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RE: Beam and Plate Element Compatibility

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The SFD that you can see is like the one as shown below.

These saw-tooth type SFD profile is due to the very nature of the arch profile modeled by the series of straight line  segments.

The sudden drop or discontinuity in SFD at the member end is due to the sudden change in curved profile which is because of the axial force transmitted by the connected member at the  end of the beam  which has its component along the shear force force direction of the beam concerned. See below the illustration.

You can check this phenomena if you create a simple curve profile with sharper bents ( see below), Here you can see the discontinuity of the  SFD .

Now, lets relatively smoothen the profile by decreasing the bent angles (by adding the intermediate beams). 

So, you can see that more we construct the curved profile by adding more intermediate member so that the sharp bend gets reduced, the SFD diagram gets  better ( approaches towards the actual diagram). Or in other words, if you draw a fictitious free hand lines joining the SFD at the mid length of every segments then you are ending up in getting the perfect smooths curved SFD profile,which indicates that if one can generate such a perfect ideal curved arch with perfect curvature (infinite number of beam segments), then the SFD will be almost perfectly smooth and curved ( no discontinuity)

See the following arch where I have increased the profile point to make relatively better curved profile ( although not perfectly pure curve). Here, you can see that the SFD gives the better impression of how SFD profiles varies along the complete stretch of the arch.

So, if you are concerned to take the SFD for design purpose, you may take the maximum value of the SFD along the beam segment which may keep you on slightly conservative and safer side. The more you create intermediate  profile point better the result would be.


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