Question

A concrete column 300mm x 300mm in section, is reinforced by 10 longitudinal 20mm diameter round steel bars. The column carries a compressive load of 450KN. Find load carried and compressive stress produced in the steel bars and concrete. Take E_s = 200GN/m² and E_c = 15GN/m² .

Answer 1

Cross sectional Area of column = 300 × 300 = 90000mm² 

Area of steel bars As = 10 × (\(\pi\)/4)(20)² = 3141.59mm² 

Area of concrete = 90000 – 3141.59 = 86858.4 mm² 

Each component (concrete and steel bars) shorten by the same amount under the compressive load, and therefore

Strain in concrete = strain in steel

\(\sigma\)_c/E_c = \(\sigma\)_s/E_s

Where \(\sigma\)_c, \(\sigma\)_s are stress induced in concrete and steel respectively

\(\sigma\)_s = (E_s \(\sigma\)_c)/E_c

= (200 × 10⁹ /15 × 10⁹ ) \(\sigma\)_c = 13.33 \(\sigma\)_c

Further,

Total load on column = Load carried by steel + load carried by concrete

P = \(\sigma\)_s.A_s + \(\sigma\)_c.A_c

450 × 10³ = 13.33\(\sigma\)_c × 3141.59 + \(\sigma\)_c. 86858.4

= 128735.8 \(\sigma\)c

\(\sigma\)_c = 3.59 N/mm² 

\(\sigma\)_s = 13.33 × 3.59 = 46.95 N/mm²

Load carried by concrete P_c = \(\sigma\)_cA_c = 3.59 × 86858.4 = 311821.656 N = 311.82KN 

Load carried by steel P_s = \(\sigma\)_sA_s = 46.95 × 3141.59 = 147497.65 N = 147.49 KN