Weld Section Modulus Calculator
Build a weld group from line segments, effective throat size, and common layouts to calculate centroid, Ix, Iy, controlling Sx, controlling Sy, and optional bending stress.
Choose a common weld group. Each preset fills the layout, line lengths, throat input, stitch data, and trial bending moments.
Weld section modulus result
| Layout | Typical use | Centroid behavior | Section modulus note |
|---|---|---|---|
| Closed rectangle | End plates, base plates, framed tabs | Usually near the geometric center | Good Sx and Sy for the same envelope |
| Side pair | Vertical bracket welds and lug sides | Centered between the two weld lines | Sy often stronger than Sx for tall pairs |
| Top and bottom rails | Flange plates and horizontal stiffeners | Centered between rail welds | Sx often stronger than Sy for wide rails |
| C, U, and L groups | Open brackets and access-limited welds | Moves toward the welded side | Use controlling extreme distance on each axis |
| Quantity | Formula basis | Calculator output | Design comment |
|---|---|---|---|
| Throat area | Effective throat x total line length | Area | Uses effective line factor for gaps and ends |
| Centroid | Sum of line length x midpoint over total length | xbar, ybar | Open groups can shift away from drawing origin |
| Ix and Iy | Line local inertia plus parallel-axis terms | Centroidal inertia | Thin throat model uses t x L cubed over 12 |
| Sx and Sy | I divided by the farthest extreme weld distance | Section modulus | Reports the smaller side value for each axis |
| Detail item | Common value | Calculator field | Use carefully when |
|---|---|---|---|
| Equal-leg fillet throat | 0.707 x leg size | Throat input method | The fillet is not equal-leg or is convex/concave |
| Effective length factor | 90% to 100% | Effective length factor | Intermittent welds, returns, or crater allowances apply |
| Axis convention | X horizontal, Y vertical | Reported drawing axes | The drawing is rotated or a local axis set is used |
| Allowable stress cue | Project specific | Reference allowable stress | Fatigue, seismic, cyclic, or code load combinations govern |
When a weld group is subject to bending load, the importance of the weld is not related to the total amount of weld metal that is present. Instead, the importance of the weld is related to the distance of that weld metal from the neutral axis of the weld group. The section modulus is the value that help to determine this distance from the neutral axis.
The weld section modulus calculator will ask for the layout of the weld, the throat size of the weld group, and the bending moment that will be applied to the weld group, and will return to you the resulting values. Each of these value has some meaning within the context of the weld group that is being evaluated. Most fabricators begin with a drawing of the welded component that is to be fabricated.
How the Weld Section Modulus Calculator Works
The fabricator will mark the locations where the welds will be made, and will make an initial guess as to the throat size of each of the welds. In many instances, however, the welded component will not hold in relation to the loads that are to be applied to the component. This issue is generally caused by the fact that the centroid of the weld group is not located at the same point as the origin of the drawing of the component.
For instance, if an open C-shape is to be welded together, the centroid will be closer to one of the back walls of the open C-shape. As a result of the shifting of the centroid of the group of weld metal to a different location, the distance of each of the welds from the neutral axis change, and thus, the section modulus change as well. Thus, two weld group that appear to be the same may have different allowable moments if the positions of their centroids are different than one another.
The weld section modulus calculator treats each of the line of weld as a strip of metal of a certain thickness (the throat size). The calculator determines the total length of each of the weld lines, the distance of each of those lines from a weighted center of the weld group, and the inertia of each of those weld lines groups about that center point. Each of the moments of inertia is divided by the distance of each of the weld lines from the center of the weld group, and the smaller of each of those two calculated distance is taken as the value of that section modulus (Sx or Sy).
Each of these values is conservative in that it accounts for the fact that one of the sides of the weld group may be further from the centroid than the other side of the weld group. Thus, the weld metal of one side of the weld may have a higher importance than that of the other side of the weld, but the weld section modulus calculator does not require the weld designer to determine which side is more important because it reports the value of the less important side. The throat size of the weld group influence two different areas of the calculation.
The throat size multiplies the length of each of the weld lines to determine the area of weld metal in the weld group. Additionally, the throat size also influence the calculation of the moments of inertia of the weld group. As such, a change in the throat size will lead to a change in each of these quantities.
For fillet welds of equal leg size, the throat size is calculated as 0.707 times the size of each of the legs of the fillet weld. This factor is incorporated into the weld section modulus calculator. Any other effective throat size can be entered into the calculator rather than relying upon the 0.707 calculation.
The output of the calculator will reflect the actual amount of weld metal rather than the amount of weld metal that would be present if the welds were of the nominal size. Another factor that must be considered in the calculation of the weld group is the effective length of each of the weld lines. The length of each of the weld lines may be less than the length of each of those lines because some of the lengths may be occupied by starts and stops allowances, returns, or gap in the weld.
