Question

Kani method is an extension of which method ?

Answer 1

Answer:

Kani’s Method:

This method was introduced by Gasper Kani’s in 1947. 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.

Moment Distribution Method:

This method was first introduced by Prof. Hardy Cross is widely used for the analysis of intermediate

structures. In this method first the structural system is reduced to its kinematically determinate form, this is

accomplished by assuming all the joints to be fully restrained. The fixed end moments are calculated for this

condition of structure. The joints are allowed to deflect rotate one after the other by releasing them successively.

The unbalanced moment at the joint shared by the members connected at the joint when it is released.

Explanation:

Analysis by Kani’s Method:

Framed structures are rarely symmetric and subjected to side sway, hence Kani’s method is best and

much simpler than other methods.

PROCEDURE:

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

a. Both ends fixed

Kij= Kji= EI/L

b. Near end fixed, far end simply supported

Kij= ¾ EI/L; Kji= 0

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

Uij= -0.5 (Kij/ ?Kji)

{THE SUM OF ROTATIONAL FACTORS AT A JOINT IS -0.5}

(Fixed end moments including transitional moments, moment releases and carry over moments are computed for

members and entered. The sum of the FEM at a joint is entered in the central 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

M?ij = Uij [(Mfi + M??i) + ? M?ji)]

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.

Mij = (Mfij + M??ij) + 2 M?ij + M?jii

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/?Kij)