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Another Roark Question - Unit Step Function

Another Roark Question - Unit Step Function

Another Roark Question - Unit Step Function

(OP)
I'm trying to use Table 8.1, case 2, Partial distributed load. The formulas use what is called a "unit step function". I looked on page 131 for the definition.

If x < a, then <x-a> = 0. If x > a, then <x-a> = (x-a).

OK, I get that. But what about when x=a? It says it's undefined. I have just that case to figure out. Can someone explain this to me?

RE: Another Roark Question - Unit Step Function

x=a is the start of the partial span load; the pic in Roark is pretty clear that the distributed load at x=a is wa.

another day in paradise, or is paradise one day closer ?

RE: Another Roark Question - Unit Step Function

Consider a simply supported beam with a point load at midspan.  In Roark's notation the shear at any location x along that beam is
P/2 - P<x-(L/2)>0
When x = L/2 the formula is undefined, but that is because the shear value is also undefined (within the limitations of the mathematical model being used).  The formula is still correct.

As for the dilemma this result might leave you in, what shear do you design the beam to withstand at its very centre?  I'd design it to take +P/2 AND -P/2.  Just in case the load wanders by an angstrom either way.

RE: Another Roark Question - Unit Step Function

just draw the beam SF diagram ... the function is discontinuous at x=a (for a non-zero wa).

in my day we'd write SF(x) = FA x<a,
= FA-w.... x>=a

another day in paradise, or is paradise one day closer ?

RE: Another Roark Question - Unit Step Function

(OP)
I'm trying to write an Excel spreadsheet to work these Roark formulas. Discontinuous functions don't work. I need to make <x-a> something. I've decided that when x <= a, then <x-a> = 0. Otherwise, <x-a> = (x-a).

RE: Another Roark Question - Unit Step Function

you will hit this problem with every beam (with a transverse load mid-span) ... at the load there are two values of shear in the beam. i tackled it by excelling the way I'd write out the math (as i posted) so that approaching x=a from one side i'm using one set of equations, appraoching from the other uses a different set. another way would be to consider two points on the beam very close to a.

another day in paradise, or is paradise one day closer ?

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