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Helically reinforced circular column

Capacity of a circular column with a helix, the helix ratio and the pitch of the helix. Reference: IS 456:2000 Cl. 26.5.3.2(d), 39.4.

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Helically reinforced circular column: worked example sheet in Equation Pad with typeset equations and results.

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# Data
D := 450 mm
cover := 40 mm
f_ck := 25 MPa
f_y := 415 MPa
A_sc := 6*pi/4*(20 mm)^2 = mm^2

# Capacity
A_g := pi/4*D^2 = mm^2
P_u := 1.05*(0.4*f_ck*(A_g - A_sc) + 0.67*f_y*A_sc) = kN

# Helix
D_k := D - 2*cover = mm
A_k := pi/4*D_k^2 = mm^2
rho_min := 0.36*(A_g/A_k - 1)*f_ck/f_y =
phi_h := 8 mm
a_h := pi/4*phi_h^2 = mm^2
D_h := D_k - phi_h = mm
p_max := pi*D_h*a_h/(rho_min*A_k) = mm
p := min(p_max, 75 mm, D_k/6) = mm
p >= max(25 mm, 3*phi_h) =

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