COLUMN DESIGN BY LIMIT STATE METHOD

The Design of R.C.C. Column is very important, as in the Framed Structured Building that is in the modern day construction the Frames are formed by networks of Columns and Beams. A Column is a Structural Member which is vertical and subjected to Compressive forces, and having it’s Length (Height) greater than the least cross-sectional dimension of it self. To Satisfactorily Complete the  Design of Column The Following Steps must followed.

STEP 1 :- Calculation of the Influence Area of the Column :

The first step is to find out the Influence Area of the Column to be Designed. The Influence Area of a column is the area of which load is being transferred to the column to be designed for. For this purpose in a framed structure small and medium building the design of column is done for the column whose Influence Area is the largest hence the load coming on the column will be so the greater of the any other column in that building hence all the other column having lesser Influence Area hence lesser Loads if provided with the same Designed parameters that required for the column having largest Influence Area, then the whole Structure will automatically become safe against the Loads.

STEP 2 :- Calculation of the Loads Coming on Column from the Influence Area :

In this step the Load Calculation is being done. This is done by calculating all the loads acting within the influence area.

The Loads acting are broadly classified as Dead Load (DL) and Live Load (LL). Dead Loads are the load of objects which cannot be moved from on place to another like the loads of Brick Work, Beams, Slabs etc. and the Live Loads are the loads coming from movable objects such as Humans, Chair, Table etc.

Thus We Need to Calculate the Dead Loads as well as Live Loads within the Influence Area, these are as follows in the general case of a Building :-

A)Dead Loads :

        I.            Due to weight of Slab                                    [25000 N/m³ ]

      II.            Due to weight of Floor Finish                        [500 N/m²]

    III.            Due to weight of Brick Masonry                   [19200 N/m³]

    IV.            Due to weight of Beam                                 [25000 N/m³]

      V.            Due to weight of Self Weight of Column        [25000 N/m³]

B) Live Load : It depends upon the Nature of the Structure, and it values for different structural nature are given in the concerned Code of Practice, like in India these are given in I.S.: 875-Part II.

For Residential Buildings it is generally considered @ 2KN/m² = 2000 N/m²

Now after correct calculation of above loads the Total Load is Calculated by,

Total Load on each floor = Dead Load + Live Load

Now this the actual load which will be acting on column for each floor, now if the building say 5 storied, then just multiply the value with the nos. of floors, like for five storied building multiply the Total Load on each story with 5.

Now thus the Total load acting on column at Column Base is Obtained and it is denoted with ‘P’.

Hence P= Total Load on each Floor X Nos. of Stories = (Dead Load + Live Load) X Nos. of Stories.

Now we shall move to the actual Designing to determine suitable Column sections and its Reinforcements so that the above load is safely resisted by the column Designed.

It can be done by Three main Methods of Design : a) Working Stress Method b) Ultimate Load Method and c) Limit State Method.

The Modern Practice is to use Limit State Method for all types of Designing, Hence I’ll discuss here the Limit State Method Of Design Of Column.

STEP 3 :- Finding The Gross Cross-Sectional Area Required For The Column :

This is the one of the most important and main step of the Design of Column.

First in the Limit State Method of Design we must increase the load acting on the column with a Load Factor so that if there will be any accidental increase of loads the column will be still safe to resist the load without a failure. The Factor of Safety for Dead Load + Live Load Combination is 1.5, hence we must multiply the load action on column (P) with the 1.5 to obtain the Ultimate Load that is the Factored Load of the Column that is P_u.

Hence Factored Load, P_u = 1.5 X P

For Design we will work with this value of load.

