Design Steps of Short Column by Limit State Method (LSM)

Column

A column is a vertical compression member which provides support to the beam. Column can be devided into two types.

i) Short Column

If the slenderness ratio of the column is less than or equal to 12, then the column is known  as short colums.

ii) Long Column

If the slenderness ratio of the column is  greater than 12, then the column is known as short colums.

There are two cases of designing short colums.

1) When the dimension(B and D) of the column are given

Given -: B, D, L `f_(ck), f_(y)` and P

• Calculate effective length of column by analysing the end conditions and using the IS 456 Table No. 28 (Page No. 94)

• Calculate the slenderness ratio and determine the type of column

Slenderness Ratio `SR =l_(eff)/(l e a s t\ latera l \ di mension)`

If `SRle12`, then the column is short else long.

•Calculate the minimum eccentricity 

`e_(min)=L/500 +(lateral\ di mension)/30`

(Use both lateral dimensions)

Check for minimum eccentricity 

`e_(min)lt0.05timeslateral\ d imension `

•Calculate Area of steel by using the relation,

`P_u=0.4f_(ck)A_c+0.67f_yA_(sc)`

•Calculate No. of Bar reaquired by assuming suitable dia bar.

No. of bar `=A_(sc)/A_(b ar)`

•Calculate the diameter of lateral ties (Max of below)

i)`1/4` of dia of longitudinal bar (biggest bar)

ii) 6mm

If the obtained value is less than 8mm then provide 8mm bar.

•Calculate the pitch of lateral ties,(Min of below)

i) least lateral dimension

ii) 16 × dia of longitudinal bar (smallest bar)

iii) 300mm

2) When the dimension (B and D) of column are not given

Given-: L `f_(ck), f_(y)` and P

•Assume percentage of steel ranging from 0.8% to 4%. (Recommended 1.2%)

Now `A_(sc)` will be `1.2% of A_g implies A_(sc)=0.012A_g`

`A_(c)=A_g-A_(sc)`

`A_(c)=A_g-0.012A_g implies A_(c)=0.988Ag`

•Calculate the value of `A_g` by using the relation,

`P_u=0.4f_(ck)A_c+0.67f_yA_(sc)`

Or,  `P_u=0.4f_(ck)0.988A_g+0.67f_y0.012A_(g)`

•Assume square column,

Now, `B=D=sqrt(A_g)`

Here we calculated B and D, Now this condition is similar to above condition. So follow the above steps for further calculation.

Notations,

`B` is short lateral dimension.

`D` is long lateral dimension

`L` is Unsupported Length of column

`l_(eff)` is effective length of column

`A_g` is Gross Area of column 

`A_c` is Area of concrete

`A_(sc)` is Area of steel

`SR` is Slenderness ratio

`e_(min)` is minimum eccentricity 

`f_(ck)` is stress on concrete

`f_y` is stres on steel

`P` is load on column

`P_u` is factored load