D-1Method for determining effective length of columns in frames

In the absence of a more exact analysis, the effective length of columns in framed structures may be obtained by multiplying the actual length of the column between the centres of laterally supporting members (beams) given in Fig. 27 and Fig. 28 with the effective length factor $K$, calculated by using the equations given below, provided the connection between beam and column is rigid type:

• a) Non-sway Fmmes (BracedFrame) [(see 4.12(a)] A frame is designated as non-sway frame if the relative displacement between the two adjacent floors is restrained by bracings or shear walls (see 4.1.2). The effective length factor, K, of column in non-sway frames is given by (see Fig. 27):

$K=\frac{\left[1+0.145\left(\beta_{1}+\beta_{2}\right)-0.265 \beta_{1} \beta_{2}\right]}{\left[2-0.364\left(\beta_{1}+\beta_{2}\right)-0.247 \beta_{1} \beta_{2}\right]}$

• b) Sway Frames (Moment Resisting Frames) [see 4.1.2(b)]

The effective length factor $K$, of column in sway frames is given by (see Fig. 28):

$K=\left[\frac{1-0.2\left(\beta_{1}+\beta_{2}\right)-0.12 \beta_{1} \beta_{2}}{1-0.8\left(\beta_{1.}+\beta_{2}\right)+0.6 \beta_{1} \beta_{2}}\right]^{0.5}$

where

$\beta_{1}, \beta_{2}$ are given, $\beta=\frac{\sum K}{\sum K_{\mathrm{c}}+\sum K}$

• $K_{\mathrm{c}}, K_{\mathrm{b}}=$ effective flexural stiffness of the columns and beams meeting at the joint at the ends of the columns and rigidly connected at the joints, and these are calculated by:

$K=C(I / L)$

Figure description:

EFFECTIVE LENGTH FACTOR

Effective Length Factor Nomogram

Annotations

• EFFECTIVE LENGTH FACTOR (text_label - position: centered within the chart area)
• FIXED (beta_1 = 0 (text_label - position: y = 0))
• HINGED (beta_1 = 1 (text_label - position: y = 1))
• FIXED (beta_2 = 0 (text_label - position: x = 0))
• HINGED (beta_2 = 1 (text_label - position: x = 1))

FIG. 27 COLUMN EFFECTIVE LENGTH FACTOR — NON-SWAY FRAME

Figure description:

PINNED 1 5.0 4.0 0.9 3.0 EFFECTIVE LENGTH FACTOR 0.8- 2.5

0.7

0.6 1.6 1.5 0.5- 1.4 B₁ 0.4- 1.3

0.3 1.2 1.15 0.2- 1.1

0.1- 1.05

FIXED 0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 FIXED PINNED P₂

FIG. 28 COLUMN EFFECTIVE LENGTH FACTOR — SWAY FRAME

• $I$ = moment of inertia of the member about an axis perpendicular to the plan of the frame.
• $\begin{aligned} L & =\text { length of the member equal to centre- } \\ & \text { to-centre distance of the intersecting } \\ & \text { member. }\end{aligned}$
• $C$ = correction factor as shown in Table 35.