Maximum Moment Calculation Multiple Loads

[WS_11796812]

Does anyone know of a more simple equation to derive the max moment of a simply supported beam. I have 12 equally spaced loads with the first and last being spaced further from the support than the typical spacing. Exterior loads are different from the interior. Heres some pictures of what im working with. The BMD diagram is my check for the moment of the HL93 Inv Loads. I've done this before when only working with a couple concentrated loads but the formula would be to long for this. Would also like to be able to check the moment at any location along the beam 

[terryhendicott]

Hi,

Here is one that does any number of loads on a simply supported beam.  Australian code based.  It shows how to handle multiple loads.

[WS_11796812]

I'm sorry but I'm having trouble with getting this to work for my situation 

[terryhendicott]

Hi,

Have stripped out all the Australian code stuff so it is far simpler

Cheers

Terry

[WS_11796812]

this is what I currently do for the max moment and then the second pic is at the location of the first concentrated load. Works fine but not very clean looking.

[Werner_E]

Unlike Terry, I have no idea about your area of expertise, so I just looked through your worksheet and noted where I thought something could be made easier.

and then

EDIT: Added gammaM.LL_x, which was missing in the sheet you posted

sheet attached

[WS_11796812]

thanks werner that helps out. I still cant figure out figure out how to correlate terry's sheet with mine. His defines specific loads to each distance where all mine all the same for those interior locations. Thats what im having trouble putting together. 

[Werner_E]

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@WS_11796812 wrote:

thanks werner that helps out. I still cant figure out figure out how to correlate terry's sheet with mine. His defines specific loads to each distance where all mine all the same for those interior locations. Thats what im having trouble putting together. 

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Can't comment on this. Guess you'll have to wait until @terryhendicott  is back here again.

[terryhendicott]

Hi,

On the sheet enclosed shows how to use the same load for all positions along the beam.

Have included the deflection calculation for the girder

[WS_11796812]

Sorry for my ignorance, I'm quite new to mathcad. What you've done is sort of what I'm looking for but here's a sheet that might can clarify more.

I'm sure this is a much more simple way to write this matrix but it gets it done to show you. I need the moment result to read in one column with the truck next to it. This picture shows the break down of the loads at each location and the corresponding truck. Maybe this can make more sense?