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Design a short column, square in cross section to carry an axial load of $2000 kN$ using $M20$ concrete mix and HYSD steel of grade $Fe415$
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$$P =2000 kN, M20\space \& \space Fe415$$

$P_u=1.5×2000=3000kN \\ \text { Assume 1% steel of gross c/s }\\ \text { 99% concrete of gross c/s }\\ A_{sc}=0.01 A_g \\ A_c=0.99 A_g \\ P_{uc}=0.4 f_{ck} A_c+0.67 f_y A_{sc} \\ 3000 ×10^3=0.4 ×20×0.99 A_g+0.67 ×415×0.01 A_g \\ A_g=280360.73 mm^2\\ \text { As it is a square column } \\A_g=side^2 \\ side =\sqrt {280360.73}\\ =529.49 \\ side ≈540mm \\ (A_g)_{\text {provided}}=540×540=291600mm^2 \\ A_{sc}=0.01×291600=2916 mm^2 \\ \text { Provide 6-25 mm∅ } \\ A_{sc}\text {provided }=6×\pi/4×25^2=2945 mm^2 \\ A_s \text {provided }=A_{qp}-A_{scp}=291600-2945=288655 mm^2 \\ Check \\ P_u=[(0.4f_{ck} (Ac)_p )+(0.62f_y (Asc)_p)] \\ P_u=[(0.4×20×288655)+(0.62×415×2945)] \\ P_u=3042.54 kN \gt3000kN \hspace {1cm}\text {Therefore Safe. }\\ \text {Lateral Ties } \\ ∅_{ties} ≥ \dfrac {∅_{main}}4=\dfrac {25}4=6.25mm ≅ 8mm \\ Spacing \\ S_1=\text { least lateral Dimension }=540mm\\ S_2=16 ×∅_{main}=16×25=400mm \\ S_3=48×∅_{ties}=48×8=384mm \\ S_4=300mm\\ \text { Provided 8mm ∅ ties @ 300 mm c/c }$

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