This factor allows the user to tell the calculator the effective length of each of the weld lines. A factor of 95% is used in cases where the weld metal does include allowances for starts and stops allowances but where the welds are not intermittent welds. For intermittent welds, lower factor are used because the welds will have larger gaps between the weld lines.
Each of the lengths, areas, and moments of inertia are scaled by this length factor prior to calculation of the centroid or section modulus of the weld group. The orientation of the weld group in relation to the drawing plane is a factor that is generally overlooked until the drawing is rotated to lie in the correct plane for viewing. The weld section modulus calculator assumes that the X-axis will be horizontal and the Y-axis will be vertical on the screen.
If the actual weld group is oriented on its side, however, each of these axes will be swapped in relation to the weld group. The “swapped axes” option in the calculator will swap the value of Ix with Iy and Sx with Sy so that the output reflects the correct orientation of the weld group. The optional calculation of the bending stress in the weld group can be made by combining the two bending moments with each of their respective section moduli, and adding those two calculated terms together.
This value will not calculate the actual bending stress in the weld metal, but it may help to provide a general idea of the importance of each of the weld lines. If this calculated value is well below the allowable bending stress that can exist in the weld metal, there is a need to verify that the weld metal can handle those moment as well as other potential loads upon the welded component. However, if the calculated value from this optional calculation is greater than the allowable bending stress for that weld metal, then the geometry of the weld group is inadequate relative to the moments that are to be applied to the component.
Open layouts of weld groups will influence the calculated values of Sx and Sy. For instance, if the weld group is comprised of a pair of side fillets, the weld metal will have excellent resistance to loads applied along one of the axis, but will have very little resistance to loads applied along the other axis. The distance of each of the fillet welds from the centroid is small, leading to the small value for Sy.
If, however, the open layout of the metal is closed (by adding returns and other weld lines), then the distance of each of the fillets of weld metal from the vertical axis will be increased. Thus, increasing Sy without increasing the vertical span of the weld lines. Each of these change will be reflected in the weld section modulus calculator if the layout of the weld group is changed in the calculator.
Another common practice is the use of an effective length factor for intermittent welds. In this case, the lengths of each of the weld lines will be calculated to exclude any gap between the weld lines, and the length factor will be applied to each of the lengths of the weld metal that are included in the calculation. Gaps dont have any length, area, or stiffness to the weld lines, and the weld section modulus calculator should not invent weld metal where there is none.
Furthermore, this calculation is useful as a means of determining the effect of gaps in the weld lines on the stiffness of each of the welded component of the welded assembly. Welded metal components do not typically experience loads that can be described as pure bending loads. Bending loads are usually accompanied by shear loads, torsion loads, and prying loads.
However, the section modulus of the weld group will bound the bending load that is applied to the welded component. Once the bending load can be bounded, it can be combined with other load effects to determine the total load that will be experienced by each component of the welded structure. The weld section modulus calculator will not calculate these combined loads, but will provide the necessary information for the weld designer to calculate those loads themselves.
The reference tables provide a general overview and the formulas that are applied to each of the outputs of the calculator. These tables are not a substitute for the calculations that are performed in the calculator, but they are a reminder to the weld designer of the types of layouts that will create a balanced weld group relative to bending loads. The number will change according to each dimension and layout that is entered into the calculator, but the reference tables will remain the same.
One of the habit of many weld metal designers is to calculate the same welded component twice with two different throat sizes. The section modulus will not change linearly with the throat size of the weld metal. A thicker throat size will provide more benefit to weld metal that is located further from the centroid of the weld metal group.
This habit can provide insight into the benefits of increasing the size of the fillet welds, or in changing the layout of the weld metal to increase the benefits to the welded component. Another of the habit of many weld designers is to observe the movement of the centroid of each of the weld metal groups when adding or removing weld metal lines. An open bracket, for instance, will appear to have the centroid located at the center of the open bracket.
The centroid, however, will move towards the side of the bracket that is welded in relation to the position of the weld metal lines. Thus, removing weld metal from one side of a welded bracket will move the centroid of that welded group towards the welded side of the metal. The movement of the centroid on the screen makes this abstract concept more concretely understood by the weld designer.
The concept of section modulus for a group of weld metal is a measure of the leverage of the weld group. More weld metal that is located further from the neutral axis will perform more work than metal that is closer to the neutral axis. This leverage can be calculated for the different type of layouts of weld metal groups.
By understanding how each of the parameters influence the calculated values, the weld designer can make adjustments to the weld metal metal group to achieve more desirable results. Thus, the weld section modulus calculator allows the designer to focus upon whether the calculated load will be within the limits of the welded component.
