Columns
A column carries axial compression from the floors above, usually with some bending from beams framing in, frame action under lateral loads, or construction inaccuracy. Reinforced concrete columns have longitudinal bars to share compression and resist bending, and transverse ties or spirals that hold the bars in place against buckling and confine the concrete core.
Columns are first classed as short or slender by the ratio of effective length to least lateral dimension. Effective length depends on end restraint: a column held against rotation and sway at both ends behaves shorter than one free to sway. Short columns fail by material crushing. Slender columns bend sideways under load, adding secondary moments that must be included in design. Every column is designed for at least a minimum eccentricity to allow for imperfections.
For an axially loaded short column the design strength is the sum of concrete and steel contributions with their partial safety factors built in. Columns with bending are designed with interaction diagrams that plot axial capacity against moment capacity for a given section and steel ratio. Biaxial bending is checked with an interaction formula. Codes limit longitudinal steel to a minimum (to resist unexpected bending and creep) and a maximum (to allow concreting), and set tie diameter and pitch. In seismic zones, special confining reinforcement is required near the column ends.
Check slenderness about both axes; a rectangular column can be short about one axis and slender about the other.
Short if le / D < 12 (each axis)Minimum eccentricity: e_min = l/500 + D/30, not less than 20 mmAxial short column (e_min ≤ 0.05 D): Pu = 0.4 fck Ac + 0.67 fy AscBiaxial: (Mux/Mux1)^αn + (Muy/Muy1)^αn ≤ 1
- Pu = 0.4 fck Ac + 0.67 fy Asc is valid only for short columns with e_min not exceeding 0.05 times the lateral dimension.
- Larger moments need interaction diagrams; slender columns need additional moments (IS 456 cl. 39.7).
Problem. A short column 400 × 400 mm, M25, Fe 500, has 8 bars of 20 mm. Find its axial design strength using the IS 456 short-column formula, which already allows for a minimum eccentricity of up to 0.05 times the lateral dimension.
- Asc = 8 × 314 = 2 513 mm² (1.57 percent, within limits).
- Ac = 160 000 − 2 513 = 157 487 mm².
- Pu = 0.4 × 25 × 157 487 + 0.67 × 500 × 2 513 = 1 574 870 + 841 855 N.
- Pu = 2 417 kN.
- Validity: for an unsupported length of 3 m, e_min = 3 000/500 + 400/30 = 19.3 mm, taken as 20 mm = 0.05 × 400, so the formula applies.
Answer. About 2 420 kN
Quick quiz
1What separates short and slender columns?
The ratio of effective length to least lateral dimension (12 in IS 456).
2Why do columns need ties?
To stop bars buckling and to confine concrete.
3Why design for minimum eccentricity?
To allow for unavoidable imperfections and accidental eccentricity.
- IS 456 (India): Plain and reinforced concrete: general rules for materials, durability, design and construction.
- IS 13920 (India): Ductile design and detailing of reinforced concrete structures for seismic forces.
Clauses and documents to read
- IS 456:2000 cl. 25.1.2 (short and slender)
- IS 456:2000 cl. 25.4 (minimum eccentricity)
- IS 456:2000 cl. 39.3 (short axially loaded members)
- IS 456:2000 cl. 39.6 (biaxial bending)
- IS 456:2000 cl. 26.5.3 (column reinforcement)
Cited by number and clause only. We do not reproduce clause text, tables or figures (BIS Act 2016, s.10(5) and s.11). Check the current edition and amendments before use.
References and further reading
Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.
- S. Unnikrishna Pillai, Devdas Menon, Reinforced Concrete Design, McGraw Hill Education (India), latest edition.
- J. K. Wight, J. G. MacGregor, Reinforced Concrete: Mechanics and Design, Pearson, latest edition.
- A. H. Nilson, D. Darwin, C. W. Dolan, Design of Concrete Structures, McGraw Hill, latest edition.
- R. Park, T. Paulay, Reinforced Concrete Structures, Wiley, 1975.
Free and official sources
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