A reinforced concrete column of 450 mm square has four steel bars of 30 mm diameter as shown in Fig. 1.27. It carries as load of 600 kN. Find the stresses in steel and concrete if their modulii of elasticity are 210 GPa and 22 GPa, respectively. Also calculate the adhesive force concrete and steel

Question

A reinforced concrete column of 450 mm square has four steel bars of 30 mm diameter as shown in Fig. 1.27. It carries as load of 600 kN. Find the stresses in steel and concrete if their modulii of elasticity are 210 GPa and 22 GPa, respectively. Also calculate the adhesive force concrete and steel.

Accepted Answer

Area of steel bars,

[latex]A_s = 4 imes \left(\pi / 4 ight) imes 30^2= 2827.4 mm^{2}[/latex]

Area of concrete,

[latex]A_c = 450 imes 450 - 2827.4 = 199672.6 mm^{2}[/latex]

Equilibrium condition: External load is shared by load in steel bars [latex]F_s[/latex] and load in concrete [latex]F_c[/latex] as follows.

[latex]F_s+ F_c= 600 imes 10^{3} N[/latex](i)

Compatibility condition: Steel and concrete will have equal extension under the load.

[latex]\Delta L_s= \Delta L_c [/latex] (ii)

Substituting stress-strain relation (assuming to be linear) in Eq. (ii),

[latex]\frac{F_s imes L_s}{A_s imes E_s} =\frac{F_c imes L_c}{A_c imes E_c} [/latex]

or, [latex]F_s =\frac{210 imes 2827.4}{22 imes 199672.6} F_c [/latex]

[latex]F_s =0.135 F_c[/latex]

Substituting in Eq. (i),

[latex]F_c=528557.4 [/latex] N

and [latex] F_s=71442.6 N [/latex]

Stress in steel, [latex]\sigma_s[/latex]=25.27 MPa

Stress in concrete, [latex]\sigma_c[/latex]=2.65 MPa

External load/unit area

[latex]=\frac{600 imes 10^3}{450 imes 450}=2.96[/latex] MPa

Additional stress in steel = 25.27 - 2.96 = 22.31 MPa

Therefore, adhesive force required between steel and concrete = [latex]22.31 imes 2827.4 = 63 imes 10^{3}[/latex] N

Question 1.17: A reinforced concrete column of 450 mm square has four steel...

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