Find out load carried and compressive stress - steel bar, Mechanical Engineering

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
E
s = 200GN/m2  and

Ec  = 15GN/m2.

Sol.: The cross sectional Area of column = 300 × 300 = 90000mm2

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

Area of concrete = 90000 - 3141.59 = 86858.4 mm2

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  = (Es σs)/Ec

= (200 × 109 /15 × 109) σc  = 13.33  σc

Furthermore,

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

P = σs.As  +     σc.Ac

450 × 103 = 13.33σ c × 3141.59 +σ   c. 86858.4

= 128735.8 c

σc = 3.59 N/mm                                                                                                           .......ANS
σ
s  = 13.33 × 3.59 = 46.95 N/mm                                                         .......ANS

Load carried by the concrete Pc =   σcAc    = 3.59 × 86858.4 = 311821.656 N = 311.82KN .......ANS

Load carried by the steel Ps  = σsAs  = 46.95 × 3141.59 = 147497.65 N = 147.49 KN      .......ANS

Posted Date: 10/23/2012 2:16:24 AM | Location : United States







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