Developing a weld 1

I think you will get better answers from the welding forum.

Blodgett’s Design of Welded Structures has a very good methodology and explanation in it. Unfortunately, mine is at my desk in the office!

Check out this thread where I dug deep into this and some related issues: Link. It gets rolling near the posting of the sketch below.

Attempted summary: by the time that you get to the section where the reinforcing is needed, coming from the unreinforced side, utilizing the reinforcement requires that you have locally developed a total shear flow equal to the VQ/It shear flow that would have been required between the termination point and the end of the member if the reinforcing had been run out the whole way. Mathematically, that's the MQ/I that you see in the literature: the missing area under the shear flow diagram as shown below. Toss in a little extra for shear/tension lag and you've got your "development length". It's much better explained with pictures so definitely review the other thread and report back here if anything requires further explanation.

[link ]Link[/url]

Interesting other thread, KootK. I haven't checked the equations thoroughly but it seems like your method checks out (as you no doubt agree…). Totally different to the way I think hence interesting. You've got S & Z backwards because you're North American - that's partly me being a smartarse and partly for the benefit of international readers.

I like the method (or way of thinking) in the image below, which fundamentally works for elastic and plastic distributions (you need to use the plastic stress distribution in plastic zones obviously) and which I presume gives the same answer if both methods are correct/equivalent. I believe your M*Q/I (elastic case) could be re-written as (delta_M * z_reinf/I)*(Area of reinforcing element) which would be equivalent to the image below if I understand correctly. BAretired's method from the other thread is a limiting case of this method, where he uses two sections at maximum and minimum bending moment (ie a fairly long distance apart) and averages the weld requirement. I've seen this before but not been convinced it gives a good distribution of welds; my provisional opinion is that it relies on weld ductility and safety margin more than I'm comfortable with, though I acknowledge that it does have a track record.

AJk1's question about concrete was astute. The development length requirements are indeed analagous to sizing the weld, but in concrete you get more 'welds' as you increase the number of reinforcing bars, and the 'weld size' is tied to the bar perimeter (and bar spacing/cover), so the variable you're left with is the length.

For the specific question in this thread of how far to develop the reinforcing element, I’d say the minimum is the depth of the reinforcing element per St Venant, perhaps 1.5*D_reinf. Work out weld requirement for that and, if it’s ridiculously large, increase the development length in proportion to how much you want to reduce the weld size. EDIT: just realised that's inconsistent with my objection to BAretired's method. Maybe don't stray too far from the St Venant weld size. Or perhaps my concern is unfounded.

steveh49 said:

I believe your M*Q/I (elastic case) could be re-written as (delta_M * z_reinf/I)*(Area of reinforcing element) which would be equivalent to the image below if I understand correctly.

Click to expand...

I believe that's correct so long as your delta_M ceases to represent the traditional, infinitesimal beam length and is instead taken as the moment at the location where the reinforcing is theoretically required less the moment at the end of the beam (zero for simple span). Of course that just reduces to the absolute moment where the reinforcing is theoretically required.

steveh49 said:

..which fundamentally works for elastic and plastic distributions..

Click to expand...

Agreed, working with the moment increment rather than the absolute shear for shear flow is advantageous for the plastic situation.

Below is AISC requirement on termination of welded cover plate, the concept is the same for beam reinforcing element.

AISC 13th said:

For welded cover plates, the welds connecting the cover plate termination to the
beam or girder shall have continuous welds along both edges of the cover plate
in the length a', defined below, and shall be adequate to develop the cover plate’s
portion of the strength of the beam or girder at the distance a from the end of
the cover plate.
(a) When there is a continuous weld equal to or larger than three-fourths of the
plate thickness across the end of the plate
a' = w (F13-5)
where
w = width of cover plate, in. (mm)
(b) When there is a continuous weld smaller than three-fourths of the plate thickness across the end of the plate
a' = 1.5w (F13-6)
(c) When there is no weld across the end of the plate
a' = 2w (F13-7)

Click to expand...

Nice contribution retired13. Paragraph (e) deals with the minimum length of the development and speaks to the tension/shear lag effect that I mentioned previously. I feel that you could make a pretty good argument that those values ought to be increased for other kinds of reinforcement where the centroid of the reinforcement is further from the connecting welds. Paragraph (d) defines the capacity of the end connection and would be in line with the discussion above.