This load bearing joint is to be welded with pure fillets or either fully or partially penetrated butt weld. Also, a mix of both is possible if another must be made in-plane with the plate surface but special care should be taken with non-symmetric design. Due to moment direc-tion the upper weld is recommended to always be a fillet to better ensure the capacity against moment. The wall thickness of the member to be joined with is a crucial factor regarding the welding which in other words is that the connecting wall must be able to support the loading caused by the wave profile and it must not be harmed with the heat input of welding. It means
that the welding must not weaken the wall to cause failure in its primary purpose. It is note-worthy that in case of the connecting wall bending capacity is concerning it must be specif-ically checked. The bending capacity is depending on the cross section of the wall and should be studied carefully. In this example case the connecting wall is assumed having sufficient capacity for bending and therefor the capacity is not studied. It should also be emphasized that the support plate can be welded to any steel surface where this kind of supporting plate is needed and that has the sufficient capacity to carry the additional loading. The construction is shown in Figure 17.
Figure 17. Illustration of case 2, the wave profile support.
The loading in the weld that is caused by the thin steel wave profile must be efficiently diverted into the connecting member. The case can be simplified to a cantilever beam under a resultant loading R. The adjacent wall and the supporting plate are assumed to have suffi-cient resistance against bending caused by the loading on the supporting plate.
Calculating the weld throat thickness requires the resultant loading being divided to shearing force and bending moment. The loading terms are defined as shown in Figure 18.
Figure 18. Loading terms due to the resultant force R.
The resultant force is divided for the welds as follows: Shear force Q is loading equally both welds and the moment effect is considered as a force pair component at the weld root. The moment is symmetric so the forces at the welds are identical in value but opposite in direc-tion. Defining the force pair components at the weld root and not at the weld toe will lead to a slightly conservative but acceptable estimation of the loading case. The assumed fracture surfaces due to three different failure modes and design criterion are shown in Figure 19.
Figure 19. Assumed fracture surfaces.
The optimal fracture can be achieved by precisely defining the throat thickness according to the loading. However, when safety is considered, the fracture can occur elsewhere as well but theoretically by calculating the minimum throat thickness the weakest surface is found at the throat plane. The fracture due to shearing of the base plate can activate due to bending moment caused by the resultant loading. It is only possible in case the wall can be considered having sufficient bending resistance. If the wall is yielding by bending the shearing is not likely to occur. The weld leg fracture is plausible in two ways. The vertical leg due to the vertical shear force and the horizontal leg due to the horizontal force component from the moment.
The calculation for throat thickness is begun with defining the stress components according to the loading. It can be assumed that there is no parallel shear stress so only transverse tension and shear stresses occur. The tension force F1 is defined according to the moment at the weld calculated from the moment caused by the resultant force and it is equal to the force F2. The moment loading is governing the weld strength along with the effect of shear force.
The moment is calculated at the weld root for conservative estimation of throat thickness
due to the shorter moment arm thus greater force. The formation of stress components is shown in Figure 20.
Figure 20. Defining the stress components corresponding the loading in case 2.
The figure is presenting the stress components in both the upper and the lower welds so that the governing stress situation can be found, and the components can be defined . It can be seen that the direction of transverse normal stresses is equal due to the forces F and Q, but the transverse shear stresses are the opposite resulting in a situation where the normal stresses add up and the shear stresses partially cancel each other. The governing situation is therefor trivial in this case and is found equal in both welds thus the resulting stress equation is applicable in both upper and lower welds and is shown in eq. 15.
โ(โ2๐น1
2๐๐ +โ2๐ 4๐๐)
2
+ 3 (โ2๐น1
2๐๐ โโ2๐ 4๐๐)
2
โค ๐๐ข ๐ฝ๐ค ๐พ๐2
(15)
Where the F1 is the force pair component of the active moment at weld root, Q is the acting shear force and l is the length of the weld. As the stress components are defined and written as a function of the weld throat plane, the throat thickness can be solved. The solution of the throat thickness is presented in eq. 16.
๐ โฅ (โ2๐ ๐กโ โ๐
๐ก+ โ1
2) ๐ ๐ฝ๐ค๐พ๐2
๐๐ข๐ (16)
Where r is the moment arm for the resultant R or the length of the support plate, t is the thickness of the support plate. The force components F1 and Q are written as a function of the resultant force R to make the equation simpler due to the relation F1=Rr/t and Q=R.
The weld throat thickness is then defined according to the strength of the adjacent members that are the shearing of the connecting wall and the bending of the support plate. First the case of shearing is studied, and the stress components are defined equal to the shear yield limit fy/โ3 of the base plate. The weld loading situation is visualized in Figure 21. The stress equation is shown in eq. 17 and the solution for throat thickness is then shown in eq. 18.
