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Re: Tapered compression edge of sawn beam

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At 05:28 PM 10/7/98 -0700, you wrote:
>I have a situation where the top edge of a sawn beam, or maybe Micro=Lam,
>wants to be tapered at a 3:12 slope to stay under the roof sheathing.  Does
>anyone have any thoughts on how a taper will effect the shear capacity of
>the beam?  The only thing I come up with is to check it as a beam with
>several notches at the compression side.
>Steve Privett

        This same situation recurs in my work. The elaborate formula for
compression-side shear strength at a single notch first appeared (replete
with a typo error)in the 1988 edition of UBC, but existed in the AITC
handbook earlier, so I suppose it applies to glue laminated beams as well as
to sawn lumber beams. (I wouldn't know as to proprietary beams, but they
usually have very high horiz shear allowables.) In the 94 UBC edition, it is
formula 6.4 in Sec 2306.4.

        I regard a long tapered cut as a series of adjoining notches. That
code formula is clumsy enough in hand calculations for one discrete notch,
let alone for a "series of notches" where you don't know the location along
the tapered cut that gives the least horizontal shear strength. 

        What I did in 1990 was create a graphical design aid for myself. I
plotted a series of "contour" lines on the "face" of a graphical beam end
that shows the curved lines for where 95% of full shear value occurs; 90%;
80%; and so on down. These curves abruptly become straight horizontal lines
where e becomes equal to d'. Where this code formula "helps" the strength is
for locations of bottom of notch horizontally closer to the face of support
than the vertical distance on down to the tension edge, ie, e < d'.

        I use my "contour map" design aid by simply drawing on it to scale
the location of the tapered cut line, or other notch configuration. Then I
can see at a glance what limiting percentage of full shear capacity is still
left, and where this least value is located. Typically it is at neither end
of the tapered cut, but somewhere along its length, even when the upper end
of the cut is several depths out from the face of the support.

        I only have this on 8-1/2 x 11 paper copies. Surely the same could
be worked up as software.

        Some caveats: the contour lines representing the code formula appear
to give absurdly optimistic results at notch locations very close to the
face of beam closer than 10% of beam depth and where little
net depth remains. The 1997 NDS at Sec gives prescriptive limits to
both notches and taper cuts on the compression edge at ends of glue
laminated beams. The 1997 NDS also addresses taper cuts in sec, but
their description and sketch are unclear. It may mean that one takes d-sub-n
arbitrarily as the net depth of the beam below the tapered cut directly
above the inside face of support. If so it would entirely wipe out the
usefulness of the notch formula and make the tapered cut a much worse
situation than an idealized series of separate notches. It would make the
notch calc a one-step affair for tapers, but at the price of significantly
understating the capacity. I think this manner of dealing with taper cuts in
this NDS is a hasty cop-out, not a good remedy. It needs more work.

        The Hankinson formula nomographs have been in the NDS for ages; why
not a convenient graphical design aid for tapered and notched beams? To see
the contour lines is to get a vivid feel for how little tapers in moderation
hurt shear capacity. 

Charles O Greenlaw, SE    Sacramento CA