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# longitudinal shear in composite sections

## longitudinal shear in composite sections

(OP)
Say I have a steel angle section and I weld a rather heavy piece of steel plate to the flange and I want the section to behave as a composite section. I have to size the weld connecting the two pieces to be able to transfer the longitudinal shear stress. However I note that there is also a transverse shear stress which is equal to the longitudial shear.

Should I size the weld based on th combination of these stresses or simply consider the longitudinal stress. Textbooks I have seem to imply the latter is sufficient.

### RE: longitudinal shear in composite sections

Since we are talking about thin walled sections here I would say that the shear stress on legs is significant only in the direction perpendicular to thickness...

### RE: longitudinal shear in composite sections

(OP)
According to what I have studied, the longitudinal and the vertical (or transverse) shear stress are equal and are complimentary stresses so I can't see what would lead you to say that only one of them is significant.

### RE: longitudinal shear in composite sections

This is the classical problem when calculating built-up I sections: you take the shear stress, whatever you call it, longitudinal or transverse (as you correctly noted, they are the same).
Both components of shear stress are present, under all circumstances, not only in the case you mention (except that of course in 3D problems you have 3+3 components). The ground for considering combination of direct and shear stresses is the Mohr's circle and a failure criterion, such as von Mises or Tresca.

prex

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Online tools for structural design

### RE: longitudinal shear in composite sections

aujwc:  Interesting question.  First, you don't combine two mutually perpendicular components of the same shear stress.  These are actually one shear stress, always coexistent.

Secondly, AISC LRFD Specification, 1999, Appendix J2.4, tells us, in words, "Fillet welds are approximately 50% stronger in the transverse direction than in the longitudinal direction" (because notice there's a 50% increase in Eq. A-J2-1 when theta = 90 deg).

Therefore, for your stated scenario, you compute and check the weld shear stress only in the longitudinal direction (applied to the weld effective throat width).  This includes (and envelops) the vertical (transverse) shear stress in your weld.

And, by the way, regarding combining the weld longitudinal normal stress, AISC LRFD, 1999, Sect. J2.4, Table J2.5, footnote (e), says, paraphrasing, "For built-up member flange-to-web welds, ignore the tensile or compressive stress in the weld longitudinal direction."

### RE: longitudinal shear in composite sections

In thin walled sections one applies Jourowski's formula where you actually get a shear flow in each leg of the open thin walled section. What I mean is than the direction of the shear flow is parallel to the longitudinal direction of each leg and that in the transverse direction (along the thickness of the leg) the shear stress formation is negligible.

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