What is Kani’s method? What are the limitations of this method?
Answers
Answer:
For fixed ends
K= I/L
K=3I/4L
Distribution Factor (DF)
DF= Ki / ∑Ki
Rotation Factor (RF)
RF = -0.5 × DF
Explanation:
This method was developed by Dr. Gasper Kani of Germany in 1947. It offers an iterative scheme for applying slope deflection method. It is an approximate method of calculation for indeterminate structures, especially portal frames and multi-story frames with fixed connections.
Other two methods used are slope deflection and moment distribution method. While these two methods become clumsy and is time consuming. It is similar to moment distribution but a much simpler and less time-consuming method. It is also known as Rotation contribution method. This method involves distributing the unknown fixed end moments to adjacent joints to satisfy the condition of continuity of slope and displacement.
Kani’s Equation:
From slope deflection equation
Mij = MFij + (2EI/L)[2θi + θj]
Replacing mij = 2EKij θi , we get:
Mij = MFij + 2mij + mji ——————–[ 1 ]
The final end moments are calculated using equation (1).
Guideline for solving problems
Problems can be of following types
Non-sway (Beams and frames)
Sway
General Procedure for solving problems with no sway or settlement of beams or frames
Calculation of the fixed end moments of each span by considering them as fixed.
Calculation of Rotation factor.
Perform iteration by gauss-Siedal method and finding out final end moments.
Fixed End Moments
All the ends are assumed to be fixed. Some commonly fixed end moments are given below.
Rotation Factor (RF)
It is half negative of distribution factor.
Consider a joint and name all the members from that joint. Find relative stiffness factor and its total.
Relative Stiffness factor (K)
For fixed ends
K= I/L
K=3I/4L
Distribution Factor (DF)
DF= Ki / ∑Ki
Rotation Factor (RF)
RF = -0.5 × DF
https://brainly.in/question/6750879
#SPJ3