Ultimate Strength of Weld Groups.xls

This spreadsheet is using the Instantenious Center of Rotation Method to determine shear capacity of weld group. This method is described in LRFD Code (2nd Edition, Volume II, p. 8-154). In theory, the weld group rotates around IC, and the displacements of each unit-weld element is proportional to the distance to instantaneous centre.

Yakov has many more calculations available from his own website - you'll find a link here.

Calculation Reference
LRFD

The Instantaneous Center of Rotation (ICR) method is a technique used to determine the shear capacity of a weld group by accounting for the effect of rotational forces in addition to the direct and shear forces acting on the welds. This method is particularly useful for eccentrically loaded weld groups, where the load does not pass through the centroid of the weld group.

To use the ICR method, follow these steps:

1. Determine the load and geometry of the weld group: Obtain the magnitude and direction of the applied force (P), as well as the weld group's geometry (number of welds, weld size, and arrangement).

2. Calculate the Moment Arm: Find the distance (e) between the applied force's line of action and the centroid of the weld group. This distance is known as the moment arm, and it creates a moment (M) that results in the rotation of the weld group.

3. Calculate the Moment: Determine the moment (M) caused by the eccentric load using the formula:

M = P * e

4. Determine the Instantaneous Center of Rotation (ICR): The ICR is the point about which the weld group appears to rotate instantaneously. To find the ICR, draw lines perpendicular to the force (P) and the moment (M) and find their intersection point. This intersection point is the ICR.

5. Calculate the Shear Forces on Each Weld: For each weld in the group, determine the distance (r) from the ICR to the weld, and calculate the shear force (V) acting on that weld using the following formula:

V = P * (r / R)

Where: R = The sum of all the distances (r) from the ICR to each weld in the group

6. Determine the Shear Capacity of Each Weld: Using the weld size and material properties, calculate the allowable shear capacity (V_allow) for each weld.

7. Compare the Shear Forces and Shear Capacity: For each weld, compare the calculated shear force (V) with the allowable shear capacity (V_allow). If the shear force exceeds the allowable capacity for any weld, the weld group does not have sufficient shear capacity for the applied load.

The ICR method provides a comprehensive approach to determining the shear capacity of weld groups, accounting for the effects of rotational forces in addition to direct and shear forces acting on the welds.