MATH: Reinforced Concrete Design 02

Problem 6.2
Design a square tied column is to support an axial dead load of 575 kN and an axial live load of 795 kN. Assume f'c = 27.6 MPa, and fy414 MPa. Use 28 nu main bars and 10 mm ties. Use mm main bars and 10mm ties.

Solution
In the design of column, first we assume value of steel ratio from 1% to 6% the gross concrete area. (Ast= O.O1Ag to O.O6Ag ). Obviously, if we assume small values of this ratio, the column size would be bigger and the steel area woul be smaller, and vice versa. The author suggests using a value less than the upper limit of 6%Ag, to provide an allowance for excess reinforcement due to availability of bar sizes. The ideal value is from 0.015Ag to 0.03Ag.

Let us assume Ast = 0.O2Ag

The axial load capacity of a tied column is
Pu = ø O.80[0.85 f'c (Ag -Ast) +fy Ast]

where ø = 0.70

Pu= 1.4DL + 1.7LL
= 1.4(575) + 1.7(795)
Pu= 2,156.5 kN

Ast= O.O2Ag
2156.5 x103 = (0.70)(0.80)[0.85 (27.6)( Ag-0.02Ag) + 414(0.02Ag)]

Ag= 123147 mm2

t2= 123,147
t= 351mm

Ast=0.02 (123147)
Ast=2463 mm2

π4 (28)2 x N= 2463
N= 4 bars

Use 355mm x 355mm column with 4-28mm bars
Spacing of ties:

16 x db=1628=448 mm
48 x tie diameter = 48 (10) = 480 mm
Least dimension of column = 355 mm

Use 10 mm ties at 355 mm o.c.