In structural engineering, columns transfer the weight of a structure to its foundation through a load transfer mechanism called compression. Columns can also be designed to resist lateral loads such as wind and earthquake.

Columns are frequently used to support beams or arches that support the upper portions of walls or ceilings or slabs. Columns have been used by many civilizations such as Egyptians, Greeks, Persians and Romans. Columns have also been made from many materials such as concrete, steel, timber and bamboo.

## Principles in column design

Columns are primarily compression members although they may also have to resist bending moments transmitted by beams. Reinforced concrete columns are subject to mainly axial loads and uniaxial moments, and this is because the usual arrangement of beams limits a large out-of- balance moments. On other hand, biaxial moments happen in corner and edge columns but the axial load will be small. This is why it is a common practice to use the same column section throughout the building. In general, compression elements such as columns are structural components that are designed to withstand compressive forces.

Columns may be classified as *short or slender*, *braced or unbraced*, depending on dimensional and structural factors. There are several sections of columns are used in practice including; circular, rectangular and square. Any form of column section can be used provided that the greatest overall cross-sectional dimension does not exceed 4 times its smaller dimension (h<4b). If it is greater, then it is advisable to design it as a wall.

## Slender and short columns

In terms of slenderness, columns can be either stocky or slender depending on a slenderness ratio. The slenderness ratio is a measure of how tall and thin an element is in relation to its width.

**Stocky columns** are less likely to bend or deform under load due to their low height-to-width ratio (slenderness ratio) and are more stable, making them better able to handle compressive forces.

**Slender columns** have a higher height-to-width ratio (slenderness ratio) and are more prone to bending or deformation under load, due to the P-Δ effect caused by large deflections. Therefore, they require more detailed design and analysis to ensure they can handle the loads they will be subjected to.

## Failure mechanisms of columns

Before carrying out a column design, it is important to understand how a column may fail under loading. There are several mechanisms by which columns can fail, including:

- Compression failure of the concrete or steel reinforcement, which is most likely to occur in short and stocky columns.
- Buckling, which is a common failure mode for long and slender columns due to the lateral instability caused by compression.
- A combination of buckling and compression failure, which can occur when a column is subjected to both compressive and lateral loads.

## Braced and unbraced Columns

A braced column is one that relies on a bracing system, such as shear walls or cores, to resist lateral loads, it only handles axial load and vertical loading-induced bending and does not contribute to the overall horizontal stability of the structure.

A column may be considered as unbraced if the lateral loads are resisted by the sway action of the column. Unbraced columns, which contribute to the stability of the structure are likely to have effective length factors greater than one. Conversely, braced elements (those that do not contribute to stability) are likely to have effective length factors smaller than one.

## Column classification chart

A column classification chart is a tool that engineers use to evaluate the characteristics and capacity of a column in relation to its dimensions and the loads it will experience.The column classification chart is divided into sections that correspond to different types of columns and their properties, including short, intermediate, long, and slender columns. Below is a sample of a column design chart.

In column design, one of the key steps is determining the slenderness ratio, λ, of the member. If this ratio is less than a specific threshold value, λlim, the column can be designed to resist only axial forces and moments resulting from an elastic analysis that takes into account geometric imperfections, known as First Order Effects.

When the slenderness ratio exceeds the limiting value, it is necessary to consider the additional moments that can occur as a result of structural deformations (second order effects) during the design process.

## Example on column design using Eurocode 2

Consider the design of a column of 300×300 mm with a height of 3m and a design axial load of 200kN and a bending moment of 150kNm. Let’s assume the concrete strength of the column is 30 MPa, and its reinforcement has a strength of 500MPa.

*Solution*

*Let’s first determine if the column is short;*

assuming the column is restained at both ends, then its effective length is L_{o} = 0.75 x L

where the height of the column L = 3m

L_{o} = 2.25m

The slenderness of the column, λ = L_{o}/i

where i is th radius of gyration

i = √(I/A_{c})

Cross-sectional area of the column, A_{c} = 300×300 = 90,000mm^{2}

The moment of inertia , I = bh^{3}/12 = (300×300^{3})/12 =675,000,000 mm^{4}

i = 86.6 mm

Then λ = 25.98

The limiting slenderness λ_{lim} = 20xAxBx C/ √(n) (BS EN 1992-1-1)

A = 1/(1+0.2Φ_{ef} )

Φ_{ef} is the effective creep ratio

but A can be assumed to be 0.7

B = √(1+2w) where w is the mechanical reinforcement ratio

Also B can be assumed to be 1.1

C = 1.7 – r_{m} where r_{m} is the ratio of the first order moments at the end of the column

C can also be assumed to be 0.7

The relative normal force, n = √[N_{Ed}/(A_{c}xf_{cd})]

N_{Ed} = 200 kN

Design concrete strength f_{cd} = 30/1.15 = 26.1 N/mm^{2}

n= 0.29

Then λ_{lim} = 20×0.7×1.1×0.7/(0.29) = 37.17

Since λ_{lim} > λ then the column is short.

*Determination of the column reinforcement*

The selection of reinforcement depends on design charts, and two variables are needed for this:

N/bhf_{ck} = 200×1000/(300x300x30) = 0.07

M/bh^{2}f_{ck} =150×10^{6} /(300×300^{2}x30) = 0.19

**Let then select a chart using the d _{2}/h ratio**

Assuming the bar and link size to be used in the column is H16 and R8 respectively.

Let the cover to the column also be 30 mm

d_{2} = cover + link + (bar diameter)/2

d_{2} = 30 + 8 + 16/2 =46

d_{2}/h ratio = 46/300 =0.15

when d_{2}/h = 0.15, the chart below is suitable:

using the chart A_{s}f_{yk}/bhf_{ck }= 0.55

A_{s } = 0.55 bhf_{ck } / f_{yk}

A_{s} = (0.55x300x300x30)/500 =2970 mm^{2 }

Number of bars | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Bar size (mm) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

6 | 28.3 | 56.6 | 84.9 | 113 | 142 | 170 | 198 | 226 | 255 | 283 |

8 | 50.3 | 101 | 151 | 201 | 252 | 302 | 352 | 402 | 453 | 503 |

10 | 78.5 | 157 | 236 | 314 | 393 | 471 | 550 | 628 | 707 | 785 |

12 | 113 | 226 | 339 | 452 | 566 | 679 | 792 | 905 | 1020 | 1130 |

16 | 201 | 402 | 603 | 804 | 1010 | 1210 | 1410 | 1610 | 1810 | 2010 |

20 | 314 | 628 | 943 | 1260 | 1570 | 1890 | 2200 | 2510 | 2830 | 3140 |

25 | 491 | 982 | 1470 | 1960 | 2450 | 2950 | 3440 | 3930 | 4420 | 4910 |

32 | 804 | 1610 | 2410 | 3220 | 4020 | 4830 | 5630 | 6430 | 7240 | 8040 |

Using the table above, the reinforcement in the column can be taken as 8H25 bars.

The area of reinforcement provided in the column is therefore, A_{sprov }= 3930 mm^{2}

The containment links for the column can be taken as 0.25 of the main steel

Φ_{link} = 0.25 x 25

Hence H8 bars can used in the column.

The spacing of the links = 20xΦ =20×25 = 500 mm ^{c}/_{c} (mid height)

Near the supports , the spacing is 0.6 x 500 = 300 mm ^{c}/_{c}

The links in the column can therefore be given as H8 @ 300 mm ^{c}/_{c} as shown below.

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