Another Roark Question - Unit Step Function

[vmirat]

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?

 

[IRstuff]

For a structural application, I don't think that'll matter much, but you can certainly set it at the 50% point.

TTFN
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[rb1957]

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 ?

 

[Denial]

Consider a simply supported beam with a point load at midspan.[&nbsp;] 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).[&nbsp;] 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?[&nbsp;] I'd design it to take +P/2 AND -P/2.[&nbsp;] Just in case the load wanders by an angstrom either way.

 

[rb1957]

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 ?

 

[vmirat]

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).

 

[rb1957]

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 ?