In this BLOG I have explained how to design a welded joint subjected to Bending Moment. I have also, written a BLOG on Eccentrically Loaded Welded Joint; in case you haven’t read it, I suggest first you read that as this is an extension to that.
For those of you who have already read that BLOG, firstly let’s see how is this case different from the previous one as in both the cases, the load acting on the structure is eccentric that is the line of action of the load is at some distance from the centroidal axis of the weld. But in the previous case, the load was in-plane load i.e. the eccentric load acting on the structure was in the same plane as that of the weld. The figure below shows such type of load where two plates are welded together and the eccentric load is acting in the same plane as that of the weld. Click here to learn more about the design of such welds.
However, in this case, out of the plane eccentric load is acting on the structure. The figure below shows an example where a cantilever beam is welded to a plate and the load is acting at the end of the cantilever beam making it an out of plane eccentric load. The nature of the stresses developed inside the weld is totally different in the case of out of the plane eccentrically loaded weld when compared to in-plane eccentrically loaded weld.
A cantilever beam of rectangular cross-section is welded to a support by means of two welds W1 (parallel to the x-axis) and W2 (parallel to the y-axis) as shown in the figure above. Using the principle of Applied Mechanics, the eccentric load P can be replaced by an equal and similarly directed force P acting through the plane of welds at the center of gravity ‘G’ of all the welds. By doing so a bending moment (M=P X e) will be induced acting about point G. It should be noted that this moment is acting about the x-axis as the load on the structure is along the y-axis, had it been along the x-axis then the moment would have acted about the y-axis provided that the length of the cantilever beam is along the z-axis.
The force P through the plane of welds causes the primary shear stress, which is given by:
Whereas, the bending moment M (about the x-axis) causes bending stresses in the weld whose magnitude is given by:
The detailed design procedure is explained in the video below.
For a better understanding of the concept, I have also solved a problem.
Click here to download the study material related to this topic.