Understanding Fillet Weld Geometry

A fillet weld is used to join two surfaces at an angle, typically 90 degrees. The key dimensions of a fillet weld are its 'size' and its 'throat thickness'.

• Fillet Weld Size (Leg Length): For a standard fillet weld, the size is defined as the length of the equal legs of the weld, measured from the root of the joint to the toe of the weld. Let's denote the size (leg length) as s.
• Throat Thickness: The throat thickness (t) is the shortest distance from the root of the joint to the face of the weld. It's measured perpendicular to the root.

Calculating the Ratio for a 45° Fillet

The question refers to a standard 45° fillet. This typically implies that the weld face forms a 45° angle with the base metal, and the fillet legs are equal. Consider the cross-section of such a fillet weld. It forms a right-angled isosceles triangle, where the two equal sides represent the leg lengths (s).

The throat thickness (t) is the altitude drawn from the right-angle vertex (the root of the joint) to the hypotenuse (the weld face line connecting the toes).

In a right-angled isosceles triangle with equal legs of length s, the hypotenuse has a length of $s\sqrt{2}$. The altitude to the hypotenuse in such a triangle is half the length of the hypotenuse.

Therefore, the throat thickness t can be calculated as:

$$ t = \frac{s\sqrt{2}}{2} $$

This equation can be simplified to:

$$ t = \frac{s}{\sqrt{2}} $$

To find the ratio of the size (s) to the throat thickness (t), we can rearrange the formula:

$$ s = t\sqrt{2} $$

Now, we can express the ratio s : t:

$$ s : t = t\sqrt{2} : t $$

Dividing both sides by t (assuming $t \neq 0$), we get:

$$ s : t = \sqrt{2} : 1 $$

Conclusion

The ratio of the size (leg length) of a standard 45° fillet weld to its throat thickness is $\sqrt{2} : 1$. This corresponds to option 3.