Geometrical Properties of Angle Section

Dimensions

h =   , t_w =  

b_f =   , t_f =  

Area

A_w = h·t_w ²

A_f = (b_f – t_w)·t_f ²

A = A_w + A_f ²

Centroid

S_z = A_w·t_w2 + A_f·(b_f + t_w)2 ³

y_c = S_zA

S_y = A_w·h2 + A_f·t_f2 ³

z_c = S_yA

Perimeter

P = 2·(h + b_f)

Second moments of area

I_{y_w} = A_w·(h²12 + (z_c – h2)²) ⁴

I_{y_f} = A_f·(t_f²12 + (z_c – t_f2)²) ⁴

I_y = I_{y_w} + I_{y_f} ⁴

I_{z_w} = (h – t_f)·t_w·(t_w²12 + (y_c – t_w2)²) ⁴

I_{z_f} = t_f·b_f·(b_f²12 + (y_c – b_f2)²) ⁴

I_z = I_{z_w} + I_{z_f} ⁴

I_yz = A_w·(h2 – z_c)·(t_w2 – y_c) + A_f·(t_f2 – z_c)·(b_f + t_w2 – y_c) ⁴

Principal moments of area

I₁ = I_y + I_z2 +  (I_y – I_z)²4 + I_yz^{2 4}

I₂ = I_y + I_z2 –  (I_y – I_z)²4 + I_yz^{2 4}

Angle of principal axis

α₁ = atan(I_y – I₁I_yz) ^о

Polar moment of area

I_x = I₁ + I₂ ⁴

Radii of gyration

r_y =  I_yA

r_z =  I_zA

r₁ =  I₁A

r₂ =  I₂A

r_x =  I_xA