Posted by: TriHonu ® 07/12/2007, 20:44:33 Author Profile eMail author Edit

I am not an engineer and I need some help. I am erecting a I-Beam gantry in my shop. The beam is an S8x18. The beam is 23 feet long supported only at each end. I have the formula to calculate the deflection based on a load at the center of the beam. ie 4000 lbs at center of beam will deflect just over 1 in. How do you compute when the deflection will exceed the Elastic Limit? I have searched the web and tried to find the answer in three books at the library on Statics and the Mechanics of Materials. Beam specifications from Ryerson Steel Data Book: A = Area of section - 5.41 in2 d = Depth of section - 8 in About the Horizontal axis: I = Moment of Inertia - 57.6 in4 S = Elastic section modulus - 14.4 in3 r = Radius of gyration - 3.26 in Thanks, Jeff

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Re: Computing Elastic Limit of Simple Beam Supported at Two Points
Re: Computing Elastic Limit of Simple Beam Supported at Two Points -- TriHonu	Post Reply	Top of thread	Forum

Posted by: swearingen ® 07/13/2007, 09:09:26 Author Profile eMail author Edit

One problem is that this beam is past its Lr, the length at which it is in its lateral-torsional buckling zone of its bending capacity. To put it simply, according to some quick calcs, the beam could hold a steady, non-moving 4000lbs at its center, but it would be on the verge of collapse. Any side movement or jarring would bring the beam and the load crashing to the floor. The good news is that this beam is perfectly acceptable for this use, it just must be braced properly. It's not the straightforward bending and deflection calculations you should be concerned with, it's the details of the connections and top-flange bracing that needs to be adequately dealt with. This is a tall, skinny beam, and there are special considerations to be looked at for this type of beam. Please, please, procure the services of a local structural engineer. These details that I speak of must be taken care of by a professional for your safety.

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Re: Re: Computing Elastic Limit of Simple Beam Supported at Two Points
Re: Re: Computing Elastic Limit of Simple Beam Supported at Two Points -- swearingen	Post Reply	Top of thread	Forum

Posted by: TriHonu ® 07/13/2007, 16:44:26 Author Profile eMail author Edit

Thanks for your response. Safety is the main issue. I am trying to determine what the maximum safe working load is. I threw the 4000 lb spec realizing that one inch of deflection did not seem to be much over 23 ft. But comparing to a commercially built gantry an S8x18 12 ft span would be rated at significantly less load. I suspected it had to do with deflection where the trolley would roll to the center of the beam under load. I had not considered the beam would buckle laterally with the load suspended from the lower flange on a trolley. I'll contact my local steel supplier for a referral. How difficult is it to compute the elastic limit? Is there a simple formula or do you have to compute for each load and compare to a specification? Thank you, Jeff

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Re: Re: Re: Computing Elastic Limit of Simple Beam Supported at Two Points
Re: Re: Re: Computing Elastic Limit of Simple Beam Supported at Two Points -- TriHonu	Post Reply	Top of thread	Forum

Posted by: swearingen ® 07/16/2007, 12:03:37 Author Profile eMail author Edit

The elastic "limit" is the state of stress that the beam is at the cusp of becoming unacceptable for strength use, while remaining elastic. In this case, the elastic limit is indeed involved, since it requires several larger formulas to calculate it. For a properly proportioned beam that didn't have any local or overall buckling problems, the elastic limiting stress would simply be M/S.

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