Formula: ${<span\; style="font-size:\; 14px;">\sum </span>}_{\mathrm{<span\; style="font-size:\; 14px;">i</span>}<span\; style="font-size:\; 14px;">=</span>\mathrm{<span\; style="font-size:\; 14px;">1</span>}}^{\mathrm{<span\; style="font-size:\; 14px;">10</span>}}\mathrm{<span\; style="font-size:\; 14px;">2</span>}\mathrm{<span\; style="font-size:\; 14px;">i</span>}$\sum_{i=1}^{10}2i  // Formula computes the sum of double each integer from 1 to 10

Tied Column Design:

$\mathrm{<span\; style="font-size:\; 14px;">\rho </span>}$\rho$Pu=634.3325kip$  $\mathrm{<span\; style="font-size:\; 14px;">a</span>}<span\; style="font-size:\; 14px;">=</span>\mathrm{<span\; style="font-size:\; 14px;">0.8</span>}$a=0.8

$a=0.8$  $\phi-0.65$  

$\rho_{g=0.025}$  

$\frac{Pu}{a\phi}=A_{g}\left\lbrack0.85fc^{\prime}\left(1-\rho_{g}\right)+\rho_{g}fy\right\rbrack$  

$\frac{634.3325}{0.8\cdot0.65}=A_{g}\left\lbrack0.85\cdot3\left(1-0.025\right)+0.025\cdot60\right\rbrack$  

$A_{g=306.34in^2}$  

$Use16^{\prime\prime}\cdot20^{\prime\prime}column\left\lbrack A_{g=320in^2}\right\rbrack$  

$\frac{Pu}{a\phi}=0.85fc^{\prime}\left(A_{g}-A_{s}\right)+Asfy$  

$\frac{634.3325}{0.8\cdot0.65}=0.85\cdot3$$\frac{634.3325}{0.8\cdot0.65}=0.85\cdot3\left(320-As\right)+As\cdot60,As=7.66in^2,As_{\min}=1.0\%\circ Ag=0.01\cdot320=3.20in^2,Use8-25\operatorname{mm}\&4-20\operatorname{mm}$

$As=7.66i{n}^2,$

Asmin​=1.0%of Ag=0.01⋅320=3.20in2,

$Use8-25\mathrm{mm}\&4-20\mathrm{mm}$  

Spiral Column Design :

 $P_{u}=634.332kip,a=0.85,\phi=0.7,\rho_{g}=0.025$

$a=0.85,$



$\varphi =0.7,$

${\rho }_g=0.025$

 $\frac{P_{u}}{a\phi}=A_{g}\left\lbrack0.85fc^{\prime}\left(1-\rho_{g}\right)+\rho_{g}fy\right\rbrack,\frac{634.3325}{0.85\cdot0.7}=Ag\left\lbrack0.85\cdot3\left(1-0.25\right)+0.025\cdot60\right\rbrack,Ag=267.73in^2,Ag=\frac{\pi}{4}d^2,267.77=\frac{\pi}{4}d^2,d=18.465^{\prime\prime},Use19^{\prime}Diametercolumn\left\lbrack Ag=283.53in^2\right\rbrack,\frac{P_{u}}{\alpha\phi}0.85fc^{\prime}\left(Ag-As\right)+Asfy,\frac{634.3325}{0.85\cdot0.7}=0.85\cdot3\left(283.52-As\right)+As\cdot60,As=6.69in^2,As_{\min}=1\%\circ Ag=0.01\cdot283.52=2.8352in^2,Use9-25\operatorname{mm}$

$\frac{634.3325}{0.85\cdot 0.7}=Ag\left[0.85\cdot 3\left(1-0.25\right)+0.025\cdot 60\right],$

$Ag=267.73i{n}^2,$

$Ag=\frac{\pi }{4}{d}^2,267.77=\frac{\pi }{4}{d}^2,$

$d=18.465^{\prime \prime },$

$Use19^{\prime }Diametercolumn\left[Ag=283.53i{n}^2\right],$

$\frac{P_u}{\alpha \varphi }0.85f{c}^{\prime }\left(Ag-As\right)+Asfy,$

$\frac{634.3325}{0.85\cdot 0.7}=0.85\cdot 3\left(283.52-As\right)+As\cdot 60,$

$As=6.69i{n}^2,$



$A{s}_{\min }=1\%\circ Ag=0.01\cdot 283.52=2.8352i{n}^2,$

$Use9-25\mathrm{mm}$

Tie Design of Tied Column:

Minimum size of the bar $\ge\#3,$  if longitudinal bar is $\le\#10$  Bar.

Size $\ge\#4$  bar, if longitudinal bar size is $\ge\#11$  bar.

Size $\ge\#4$  bar, if longitudinal bar are bundle.

Spacing

$S\le16d_{b}\left\lbrack d_{b}\right$ = diameter of main reinforcement]

$S\le48d_{t}\left\lbrack d_{t}\right.$ = diameter of tie]

$S\le$  Least diameter of the column.

Spacing :

$S=16\cdot20=320\operatorname{mm}=12.56^{\prim$

$S=48\cdot10=480\operatorname{mm}=18.897^{\prime\prime$

$2.\; S=48\cdot 10=480\mathrm{mm}=18.897^{\prime \prime }$

$3.\; S=16^{\prime \prime }$  

Moment Calculation 

Long Direction :