HOW2 compute ea. column's load ...... from an irregularly loaded beam with only end columns for support ?

Dear Courtney Thomas:

Sum the moments of each infintessimal slice about one end (aka. integration). The other end support must have an equal and opposite moment. If the support column is moved in from the end, watch your signs.

The other column's supporting force is the difference between the total downward loading, and the support force determined above.

David A. Smith

Number the loads starting from the nearest to one end, so load1 at distance1, load2 at distance 2, load 3 at distance3 etc. Exlude loads directly over columns which transmit force directly.

All distances measured from one end. These loads exert a turning moment, which are resisted by a reaction forceN at the far column which is at distanceN. The beam does not in fact rotate so these moments balance: L1 X D1 + L2 X D2 + L3 X D3... = forceN X Dn (Dn is the length of the beam between columns)

So the reaction on the far column is ForceN = (L1 X D1 + L2 X D2 + L3 X D3) / Dn

And the reaction on the near column is force near = (L1 + L2 + L3...) - ForceN

Brian W

Get a copy of Machinery's Handbook and turn to the section "Strength of Materials". Under that look up "Beams" and "Reactions at the Supports". it tells you every thing that you need to know and gives you all the formulas required.

Jim Y

Go to

Put in data for your beam span. Go to the "Supports" tab... Choose an "Advanced" support type for each of the beam supports. Fix each of them in the X and Y directions. Put in an arbitrary spring constant for the rotational spring, kz. ( this effectively simulates a column which has rotational stiffness ) Put your loads on your beam as you've described them. Do an analysis.

Go back to your model. Try altering your spring constants and varying your loads and rerun. Do again and again to get a feel for how the loads distribute.

If you want to do this by hand... you'll need to use superpostion and deformation compatibility concepts to do the analysis... or ... moment distribution for frames, including corrections for sidesway discrepancies.

Dan :-)