Properties

• \(s\) – weld size
• \(t\) – weld throat dimension, equal to \(0.707s\) for typical fillet welds (joint angles between 80 and 100 degrees)
• \(d\) – height of weld shape
• \(b\) – width of weld shape
• \(A_u\) – unit weld area
• \(I_{u,x}\), \(I_{u,y}\) – unit area moment of inertias, x-x and y-y axes, respectively
• \(J_u\) – Unit polar moment of inertia

Unit properties are defined in terms of unit weld size. Multiply their values by the throat dimension to obtain the actual value of the property, which is used in calculations when the weld size is known:

Table

Shape		$$ \bar{x} $$	$$ \bar{y} $$	$$ A_u $$	$$ I_{u,x} $$	$$ I_{u,y} $$	$$ J_u $$
Line		0	$$ \frac{d}{2} $$	$$ d $$	$$ \frac{d^3}{12} $$	$$ \frac{dt^3}{12} \text{*}$$	$$ \frac{d^3}{12} $$
Double Line		$$ b/2 $$	$$ d/2 $$	$$ 2d $$	$$ \frac{d^3}{6} $$	$$ \frac{db^2}{2} $$	$$ \frac{d(3b^2+d^2}{6} $$
L		$$ \frac{b^2}{2(b+d)} $$	$$ \frac{d^2}{2(b+d)} $$	$$ b+d $$	$$ \frac{d^3(d+4b)}{12(b+d)} $$	$$ \frac{b^3(d+4b)}{12(b+d)} $$	$$ \frac{b^4 + d^4 + 4bd(b^2+d^2)}{12(b+d)} $$
C		$$ \frac{b^2}{2b+d} $$	$$ \frac{d}{2} $$	$$ 2b+d $$	$$ \frac{d^2}{12}(d+6b) $$	$$ b^3\left( \frac{b+2d}{3(2b+d)} \right) $$	$$ \frac{d^2}{12}(d+6b) + b^3\left( \frac{b+2d}{3(2b+d)} \right) $$
Box		$$ \frac{b}{2} $$	$$ \frac{d}{2} $$	$$ 2(b+d) $$	$$ \frac{d^2}{6}(d+3b) $$	$$ \frac{b^2}{6}(b+3d) $$	$$ \frac{(b+d)^3}{6} $$
Circle		$$0$$	$$0$$	$$ 2\pi r $$	$$ \pi r^3 $$	$$ \pi r^3 $$	$$ 2\pi r^3 $$

* Typically not defined for this axis, but this allows one to compute a bending stress given a y-y moment.

References

1. Collins, Busby, Staab. Mechanical Design of Machine Elements and Machines. 2nd Ed.