bending calculations for non-typical beam situation

huangyhg

bending calculations for non-typical beam situation
i have a horizontal mild steel i-beam that requires a 3/8" thick flat plate (also mild steel) to be welded across the bottom flange – this plate will be vertically oriented and intersect at the center of the lower flange (in other words the plate hangs vertically down from the lower i-beam flange).  the plate is equal in width and thickness to the flange of the beam. the plate will be joined to the flange with a full penetration weld all around. now the oddity is that this plate must be recessed into the flange, so that we must remove a 3/8" wide strip across the full width of the flange and recess this plate into this removed strip.  in this way we can weld the beam and flange together from top and bottom of the intersection.
so we are removing material from the tension side of the flange, but replacing it with material of equal or slightly greater strength. the weld joint must meet x-ray quality before the structure is put into service.  however i see this intersecting plate as a discontinuity in the tension side of this beam but cannot calculate it's affect on the bending strength by ordinary beam calculations. we do not have fea capability.   
can anyone advise on the how to calculate the bending strength of this beam without fea methods?      

check out our whitepaper library.
is this a rolled section or a built-up   
it is a rolled i-beam.
we didn't spec it this way, our customer did and it is to address accessibility issues to complete the full penetration weld and then x-ray inspect it afterwards.
by recessing plate into flange we can perform most of the weld from above with easy access and then add a minor fillet reinforcement with restricted access from below. same situation of acces with the x-ray where we can shoot it from above but not easily from any other position.  
it sounds to me like you're extending the web of the i-beam, and that you're grinding a 3/8" slot into the lower flange, under the web ?  how much material is left around the slot ?
first question that popped into my head is are the plate and beam the same material.  they should be - other wise the math gets harder.
okay, first assumption would be the section is homogeneous.  then it should be as simple as combining the sections:
i_total = i_beam + a_beam (d_beam/2 - y_bar)^2 + i_plate + a_plate (d_pl + d_beam - recess - y_bar)^2.
y_bar is the centroid of the combined section.
now a question: instead of full pen welding the plate why not a fillet weld on each side.  two 5/16" fillets should equal one 3/8" full pen weld.  and besides, i don't think i can picture a pre-approved welding procedure for full pen welding a groove joint that is actually recessed.
is the plate in line with the web or perpendicular to it?  i can only see being able to complete the weld from above if it is perpendicular to the web.
is this an existing beam?  
if you can't get in to weld it from below, how are you going to cut the recess in the beam from below?
let me see if i can address these clarifications in an orderly fashion:
1.plate and groove will run across the full width of the flange (perpendicular to web).
2. beam is not existing and so can be prepped beforehand, but   
if this is being fab'd in the shop, why not full pen weld to the bottom flange without cutting the flange.  
otherwise, what you are doing is really no different than any other full pen weld and can be treated as such (i.e. the weld fully develops the section and no further checks are necessary as long as the typical strength equations for a typical beam of that size without the welds work out).
as you are replacing the cut out material more or less in kind, there is no reduction in strength.  that is, the tension in the bottom flange can travel thru the weld and plate to the bottom flange on the other side of the plate.
however, there is a dramatic change in section at the interface of the flange and the plate.  my gut tells me that you are going to see a stress rise in the flange at this point.  impossible to tell how much without a finite element or lab test.  i would be very careful if this is dynamically loaded.  for static loads, i would add a little conservatism (10%) to the design.
so you're cutting a slot in the lower flange, severing the loadpath ?  the weld is the new loadpath (across the slot, thru the new web) ?  sounds more of an issue if your on the tension flange.
so let me get this straight - you are putting the plate so that if you drew a section looking down the beam you would see the width and depth of the plate, not a skinny 3/8"?
if that is true, and your welds are good and not required to transfer any stress from the plate to the beam, then the bending capacity of the beam has not changed.