stress in plates

huangyhg

stress in plates
two steel plates 12" x 12" x 0.75"  are welded to a third plate 12" x 28" x 0.75" such that they essentially form the shape of a wf beam 28" deep 12" long with 12" flanges.  the bottom flange is welded or bolted to a structure below. an axial horizontal load is applied to the end of the top flange and web. how would you calculate the max tension and shear stress in the plates.  
the eccentricity between the applied force and the resisting weld (the weld to the structure below) will cause a moment, putting one end of the assembly in tension and one other side in compression.  i'd start by checking for buckling in the web.  you'd then need to check the weld strength for the welds between the flange and webs.  you can do this easily by using the aisc steel manual welding tables.  you will need to also check the weld/bolt to the structure in the same manner.  
chances are one of those factors will control before shear in the plates.
the web plate is 12 x 0.75 with an area of 9 sq. in. and a section modulus of 18 in^3.
if the applied load is f, the maximum shear stress at the middle of the web is 3/2 * f/a = f/6.
moment in the junction of web to bottom flange is f*28, so maximum fiber stress in web = f*28/18 = 1.555f.
stresses in the bottom flange will depend on how it is welded or bolted to the structure below.  an exact elastic solution is not straightforward because the section being analyzed is too close to the applied forces.  finite element analysis techniques would be needed if an exact solution is required.
ba
ba - i must have a mental block.  please help. how does the section modulus od the lplate 12" x 3/4" become 18"^3 ?
bd2/6 = 0.75 * 122/6 = 18.0 in3
what do you get, rittz?
ba
but the web is 28" deep (and the flange is 12" wide) ...
does "horizontal" mean "axial" ? so you have a wf 28" deep, 12" wide, 12" long; anilled to the rest-of-the-world along the bttm flange; and with an axial load applied to the upper flange.
start (as always) with a free body diagram.  where's the load ? where's the force reaction ? is there another reaction (a couple) to maintain moment equilibrium ??  once you see this who should be a long way along to answering your own questions.
rb1957 is quite right.  it is very easy to misinterpret the geometry without a sketch.
ba