This document discusses short columns and long columns according to IS 456:2000. It defines the unsupported length and effective length of columns. The slenderness ratio is used to determine whether a column is short or long. Short columns have slenderness ratios less than 12 and fail by crushing, while long columns have at least one slenderness ratio greater than 12 and fail by buckling. Two examples are provided to illustrate how to calculate the slenderness ratios and classify columns as short or long based on the ratios.

1. Long Column, Short Column
Nadya Baracho
Assistant Professor
Don Bosco College of Engineering, Fatorda, Goa

2. UNSUPPORTED LENGTH
 FOR BEAM-SLAB CONSTRUCTION
(IS 456:2000 CLAUSE 25.1.3 b)
 Clear distance between the floor
and the underside of the shallower
beam framing into the columns in
each direction at the next higher
floor level.
 The unsupported length is denoted
by l in the figure on the right.

3. EFFECTIVE LENGTH
l is the unsupported length
Refer Annex E (Clause 25.2), IS
456:2000 for effective length

4. SHORT & SLENDER
(LONG) COLUMN
IS 456:2000 CLAUSE 25.1.2
When BOTH the slenderness
ratios
𝑙 𝑒𝑥
𝐷
< 12
And,
𝑙 𝑒𝑦
𝑏
< 12
Column in short compression
member.
Else it is a slender compression
member.
NOTE: If the beam
depth in both
directions is same, then
𝑙 𝑒𝑥 = 𝑙 𝑒𝑦

5. EFFECTIVE LENGTH
 𝑙 𝑥= unsupported length in respect of the major axis,
 𝑙 𝑒𝑥= effective length in respect of the major axis,
 D = depth in respect of the major axis,
 𝑙 𝑦= unsupported length in respect of the minor axis,
 𝑙 𝑒𝑦= effective length in respect of the minor axis,
 b = width of the member.
 To calculate effective length
 𝑙 𝑒𝑥 = 𝑘 × 𝑙 𝑥
 𝑙 𝑒𝑦 = 𝑘 × 𝑙 𝑦
 k is the co-efficient based on end conditions (Table 28, IS
456:2000)

6. Example
 Find whether a column of
unsupported length 3.5 m and
400mm x 230mm is short column or
long column. The column is
effectively held in position and
restrained against rotation at both
ends.
 Solution:
𝑙 = 3500 𝑚𝑚
𝑙 𝑒𝑥 = 𝑙 𝑒𝑦 = 3500 × 0.65 = 2275 𝑚𝑚
(k = 0.65, as per Table 28)
𝑏 = 230 𝑚𝑚
𝐷 = 500 𝑚𝑚
𝑙 𝑒𝑥
𝐷
=
2275
400
= 5.68 < 12
𝑙 𝑒𝑦
𝑏
=
2275
230
= 9.89 < 12
∴ the column is a short column.

7. Example
 Find whether a column of effective
length 3.5 m and 400mm x 230mm is
short column or long column. The
column is effectively held in position at
both ends but not restrained against
rotation.
 Solution:
𝑙 = 3500 𝑚𝑚
𝑙 𝑒𝑥 = 𝑙 𝑒𝑦 = 3700 × 1 = 3500 𝑚𝑚
(k = 1, as per Table 28)
𝑏 = 230 𝑚𝑚
𝐷 = 400 𝑚𝑚
𝑙 𝑒𝑥
𝐷
=
3500
400
= 8.75 < 12
𝑙 𝑒𝑦
𝑏
=
3500
230
= 15.21 > 12
∴ the column is a long column.

8. Failure Mode
 Short Column fails mainly by
crushing.
 Long Column fails mainly by
buckling
Image Source : chegg.com

9. Thank You