Calculations of Properties for Selected Section Types

This topic displays the formulas that are used for calculating the properties of user-defined sections (on the Parametric tab).

These formulas comprise thin-walled sections as well as thick-walled ones (including solid sections). All formulas are derived for prismatic elastic members.

The following conventions are used in the formulas:

Ax - Area
Ay - Shear rigidity factor (reduced sectional area considering the influence of shear forces)
Az - Shear rigidity factor (reduced sectional area considering the influence of shear forces)
Wx - Section modulus for calculation of torsion stresses
Wy - Shear area - reduced extreme shear stress coefficient Qy (tymax=Fy/Wy)
Wz - Shear area - reduced extreme shear stress coefficient Qz (tzmax=Fz/Wz).

PIPE SECTION

R - Outer radius

r - Inner radius

Thick-walled sections (r < 0.83)	Thin-walled sections (r > 0.83)
Ax = p (R^2-r^2) Ay = 27/32Ax Az = 27/32Ax Wx = p (R^4-r^4)/2R Wy = 3/4Ax Wz = 3/4Ax	Ax = p (R^2-r^2) Ay = 1/2Ax Az = 1/2Ax Wx = p (R^4-r^4)/2R Wy = 1/2Ax Wz = 1/2Ax

Thick-walled sections (r < 0.83)

Thin-walled sections (r > 0.83)

Ax = p *(R^2-r^2)

Ay = 27/32*Ax

Az = 27/32*Ax

Wx = p *(R^4-r^4)/2R

Wy = 3/4*Ax

Wz = 3/4*Ax

Ax = p *(R^2-r^2)

Ay = 1/2*Ax

Az = 1/2*Ax

Wx = p *(R^4-r^4)/2R

Wy = 1/2*Ax

Wz = 1/2*Ax

BOX SECTION

h - Web height

tw - Web thickness

tf - Flange thickness

b - Flange width

Thick-walled sections (Ax > 1/3 b*(h+2tf))	Thin-walled sections (Ax ≤ 1/3b*(h+2tf))
Ax = (h+2tf)b - h(b-2tw) Ay = 5/6Ax Az = 5/6Ax Wx = 0.23Axmin(b,h) Wy = 2/3Ax Wz = 2/3Ax	Ax = (h+2tf)b - h(b-2tw) Ay = 2btf Az = 2(h+2tf) tw Wx = 2(h+tf)(b-tw) * min(tw,tf) Wy = 5/6Ay Wz = 5/6Az

Thick-walled sections (Ax > 1/3 b*(h+2tf))

Thin-walled sections (Ax ≤ 1/3b*(h+2tf))

Ax = (h+2*tf)*b - h*(b-2*tw)

Ay = 5/6*Ax

Az = 5/6*Ax

Wx = 0.23*Ax*min(b,h)

Wy = 2/3*Ax

Wz = 2/3*Ax

Ax = (h+2*tf)*b - h*(b-2*tw)

Ay = 2*b*tf

Az = 2*(h+2tf)* tw

Wx = 2*(h+tf)*(b-tw) * min(tw,tf)

Wy = 5/6*Ay

Wz = 5/6*Az

RECTANGULAR SECTION

h - Total width

tfw - Thickness of the flange and the web

b - Flange width

Thick-walled sections (Ax > 1/3 b*h)	Thin-walled sections (Ax ≤ 1/3b*h)
Ax = hb - (h-2tfw)(b-2tfw) Ay = 5/6Ax Az = 5/6Ax Wy = 2/3Ax Wz = 2/3Ax	Ax = hb -h(b-2tfw) Ay = 2btfw Az = 2htfw Wx = 2(h-tfw)(b-tfw)tfw Wy = 5/6Ay Wz = 5/6Az

Thick-walled sections (Ax > 1/3 b*h)

Thin-walled sections (Ax ≤ 1/3b*h)

Ax = h*b - (h-2*tfw)*(b-2*tfw)

Ay = 5/6*Ax

Az = 5/6*Ax

Wy = 2/3*Ax

Wz = 2/3*Ax

Ax = h*b -h*(b-2*tfw)

Ay = 2*b*tfw

Az = 2*h*tfw

Wx = 2*(h-tfw)*(b-tfw)*tfw

Wy = 5/6*Ay

Wz = 5/6*Az

I-SECTION

h - Web height

tw - Web thickness

tf - Flange thickness

b - Flange width

Thick-walled sections (Ax > 1/3 b(h+2tf))	Thin-walled sections (Ax ≤ 1/3b(h+2tf))
Ax = htw + 2btf Ay = 5/6Ax Az = 5/6Ax Wx = Ix / max(tw,tf) Wy = 2/3Ax Wz = 2/3*Ax	Ax = htw + 2btf Ay = 2btf Az = htw Wx = Ix / max(tw,tf) Wy = 8Iz / (b^2-tw^2) Wz = 8twIy / ((h+tf)b4tf+h^2*tw)

Thick-walled sections (Ax > 1/3 b*(h+2*tf))

Thin-walled sections (Ax ≤ 1/3b*(h+2*tf))

Ax = h*tw + 2*b*tf

Ay = 5/6*Ax

Az = 5/6*Ax

Wx = Ix / max(tw,tf)

Wy = 2/3*Ax

Wz = 2/3*Ax

Ax = h*tw + 2*b*tf

Ay = 2*b*tf

Az = h*tw

Wx = Ix / max(tw,tf)

Wy = 8*Iz / (b^2-tw^2)

Wz = 8*tw*Iy / ((h+tf)*b*4*tf+h^2*tw)

Note: Values of the properties for sections provided in the section databases are calculated using the formulas in this topic.