Table of Contents

**Short Column:**

When the slenderness ratio, l_{ex}/d and l_{ey}/b both, of the column is less than 12 then that column is known as short column. Here we only discuss about the design of short column.

Depending upon the loading, column is classified as axially loaded, un-axially loaded and bi-axial loaded. Practically there is no column subjected under perfect axial load. But if the maximum eccentricity is less than 5 % of the lateral dimension then it is treated as axially loaded for the calculation.

Normally the shape of column are circular, square and rectangular. Circular column are normally used as decorative purpose. The square column is used for axially loaded and bi-axially loaded column whereas rectangular column is used for uni-axially loaded column.

**Design step of short column without bending moment (axially loaded):**

Though column is axially loaded, it shall be designed for a minimum eccentricity of e_{min} = L/500 + D/30 subject to a minimum of 20mm.

Where, L = unsupported length

D = lateral dimension of column in the direction under consideration

**Step 1: Preliminary design of column**

The preliminary design of column is already discussed before. Click here for details.

**Step 2: Calculate factored load on the column**

The factored load of axially loaded column can be easily calculated manually as described in preliminary design of column. The intensity of live load is decreased by 10% for each floor above up to 40%.

*Note: It is not necessary to recalculate the factored load if the assumed load of column (ie. 20%) is satisfactory.*

**Step 3: Calculate the percentage of steel**

The percentage of steel is calculated for given size of column adopted from preliminary design. The percentage of longitudinal reinforcement can be calculated as,

P_{u} = 0.4 f_{ck} A_{c} + 0.67 f_{y }A_{sc}

Where, P_{u} = factored axial load

f_{ck }& f_{y }= characteristic strength of concrete and steel

A_{c }& A_{sc }= Area of concrete and steel

Here A_{sc} & A_{c} are expressed in percentage of gross area.

**Step: 4 Calculate the number of longitudinal bar**

It’s not a great deal to convert the percentage of steel in number of bar.

Area of longitudinal bar A_{sc }= percentage of steel * size of column

Assume the diameter of bar such that the number of reinforcement bar nearly equal to multiple of 4.

Area of longitudinal bar A_{sc} = number of bar * area of a reinforcement bar

**Step: 5 Calculate lateral ties**

- The diameter of lateral ties shall be greater than 1/4
^{th}of diameter of longitudinal bar but not less than 6mm - The spacing of lateral ties shall be least of following

= least lateral dimension

= 16 * diameter of longitudinal bar

=300mm

**Step: 6 Design summary with diagrammatic arrangement.**

*Note: In the rear field, the column without bending is rarely found and it is very simply to calculate.*

**Design step of short column bending moment (uni-axially or bi-axially loaded):**

The columns mostly found in field are bi-axially and uni-axially loaded. Let’s calculate about about the design steps:

**Step 1: Preliminary design of column**

The preliminary design of column is already discussed before. Click here for details.

**Step 2: Calculate of eccentricity along both axes**

The eccentricity of the column can be calculate by using code IS 456:2000 of clause 25.4

e_{min }= unsupported length / 500 + lateral dimension / 30 ≥ 20mm

**Step 3: Calculate factored axial force and bending moment on the column**

The axial force can be calculate easily as described in above design steps. The loads do not acted along the CG of the column in case of un-axially and bi-axially, so the bending moment acted on column. Simply bending moment is equal to factored load times the eccentric distance between CG of column and loads. There are different theoretical, empirical and approximate methods to calculate bending moment of the column like moment distribution and column analogy. Mostly these method are so complex, tedious and time consuming.

From the 19^{th} century, the practice of calculation of complex bending moment changed and now almost all the structure are designed through software. Here we only discussed about the moment calculation from the design analysis software.

**Step: 4 Calculate the ratio of effective cover to lateral dimension**

The lateral dimension (b, D) is derived from the preliminary design of column. Assume the size of longitudinal reinforcement and clear cover to calculate effective cover.

Note: The ratio of effective cover to lateral dimension (d’/b and d’/D) can be directly assumed for further calculations.

**Step 4: calculate p/f _{ck} and P_{u}/f_{ck}bD**

Where, p = percentage of steel

Either we can directly assume the percentage of steel [ 2%] or we have to calculate percentage of steel is calculated for given size of column adopted from preliminary design. The percentage of longitudinal reinforcement can be calculated as,

P_{u} = 0.4 f_{ck} A_{c} + 0.67 f_{y }A_{sc}

Where, P_{u} = factored axial load

f_{ck }& f_{y }= characteristic strength of concrete and steel

A_{c }& A_{sc }= Area of concrete and steel

Here A_{sc} & A_{c} are expressed in percentage of gross area.

*[Note: since the reinforcement also have to resist the bending moment acting on the column so assume steel should be greater than that from the above formula]*

**Step: 5 Calculate M _{ux1 }and M_{uy1}**

The moment M_{ux1 }and M_{uy1 }can be calculated from charts of SP16.

From clause 39.6 of IS code 456:2000,

The value of α_{n} can be calculated from the relation

α_{n }= 0.667 + 1.661 * P_{u}/P_{z}

where, P_{z} = 0.45 f_{ck} A_{c} + 0.75 f_{y }A_{sc}

** Step 6: Check for safe**

For the design to be safe check the equation given in 39.6 of IS 456:2000.

**Step 7: Calculate the number of longitudinal bar**

It’s not a great deal to convert the percentage of steel in number of bar.

Area of longitudinal bar A_{sc }= percentage of steel * size of column

Assume the diameter of bar such that the number of reinforcement bar nearly equal to multiple of 4.

Area of longitudinal bar A_{sc} = number of bar * area of a reinforcement bar

**Step: 8 Calculate lateral ties**

- The diameter of lateral ties shall be greater than 1/4
^{th}of diameter of longitudinal bar but not less than 6mm - The spacing of lateral ties shall be least of following

= least lateral dimension

= 16 * diameter of longitudinal bar

=300mm

**Step: 9 Design summary with diagrammatic arrangement.**

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