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 = 27/32*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+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 = 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+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.