A R.C.C. column is 300mm x in section. It is provided with 8 bars of 20mm diameter. Determine the stresses induced in concrete and steel bars, if it carries a load of 180 kN.

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teamques10 ★ 69k

$\begin{array}{l}{\text { Data: } \mathrm{P}=180 \mathrm{kN} \quad E_{s}=210 G p a=210 \times 10^{3} \mathrm{N} / \mathrm{mm}^{2}} \ {E_{c}=14 G P a=14 \times 10^{3} \mathrm{N} / \mathrm{mm}^{2} \quad \text { Find: } \sigma_{s}=? \sigma_{c}=?}\end{array}$ ![enter image description here][1]

$\begin{array}{l}{\frac{\sigma_{s}}{E_{s}}=\frac{\sigma_{c}}{E_{c}} \quad \sigma_{s}=\frac{E_{s}}{E_{c}} \times \sigma_{c}} \ {\sigma_{s}=\frac{210 \times 10^{3}}{14 \times 10^{3}} \times \sigma_{c}} \ {\sigma_{s}=15 \times \sigma_{c}} \ {P=\sigma_{s} \times A_{s}+\sigma_{c} \times A_{c}}\end{array}$

$\begin{array}{l}{A=300 \times 300=90000 m m^{2}} \ {A_{s}=\frac{\pi}{4} \times 20^{2}=2513.27 m m^{2}} \ {A_{c}=A-A_{s}=87486.73 m m^{2}} \ {180 \times 10^{3}=\left(15 \times \sigma_{c} \times 2513.27\right)+\left(\sigma_{c} \times 87486.73\right)} \ {180 \times 10^{3}=\left(37699.05 \times \sigma_{c}\right)+\left(\sigma_{c} \times 87486.73\right)} \ {180 \times 10^{3}=\left(125185.78 \times \sigma_{c}\right)}\end{array}$

$\begin{array}{l}{\sigma_{c}=\frac{180 \times 10^{3}}{125185.78} \quad \sigma_{c}=1.437 N / m m^{2}} \ {\sigma_{s}=15 \times \sigma_{c}} \ {\sigma_{s}=15 \times 1.437} \ {\sigma_{s}=21.555 \mathrm{N} / \mathrm{mm}^{2}}\end{array}$

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