Kani's Method & Column Analogy Method

Part A — Kani's method

1. Idea

Kani's method (Gaspar Kani, 1940s) is an iterative displacement method like moment distribution, but instead of distributing moments it distributes rotation contributions of the joints. Its great advantage: an error made in one cycle corrects itself in later cycles, because each cycle recomputes from the latest values.

2. Basic terms

• Fixed-end moments $M_F$ for each member end (as in other methods).
• Restraint moment at a joint $M_r=\sum M_F$ of the members meeting at it.
• Rotation factor of member $ij$ at joint $i$:

• Rotation contribution of joint $i$ to member $ij$:

where $\sum M_{ji}^{\prime }$ is the sum of the rotation contributions arriving at joint $i$ from the far ends of its members.

3. Procedure (no sway)

1. Compute fixed-end moments and restraint moments $M_r$ at each joint.
2. Compute rotation factors $u_{ij}$ at each joint.
3. Start with far-end contributions taken as zero; at each joint in turn compute $M_{ij}^{\prime }$ with the latest values.
4. Repeat cycles until the values stop changing.
5. Final end moment:

Fixed supports have zero rotation contribution; for a hinged far end the stiffness is modified (or the joint is treated as a free joint).

4. Frames with sway

For a storey that can sway, add a displacement factor for the columns:

and a displacement contribution $M^{\prime \prime }$ for each column of the storey, iterated along with the rotation contributions. The final moment becomes $M_{ij}=M_{F,ij}+2M_{ij}^{\prime }+M_{ji}^{\prime }+M_{ij}^{\prime \prime }$.