Find out load carried and compressive stress:
The concrete column 300mm x 300mm in section can be reinforced by 10 longitudinal 20mm diameter round steel bars. The column carries compressive load of 450 KN. Find out load carried and compressive stress produced in steel bars and concrete. Take
Es = 200GN/m^{2} and
Ec = 15GN/m^{2}.
Sol.: The cross sectional Area of column = 300 × 300 = 90000mm^{2}
Area of steel bars As = 10 × ( Π /4)(20)^{2} = 3141.59mm^{2}
Area of concrete = 90000 - 3141.59 = 86858.4 mm^{2}
Each component shorten by the same amount under compressive load, and thus
Strain in concrete = strain in steel
σ c/Ec = σ s/Es
Where σc, σ s are stress induced in the concrete and steel respectively
σs = (E_{s} σ_{s})/E_{c}
= (200 × 10^{9} /15 × 10^{9}) σ_{c} = 13.33 σ_{c}
Furthermore,
Total load on column = Load carried by steel + load carried by concrete
P = σ_{s}.As + σ_{c}.Ac
450 × 103 = 13.33σ c × 3141.59 +σ c. 86858.4
= 128735.8 c
σ_{c} = 3.59 N/mm^{2 } .......ANS
σ_{s} = 13.33 × 3.59 = 46.95 N/mm^{2 } .......ANS
Load carried by the concrete P_{c} = σcAc = 3.59 × 86858.4 = 311821.656 N = 311.82KN .......ANS
Load carried by the steel P_{s} = σ_{s}A_{s} = 46.95 × 3141.59 = 147497.65 N = 147.49 KN .......ANS