simple beam pressure distributions

huangyhg

simple beam pressure distributions
see attached. anyone have any quick closed form solutions for these pressure distributions on simple beams. looking for vmax, mmax, and max deflection. already looked through roark stress and strain & aisc manuals. didn't want to reinvent the wheel by intergrating.
check this site out, and downlaod the "beamanal" file. i think this is what you're looking for...
whilst it might be reinventing the answer (since someone somewhere has already solved these) i'd derive the answer myself; it ain't rocket science.  
btw, not sure about your vmax for partial span loading.
thes will all be in roarks stress and strain, or try looking up the back of the steel designers handbook.
great homework problems for your first college structures class.  or, it might be a fun intellectual exercise when work is slow....  
but, the only ones you will use in reality are the ones that are already in the steel manual.  
parabolic, semi-circular and sine loads..... seriously?!  a) this isn't a particularly realistic design load.
b) if you were to encounter something like this you should  simplify the loading
c) if you can't simplify the loading then just use risa, enercalc, or excel/mathcad or something rather than doing all the math yourself.
i have not developed the expressions for the characteristical values but plotted values for the whole span using mathcad numerical solutions, so you can have the value at any point in the span. some problems may be amenable to symbolical solution as well, others i think more difficultly just with mathcad directly without using own resources. email me and will send the sheets for the 16 cases, 2 i think (parabolic load cases) i think you have redundant or explain in what are different.
josh, you didn't mention staadpro as one of your options...
  
if you "heard" it on the internet, it's guilty until proven innocent. - dcs
indepth,
you are approaching this problem in the wrong way.  it is much better that you understand what you are doing rather than blindly plugging a formula.
these are all very simple loads which can be solved by hand methods.  instead of trying to remember myriad formulas, learn to reason the thing out for yourself.
in your second example (assuming they number from left to right), you show a partial uniform loading of length "b" symmetrically situated on the beam with distance "a" at each end.  it is obvious by inspection that vmax will be wb/2, yet you show wb(2a + b)/2l, failing to note that 2a + b = l so the expression can be simplified to wb/2.
for deflections, learn the moment-area theorems or the conjugate beam method.  you do not have to integrate to solve these simple problems.
even if i had all of the "closed form solutions" at hand, which i do not, i would not give them to you because i firmly believe you are following the wrong path.  
figure it out for yourself and you will have a real "indepth" solution.
  
ba