Cantilever Deflection Question

[bsmet95]

I am an engineer for a crane and hoist manufacturer and at times we must design a bridge crane with a long overhang, which may have multiple loads. Is there any way to calculate deflection? I haven't found anything in Machinery's Handbook or other places.

Thanks.

 

[btrueblood]

Get yourself a copy of Roark's Formulas for Stress and Strain. Recall that the principle of superposition works for linear beam theory - you can add the stresses/deflections from seperate load cases, i.e. solve for the P1 load and add to the solution for the P2 load.

 

[bsmet95]

OK, I can do that. Will it also account for angular deflection due to the first load?

 

[dhengr]

Bsmet95:
If you work for a crane manuf’er. you likely have a copy of the AISC Steel Manual around the office. Look at the Beam Diagrams and Formulas, probably #’s 21 & 22. As Btrueblood suggests, superposition works for this problem. Do each load calculation independently and plot the deflections at the 10th points along the canti. length, plus the deflections at the points of the loads, then just add the two deflections at each 10th point for the total deflection curve. There are several deflection formulas, one for max. deflection and others for deflection anyplace along the beam. But, there is more to this problem than just the canti. deflections under load. Someone must also be sure that these canti. beams are not over stressed and are stable under load. That’s part of the entire crane rail beam design process.

 

[rb1957]

the principle of superposition says for example that the moment in the beam for the combined loading is the sum of the moments due to the individual moments; from moments come displacements. the slope of one load doesn't affect the results of another. unless the structure is indeterminant (which your cantilever isn't).

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

 

[bsmet95]

In the case in question, applied stress is well below the allowable for the cantilever. I just needed to check deflection.

 

[drawoh]

bsmet95,

The equations in the Machinery's Handbook and in Roark's Equations for Stress and Strain almost certainly are based on the double integration method you were taught in college. Your beam is simply supported, making double integration fairly easy.

You were taught double integration method, right?

--
JHG

 

[robyengIT]

here a simple program to calculate deflection : the sheet "single-span beam - cantilever"

 

[bsmet95]

Thanks, robyengIT