ,and rotational factors are entered in the square drawn at the joint .

3. Iterations can be commenced at any joint however the iterations commence from the left end of the structure generally given by the equation

mab = rab [(Mfi + msi) +sum of mba)]

4. Initially the rotational components ? Mji (sum of the rotational moments at the far ends of the joint) can be assumed to be zero. Further iterations take into account the rotational moments of the previous joints.

5. Rotational moments are computed at each joint successively till all the joints are processed. This process completes one cycle of iteration.

6. Steps 4 and 5 are repeated till the difference in the values of rotation moments from successive cycles is neglected.

7. Final moments in the members at each joint are computed from the rotational members of the final iterations step.

Mab = (Mfab + msab) + 2 mab + mba

The lateral translation of joints (side sway) is taken into consideration by including column shear in the iterative procedure.

8. Displacement factors are calculated for each storey given by

Uij = -1.5 (Kij/ sum of Kij)