Figure 21. Case 2 weld stress components according to base plate shear strength.
โ(๐๐ฆ๐
โ6๐)
2
+ 3 (๐๐ฆ๐
โ6๐)
2
โค ๐๐ข
๐ฝ๐ค๐พ๐2 (17)
๐ โฅ โ2 3
๐ฝ๐ค๐พ๐2๐๐ฆ
๐พ๐0๐๐ข ๐ (18)
Where s is the thickness of the wall. This method estimates equal strength for the weld that the wall can bear due to the moments lateral force component.
The throat thickness can be estimated also according to the bending of the support plate by defining the strength of the weld equal to the plastic bending moment. The plastic moment is calculated as fyt2/4ฮณM0 and is written into the stress component equation as shown in eq.
19. The solution for throat thickness then yields eq. 20. The plastic bending moment situation as well as the corresponding weld stress components are visualized in Figure 22.
Figure 22. Case 2 weld stress components according to the plastic moment capacity.
โ( ๐๐ฆ๐ก2 4๐พ๐0๐๐โ2)
2
+ 3 ( ๐๐ฆ๐ก2
4๐พ๐0๐๐โ2 )
2
โค ๐๐ข
๐ฝ๐ค ๐พ๐2 (19)
๐ โฅ โ1 2
๐ฝ๐ค๐๐ฆ๐พ๐2
๐๐ข๐พ๐0๐ ๐ก2 (20)
Where t is the thickness of the support plate and l is the length of the weld. This method is assuming the weld load bearing capacity equal to the plastic bending moment capacity of the supporting plate. Generally, it means that the supporting plate will eventually yield by bending before the fracture of the weld due to the weld capacity being defined for the plastic bending limit of the plate. The supporting plate is usually as short as possible which on the other hand is decreasing the vulnerability for bending under the occurring loading. In other words, defining the weld size according to the plastic moment of the plate might result in overly conservative estimation in this case.
The load bearing capacity of the leg of the weld, z, against shearing must be assessed. The calculations are conducted using the fore defined force component F1 that is acting exactly
on the weld leg and the shear force due to the loading R. The situation and factors are illus-trated in Figure 23. These weld leg stresses are compared to the maximum stress according to the EC3 stress clause. The comparison for weld leg failure due to the moments force component F1 is shown in eq. 21. Another similar comparison must be conducted for the transverse leg shearing due to the shear force Q which is then shown in eq. 22.
Figure 23. Illustration of factors for weld leg fracture.
๐น1
๐ง๐ โค ๐๐ข
๐ฝ๐ค ๐พ๐2 (21)
๐
2๐ง๐ โค ๐๐ข
๐ฝ๐ค ๐พ๐2 (22)
If the equations 21 and 22 are true with the chosen throat thickness the capacity against the leg rupture of the weld is sufficient.
Intermittent weld is not allowed in load bearing joint. Therefor it is advised to design a con-tinuous weld with a minimum sufficient material thickness. Welding both sides equally re-sult the lowest amount of distortion and is the strongest possible alternative. These calcula-tions apply for double sided symmetric fillet welds. The 1) Double-sided symmetric fillet weld is recommended for the joint but there are alternative possibilities also that are shown in Figure 24.
Figure 24. Possible weld types for the case 2.
The alternatives, 2) single-sided full penetration and 3) double-sided full penetration, should be avoided by all means due to the rational dimensioning of a butt weld. In other words, if using these types, the weld should be designed as thick as the supporting plate. Meaning strictly a full penetration weld which in most cases leads to excess welding regarding the actual requirement due to the loading. The alternatives 2 or 3 can be considered due to the manufacturability reasons. All in all, in case there occurs a need for the alternatives 2 or 3 it is simply recommended to assess the situation again with the type 1 joint. It is worth empha-sizing that the equations yield results only for the weld type 1. The type of the weld has a considerable effect on the manufacturing of the joint but also to the load carrying capacity.
In other words, the calculated throat thickness is only ensuring the sufficient load bearing capacity through the defined weld throat. The position of the throat and geometry of the weld cross section do have an impact on the load bearing capacity. Not only large fillets divide the load for a greater area on the base plate, but it also helps the joint divert the moment for a better route to the base plate. Comparing a T-butt joint to a double-sided symmetric fillet joint one can imagine the moment arm being larger in the fillet weld. Therefor the calcula-tions according to the loading only apply for the fillet weld. The butt joints are possible alternatives when the weld is designed according to the full strength of the support plate.