How is the slenderness ratio taken for a column versus a wall?

Column: greater of the two directions; wall: lesser of h_ef/t and L_ef/t

Column: lesser of the two; wall: greater of the two

When does the area reduction factor k_a = 0.7 + 1.5A apply?

When the cross-sectional area A is less than 0.2 m^2, as in most columns

What is the final check in designing an axially loaded column?

sigma = P/A must not exceed f_c = f_b k_s k_a k_p, otherwise increase size or strength

Only the slenderness ratio is checked

2082 Baisakh · 5+3 marks

Design steps of axially loaded brick column

Short answer

Assume column size, compute effective height (0.75H if fully restrained), ensure slenderness ratio ≤12, obtain basic compressive stress fb, apply stress reduction factor ks, area reduction factor ka (0.7+1.5A for A<0.2 m²), and shape factor kp, then check σ = P/A ≤ fb·ks·ka·kp. A column differs from a wall: SR limit 12 vs 27, uses greater slenderness of two directions, area reduction normally applies, and design treats the whole section, not per metre length.

Explain in detail the design steps of an axially loaded brick masonry column. How does it differ from the design of an axially loaded brick masonry wall?

Design steps for an axially loaded brick masonry column (IS 1905)

Assume column size (least dimension not less than about 200 to 230 mm and area as needed) and unit and mortar grade.
Loads: find axial load $P$ from roof or floor, add self weight of column.
Effective height (cl. 4.3.2): actual height for the direction in which it is laterally supported, twice the height for an unsupported direction; $0.75H$ if fully restrained at both ends (Table 4).
Slenderness ratio $SR = h_{ef}/t$ in each principal direction; take the greater. It must not exceed 12 for a column (Table 7).
Basic compressive stress $f_b$ for the unit strength and mortar grade (Table 8).
Factors: stress reduction factor $k_s$ from Table 9 for $SR$ and $e=0$ ; area reduction factor $k_a=0.7+1.5A$ when $A<0.2$ m $^2$ ; shape factor $k_p$ for the unit height-to-width ratio (Table 10).
Permissible stress $f_c=f_bk_sk_ak_p$ .
Check: $\sigma = P/A \le f_c$ . If not satisfied, increase size or unit/mortar strength and repeat.
Detail: stagger joints, use header courses, tie to beam or slab, avoid chases.

Difference from an axially loaded wall

Point	Column	Wall
Slenderness limit	$SR\le12$ (Table 7)	$SR\le27$ for cement mortar (20 for lime mortar)
Slenderness ratio	Greater of the two directions, $h_{ef}/t$	Lesser of $h_{ef}/t$ and $L_{ef}/t$ (horizontal stiffening by cross walls)
Effective length	Not used	Used; depends on cross walls, piers or buttresses
Area reduction factor $k_a$	Usually applies ( $A<0.2$ m $^2$ )	Normally 1.0 (analysed per metre run, 0.2 m $^2$ or more)
Design unit	Whole section	Per metre length of wall
Effective thickness	Actual thickness of column	Actual thickness; stiffening coefficient where piers or cross walls (Table 6)
Effective height	Based on lateral support in both directions	Based on top and bottom restraint (Table 4)

✓ Answer checked by Claude Opus 5.5 (high effort)

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Design steps of axially loaded brick column

Design steps for an axially loaded brick masonry column (IS 1905)

Difference from an axially loaded wall

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