Beam Deflection Question 2

[Sam R]

Hi all,

I've been working through some designs at work, and I came across a condition of loading where I was unsure of the way to calculate actual deflection. I had 3 unequal point loads, unevenly spaced.

For example:
l = 10ft

P1 = 1kip
x1 = 1ft
P2 = 2kip
x2 = 3ft
P3 = 1.5kip
x3 = 7ft

At first, I figured a simplified way to calculate this was complete a deflection calculation of each individual deflection and sum the results. Would this provide a close enough, preferably more conservative, deflection calculation?

 

[jayrod12]

Yes this would most definitely be a conservative route.

Sometimes for a quick first run I'll sum the loads and apply then as a single point load at midspan. I've got that deflection formula memorized. If that beam size comes back reasonable, then no need to go further.

 

[BAretired]

A beam program makes sense, but you should know how to calculate deflection at any point in a simple span by hand for any type of loading. The Conjugate Beam Method would be a good choice.

BA

 

[BEMPE16524]

FYI:

http://webstructural.com/beam-designer.html

R.Efendy

 

[XR250]

Sometimes for a quick first run I'll sum the loads and apply then as a single point load at midspan. I've got that deflection formula memorized. If that beam size comes back reasonable, then no need to go further.

I do the same.

 

[jayrod12]

I do the same.

Work smarter.. something something.

 

[Sam R]

I guess I left that a little open ended to me wasting my time at work with attempting to do everything by hand. I do have all the available resources at work, but I would like to personally know the computation for myself. I am working on a simplified spreadsheet for what I do to compile a little bit of everything I do in a project into one package.

I'm familiar with Alex Tomanovich's "BEAMANAL" spreadsheet, but I am not familiar with the (P*(L-a)^3)/(6EI) equation he uses for multiple point load situations. I figured it could have been a simplification towards a more conservative route.

 

[rb1957]

calculating the displaced shape of a beam due to a point load isn't that difficult (double integration of M(x)/EI) ... should be in most text books. Superposition of several loads is also easy.

I think it is a good "waste of time" to do the hand calcs yourself at least once.

I think it's an excellent idea to look at different ways of applying these loads (like a single mid-span load (most conservative) or as a UDL (least conservative) to develop your own feel for the solution (and not rely on something you read on the internet)

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

 

[trilinga]

I agree with rb1957.
It will hardly take a few minutes to get the equation for the deflection at any point using double integration/McCaulay's method.
equating the slope equation to zero, the location of max. deflection and thereby he max. deflection can be found.

 

[jrfroe]

Double integration would work well as mentioned. Personally, if I wanted to verify it by hand, I would put together a simple Excel spreadsheet to superimpose the deflection equations for each of the three point loads. I would use AISC Beam Equation #8 to calculate the deflection at regular intervals along your beam for each of the 3 point loads and sum the 3 deflections to come up with the total deflection. Not only is the math simpler, you also get a cool looking graph of your deflection, which also gives you an additional visual check that your results make sense.

 

[rb1957]

I'd use double integration for a single load, ie the general case, then calc for the different loadings, then superimpose the three deflected shapes (note max deflection for a point load isn't at the loading point). I'd use the handbook to check my work.

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