Calculated Properties

The following section properties are calculated as indicated when they are not present for the profile.

Property

Formula

AX

$=T\left(D-T+B\right)$

AY

$=\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.D\times T$

AZ

$=\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.B\times T$ when D > B (unequal leg angles)

$=\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.D\times T$ when D = B (equal leg angles)

IX

$=\frac{1}{3}{T}^3\left(B+D-\raisebox{1ex}{$T$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)$

IY

$=\mathsf{\text{ZII}}+\mathsf{\text{YII}}-\mathsf{\text{IZ}}$

where

CYI	=	$\frac{\left(B-T\right)T^2+T{D}^2}{2\mathsf{\text{AX}}}$
CZI	=	$\frac{\left(D-T\right)T^2+T{B}^2}{2\mathsf{\text{AX}}}$
YII	=	$\left(D-T\right)T{\left(\frac{\mathsf{\text{CZI}}-T}{2}\right)}^2+\frac{\left(D-T\right)T^3}{12}+\frac{T{B}^3}{12}+BT{\left(\frac{\mathsf{\text{CZI}}-B}{2}\right)}^2$
ZII	=	$\left(B-T\right)T{\left(\frac{\mathsf{\text{CYI}}-T}{2}\right)}^2+\frac{\left(B-T\right)T^3}{12}+\frac{T{D}^3}{12}+DT{\left(\frac{\mathsf{\text{CYI}}-D}{2}\right)}^2$

IZ

$=\frac{\mathsf{\text{ZII}}+\mathsf{\text{YII}}}{2}+\frac{\mathsf{\text{ZII}}-\mathsf{\text{YII}}}{2}\text{cos}2ɑ-\mathsf{\text{IZYCG}}\times \text{sin}2ɑ$

where

IZYCG	=	$\frac{D^2{T}^2}{4}+\frac{T^2}{4}\left(B-T\right)\left(B+T\right)-\mathsf{\text{AX}}\times \mathsf{\text{CYI}}\times \mathsf{\text{CZI}}$
$ɑ$	=	angle between the geometric and principle axes, in radians $\frac{1}{2}\text{arctan}\left[\frac{2BD\left(B-T\right)\left(D-T\right)T}{4\left(B+D-T\right)\left(\mathsf{\text{ZII}}-\mathsf{\text{YII}}\right)}\right]$ when D > B (unequal leg angles) = 0.78539816 rad when D = B (equal leg angles)

RMIN

$\sqrt{\frac{\mathsf{\text{IY}}}{\mathsf{\text{AX}}}}$

SY

$=\frac{\mathsf{\text{IY}}}{\text{max}\left(\mathsf{\text{DY1}},\mathsf{\text{DY2}}\right)}$

where

DY1	=	$=\left(D-\mathsf{\text{CYI}}\right)+\mathsf{\text{CZI}}\times \text{tan}ɑ\text{cos}ɑ$
DY2	=	$=D\text{cos}ɑ+B\text{sin}ɑ-\mathsf{\text{DY1}}$

SZ

$=\frac{\mathsf{\text{IZ}}}{\text{max}\left(\mathsf{\text{DZ1}},\mathsf{\text{DZ2}},\mathsf{\text{DZ3}}\right)}$

where

DZ1	=	$=\left(D-\mathsf{\text{CYI}}+\mathsf{\text{CZI}}\times \text{tan}ɑ\right)\text{sin}ɑ-\mathsf{\text{CZI}}/\text{cos}ɑ$
DZ2	=	$=D\text{sin}ɑ-\mathsf{\text{DZ1}}$
DZ3	=	$=B\text{cos}ɑ-\mathsf{\text{DZ2}}$

PY

$1.8\times \mathsf{\text{SY}}$

PZ

$1.8\times \mathsf{\text{SZ}}$