Effective height, thickness and slenderness ratio

Definitions

• Effective height ($H_{eff}$): the height of the wall that is considered to buckle, obtained by multiplying the actual (unsupported) height $H$ by a factor depending on end restraint.
• Effective length ($L_{eff}$): the horizontal length considered to buckle between cross walls or other vertical supports, modified for the edge restraint.
• Effective thickness ($t_{eff}$): the thickness used in slenderness calculation. For a solid single leaf wall it is the actual thickness $t$; for a wall with piers or cross walls a stiffness factor increases it (1.0 to 2.0); for a cavity wall it is taken as two-thirds of the sum of the leaf thicknesses.
• Slenderness ratio ($SR$):

$$SR = \frac{H_{eff}}{t_{eff}} \quad \text{or} \quad \frac{L_{eff}}{t_{eff}}, \text{ whichever is smaller}$$

For a column, $SR$ is the effective height over the least lateral dimension.

Effective height (IS 1905)

 slab  ======  top fixed       free top -> 1.5H / 2.0H
        ||                         |
        ||  H                      |  H
        ||                         |
 ground ======  base fixed      #########
 0.75 H                          cantilever

Importance of slenderness

• A slender wall fails by buckling at a stress much lower than the crushing strength. The permissible stress is therefore reduced by $k_s$, which decreases as $SR$ rises.
• The code limits $SR$ (27 for load-bearing walls), so walls cannot be made taller or thinner than a certain limit.
• Slenderness can be reduced by increasing the thickness, adding piers or cross walls, or providing restraint at the top.