What should be column and beam size for 6m span,size of column depend on total load applied on the column, alignment of column and span between two column, There are axial loads and lateral loads. It also depends on various factors like number of floors, span between two column, is it short or slender.
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You cannot fix the beam depth based solely on these parameters. How high is the column?,What is the load?,Are these steel beams and columns or are they reinforced concrete columns?,If so what grade of steel, or what grade of Concrete?,Without knowing all this no definite answer is possible.
What should be column and beam size for 6m span
Column size depends on various factors like number of floors, span between two column, is it short or slender, For 6m span 1 storey/single floor/ground floor/G+0 residential building, it could be 230mmx230mm (9″×9″), for G+1 it could be 300mmx 300mm (12″×12″), for G+2 it could be 300mmx 380mm (12″×15″),for G+3 it could be 380mmx 450mm (15″×18″) and for G+4 it could be 380mmx 530mm (15″×21″) using M20 grade of concrete ratio 1:1.5:3 with Fe500 grade of steel when a tributary area 18m×18m and span between each column is 6m consists of 16 column where 445kN to 2227kN load is applied on each column.
For simply supported beams, L/d = 20, as per IS 456–2000, so beam depth d = L/20 = 6000mm/20 = 300mm, this should also be not more than 1/4 th of the clear span as per IS 13920–2016, d= 1/4*6000 = 1500mm,hence depth can be taken as d = 300mm, b/d ratio of beam should preferably be more than 0.3, as per IS 13920–2016,so b/d = 0.3,b = 0.3d = 0.3×300 = 90 mm, but width should not be less than 200mm, as per IS 13920–2016, So take minimum width b = 230mm because brick wall construction 9 inch thick common in India.
The size of the beam depends on the span of the beam and the load on the beam. In multi-storey design plans, the size of the plinth beam, primary and secondary beams depend on the number of stories and loads acting on the beam. For 6m span size of beam should be 230mm×300mm (9″×12″) for residential building in which width is 230mm (9″) and beam depth is 300mm (12″) using M20 grade of concrete and Fe500 grade of Steel.