What is the physical meaning behind the concept of shear lag in fibre reinforced composite structures or the concept in general for any structure?

  • 2
    $\begingroup$ This question is pretty broad. Have you looked at the definition other places and something didn't make sense? Is there any specific part of it that you are confused with? $\endgroup$
    – hazzey
    Aug 27 '15 at 1:06
  • $\begingroup$ I'm putting your question on hold so you can edit to clarify your specific question. As hazzey noted, this can be a broad question. Putting your question on hold allows you to edit it with less concern about invalidating existing answers. $\endgroup$
    – user16
    Sep 1 '15 at 11:50

Here is how I visualize what is physically happening (for steel sections):

Shear Lag enter image description here

As you get closer to the connection to the gusset, all the force needs to be transferred through the bolts, so the stress has to flow toward the connected portion of the angle. In the limit, (L = 0) the net effective area would simply be the net area of the connected portion of the element.

  • 5
    $\begingroup$ You need to stop making these drawings. You're putting the rest of us to shame. >.> $\endgroup$
    – Wasabi
    Aug 27 '15 at 17:18
  • $\begingroup$ @Wasabi, no kidding, these are good! $\endgroup$
    – grfrazee
    Aug 27 '15 at 17:38
  • $\begingroup$ @CableStay, this is pretty much what was going through my head too, but I think you illustrated it better than I would have. $\endgroup$
    – grfrazee
    Aug 27 '15 at 17:38
  • 1
    $\begingroup$ +1 for the excellent drawings. $\endgroup$ Aug 27 '15 at 19:13
  • $\begingroup$ @CableStay Your drawing was helpful in understanding the concept. Thank you. I have a further question in connection with this topic - In a short fibre/matrix system will the ends of the fibres be more loaded than the other portions? $\endgroup$
    – Willis
    Aug 29 '15 at 19:45

I can't speak to fiber-reinforced composites, but the general concept of shear lag is summed up in the AISC 360-10 Specification, Commentary Section D3 as such:

Shear lag is a concept used to account for uneven stress distribution in connected members where some but not all of their elements (flange, web, leg, etc.) are connected. The reduction coefficient, $U$, is applied to the net area, $A_n$, of bolted members and to the gross area, $A_g$, of welded members. As the length of the connection, $l$, is increased, the shear lag effect diminishes. This concept is expressed empirically by the equation for $U$. Using this expression to compute the effective area, the estimated strength of some 1,000 bolted and riveted connection test specimens, with few exceptions, correlated with observed test results within a scatterband of ±10% (Munse and Chesson, 1963). Newer research provides further justification for the current provisions (Easterling and Gonzales, 1993).

Basically, shear lag is a concept where the forces in a connection require a certain length to properly "get out." This is partially dependent on the relative stiffness of the connection vs. the direction of the application of the load.

For example, consider the figure below from the AISC 360-10.

angle connection

The example on the left is more impacted by the effects of shear lag since the force in the connection has to transfer along the length $l$ of the weld. The $U$ value would likely be less than 1.0, indicating the influence of shear lag.

In the middle example, the weld at the end of the angle is perpendicular to the force. In this case, the $U$ value would likely be 1.0 (assuming the outstanding leg of the angle is also welded similarly) since the force is transferred uniformly to the perpendicular weld.

Table D3.1 of the AISC 360-10 tabulates the calculation of different $U$ values based on the connection geometry. I have pasted a snippet of it below for a couple examples. Your code of record may vary depending on your country and jurisdiction.

lag factors

  • $\begingroup$ To clarify, the middle example would only have U = 1.0 if the vertical leg is also connected. If only one leg is connected, shear lag still applies. $\endgroup$
    – CableStay
    Aug 27 '15 at 16:44
  • $\begingroup$ You're right, thanks for pointing out my oversight. $\endgroup$
    – grfrazee
    Aug 27 '15 at 17:34

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