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I have a small machine shop and need to size a beam for a gantry crane. The design is a 4 post fixed design with 2 horizontal beams running parallel across the shop ends with 1 beam to be mounted perpendicular on trolleys on top of the two parallels making a crane that can traverse x and y travel with an electric hoist rasing and lowering loads.

The span is approximately 28 feet and the biggest hoist I have is a mere 1 ton but would like to size it so that I have 3000-4000lbs load capacity. Also consider that the x and y axis trolleys are not motorized so a small dynamic/torsional load will be imparted in the x and y when the payload is pulled around.

I'm thinking a wide flange 12*45 would be a decent size. I'm unsure though if in beam calculators they account for the weight of the beam or if it is just the payload. With a centered load and 4000lbs the deflection shows .311" over 28 feet which seems reasonable enough if I understand what I'm looking at.

I'm thinking I'm looking for a moment of inertia in the x axis if the beam is standing in the traditional direction. I'm also not too clear on deflection limitations on steel.

Thanks for the help.

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    $\begingroup$ 3000 - 4000 ounces, pounds, stones, kilograms or tons ? $\endgroup$ – Solar Mike Sep 14 at 6:37
  • $\begingroup$ Pounds forgot to add that $\endgroup$ – Joe howell Sep 14 at 6:57
  • $\begingroup$ That is a significant beam. From industrial gantrys I have seen , you should probably be thinking -truss. $\endgroup$ – blacksmith37 Sep 16 at 18:45
  • $\begingroup$ I had all the beams and steel needed for everything just needed an appropriately sized spanner beam. It will look nearly identical to this one ton here cdn.shopify.com/s/files/1/0051/2291/6416/products/… I don't mind it being oversized or less than efficient I have the ceiling space for it all. I priced a w14 * 43 and that would still come in under 4k lbs over head. 2500 for load and 1200 for beam weight $\endgroup$ – Joe howell Sep 17 at 0:58
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Although this is probably a question best answered by @kamran (I'm not familiar with imperial units or with safety factors in US) I'll give it a shot (just to improve my game).

Assuming the wide flange properties I found are correct

  • $I_{xx}= 350 [in^4]$
  • $h = 12.06 [in]$ depth of beam
  • $m_{beam}= 45 \frac{lb}{ft} $

Although the mass of the beam is distributed, I am assuming that it is located in the center to make a more conservative estimation. the total load should be:

$$P_{tot}[lbf] = m_{beam}g L + P_{Load} $$

where:

  • $ m_{beam}\cdot L \cdot g = 1260 [lbf]$
  • $ P_{beam}\cdot L \cdot g = 4000 [lbf]$

The maximum bending moment is at the center :

  • $ M_b = P_{tot}*\frac{L}{2}= 73640 [lbf\cdot ft]$

Then the maximum stress is $$\sigma_b = \frac{M_m}{I_xx}\cdot \frac{h}{2} = 15.2245 [ksi] = 105[MPa]$$

$$\delta = \frac{P \cdot L^3}{48\cdot E \;I_xx}= 0.4 [in]$$

For the static calculation, this is marginally ok. The safety factor seems to be about 2-3. However since you mention dynamic loads, I would feel prefer it to be slightly more beefy.

In any case, I would wait for @kamran's verdict.

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  • $\begingroup$ Yeah the beam I had on hand to use was around a w12 and about 80 lb ft and the weight of it was more than what I wanted to use. Plus it was welded in the center and not a solid beam. I've heard before that load bearing cranes and what not have a safety factor of 10x in commercial settings. This isn't a shop where anyone but myself works in and if it has a safety factor of 2-3 on a 4k lb load I'd be comfortable hanging ~2500lbs off of it. My electric hoist is 200lbs plus 50lbs chain, another 50 for trolley and the hoist will lift a tad over 1 ton. I appreciate the input. $\endgroup$ – Joe howell Sep 14 at 11:17
  • $\begingroup$ That's why I suggested in the first place to wait for kamran. He usually responds to this type of answers and his reponses are usually a treasure trove of succinct knowledge and experience. $\endgroup$ – NMech Sep 14 at 11:19

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