Now before going on I’m here to say that I will design according to the Code Of Practice of I.S.: 456-2000

The Ultimate Load of a Column is given by,

P_u = 0.4.f_ck.A_c + 0.67.f_y.A_sc   [Equation I]

Where, P_u = Ultimate Load of the Column in N/mm²

              f_ck= Yield Strength of Concrete in N/mm²

              A_c = Area of Concrete (Cross-Sectional Area) of Column in mm²

               f_y = Yield Strength Of Steel in N/mm²

            A_sc = Area of Steel (Cross-Sectional Area) in Column in mm²

Now the column consists of Concrete and as well as Steel in the form of Reinforcements hence the Total Cross-Sectional Area of Column is made of Area of Concrete and Area of Steel.

The Total Cross-Sectional area of Column can be also termed as Gross Cross-Sectional Area of Column and it’s denoted by A_g.

Hence, Gross Cross-Sectional Area of Column = C/S  Area of Concrete + C/S Area of Steel

Therefore, A_g = A_c + A_sc

And hence, A_c = A_g - A_sc

Now putting the above obtained value in the original equation (Equation I) we get,

P_u = 0.4.f_ck.(A_g-A_sc) + 0.67.f_y.A_sc  [Equation II]

Now Assume the Percentage of Steel you want to use ranging anywhere from 0.8% to 6% with Respect to Gross Cross-Sectional Area of the Column (A_g). Say Assuming Steel as 1% of A_g it means Area of Steel A_sc = 1% of A_g = 0.01A_g

The higher will be the percentage of steel used the lower will be A_g and thus lesser will be the cross-sectional dimension of the column. But the as the Price of Steel is very high as compared to the Concrete hence it is desirable to use as less as steel possible to make the structure economical, again if the percentage of steel is lowered then the A_g will increase at higher rate, about 30% with decrease of just 1% of steel and so each lateral dimension of the column will increase and will cause a gigantic section to be provided to resist the load. Therefore both the factors are to be considered depending upon the amount of loadings.

My suggestion is to use the following Percentage of steel for the Design, Which I’ve found to be effective and to produce economical and safe section of Column.

Loading (P_u) in N                           Percentage Of Steel  for Satisfactory Design

Below 250000 --------------------------------------------0.8%

250,000 to 500,000 --------------------------------------1.0%

500,000 to 750,000 --------------------------------------1.5%

750,000 to 1000,000 -------------------------------------2.0%

1000,000 to 1500,000 -----------------------------------2.5%

1500,000 to 2000,000 -----------------------------------3.0%

And so on, with increase of each 250,000 N increasing the Percentage of Steel as 0.5%.

Now  input the value of the A_sc in the form of A_g in the Equation I. For example suppose 1% Steel is used then the equation will be like the one below :-

P_u = 0.4.f_ck.(A_g-0.01A_g) + 0.67.f_y.0.01A_g

Therefore, if we know the Grade of Concrete and Grade of Steel to be used and Factored Load coming on the Column and Assuming the Percentage of steel required appropriately then we can Very Easily Calculate the Gross-Sectional Area (A_g) of the Column required from the above form of the equation.

Now as the Ag is obtained thus the Lateral Dimensions of the Column that are the sides of the column can be easily determined.

The A_g or Gross-Sectional Area of the Column means that it is the product of the two lateral sides of a column [i.e. Breadth (b) X Depth (D)], hence reversely knowing the A_g we can determine the Lateral Dimensions.

For making a Square Section just Determine the Root Value of the A_g. Like if the Value of A_g is 62500 mm² Then considering square section of a column we can get each side

Also Rectangular Column Sections Can be made by using different proportion say b : D = 1 : 2 , Hence D=2b , Therefore, A_g = b X D = b X 2b = 2b² or b=

Hence D can be also determined as D=2b after Calculating the b.

Most of the times after calculating the sides of a column it will give results such as 196.51mm or 323.62 etc. values, which practically cannot be provided at field, hence we must increase those values to the nearest greater multiple of 25mm (i.e. 1 inch). For examples a value of 196.51mm may be increased to 200mm or 225mm or 250 mm even, and a value of 323.62mm may be increased to 350mm. more it will be increased the more it will be safer, but it is uneconomical to increase by a very high amount, it should not be increased more than by 75mm to consider the economical factor.