bridge crane help

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If we limit the deflection under load to L/240 the steel stress should be OK.

So for a 28 foot span the allowable center deflection is 1.4 inches.

Using the beam bending equation:

Deflection = W L^3 / (48*E*I)

For steel use E = 300000 0

L = 28 * 12 or 336 inches Solve for W

W = 1.4 * 48 * 300000 0 * I / 336 ^ 3

W = 53.1 * I

Looking up Ixx in the table,

We find a W12x14 beam has an Ixx of 88.6
and could support 4705 pounds at the mid point. This is the TOTAL, so subtract out the dead weight of the trolley for useable capacity

A W12x22 beam has an Ixx of 156
and could support 8291 pounds at the mid point

(You can look up the others on your own. Measure the thickness and width of the flanges to figure out what size beam you have).

Very important:
The classic beam bending equation ignores the possibility of compression flange buckling. This is when the beam twists or rotates out of plane under load. In structures this is usually addressed by laterally supporting the compression flange, typically because it is built into a floor. This bracing holds the beam in one vertical plane and enables it to develop its full load capacity. A beam which is NOT laterally supported on the compression flange (the top flange in your case) supports far less total load before compression flange or lateral/torsional buckling limits it. So don't use the method above if you can't laterally brace the beam at (say) the 1/4, 1/2, and 3/4 points.

To design bar joists, you first get the load per lineal foot. For a 40psf load and a 7.5 foot tributary width, you have 40*7.5 or 300 pounds live load per lineal foot. Allowing for a 10psf dead load (assuming this is a roof), we get 375 pounds per lineal foot total load.

To choose a joist, you look it up in a manufacturer provided table. The most common bar joist is a "K series".

You can find a table here:

Link

For the stated conditions, a 26K12 appears to be the smallest joist that would meet live plus dead criteria (this is the relaxed L/240 live load for a roof; it is too bouncy for a floor). At 26 inches tall, you may object to the depth, but this is to be expected for such a long span. At 16 pounds per foot, this should be reasonably economical -- maybe $32 per foot or $1440 per joist.

The seller of these joists should double check the specifications and size the joists for free -- don't take my word for any of this. But this ought to help you see if you are in the ballpark.

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