bookshelf test..

admin

I'm building a book case.  this is a prototype for a shelf.  I'm no engineer, so I'm building a prototype shelf and gonna stand on it to see if it will hold my fat *** up.  Since it will span 6' 6" with no center support, the books that will be on it will be heavy.  You're looking at one end of the shelf.  The shelf will be 14 inches deep.  The front and rear of the shelf is in the picture the green pieces in the SketchUp pic.  There will be another 1x1 going across in the center (the red piece in the SketchUp).So, if there are any engineers here, will 3 pieces of 1x1x14gauge spaning 6'6" hold up evenly distributed 200lb's?  I bought some 1x1.5x14gauge in case these square tubings won't work.anyway, on to the pictures:material is all 1"x1"x.072 (14gauge).  This is where I began to go a little crazy.  Taking a smoke break, and put a new battery in my digital caliper. 0.012 tolerance, boohoo.  FWI, the mitering was done on an Ellis 1800.
Reply:Originally Posted by oxy moronI'm building a book case.  this is a prototype for a shelf.  I'm no engineer, so I'm building a prototype shelf and gonna stand on it to see if it will hold my fat *** up.  Since it will span 6' 6" with no center support, the books that will be on it will be heavy.  You're looking at one end of the shelf.  The shelf will be 14 inches deep.  The front and rear of the shelf is in the picture the green pieces in the SketchUp pic.  There will be another 1x1 going across in the center (the red piece in the SketchUp).So, if there are any engineers here, will 3 pieces of 1x1x14gauge spaning 6'6" hold up evenly distributed 200lb's?  I bought some 1x1.5x14gauge in case these square tubings won't work.anyway, on to the pictures:material is all 1"x1"x.072 (14gauge).  This is where I began to go a little crazy.  Taking a smoke break, and put a new battery in my digital caliper. 0.012 tolerance, boohoo.  FWI, the mitering was done on an Ellis 1800.
Reply:I agree.  But there will be something going into the open ends on the ~3.5" later.
Reply:Ahh ok see that wasn't mentioned earlier in the op sorry. And to answer your original question I'm not an engineer. It I don't see why it wouldn't hold 200lb if it's spread out across the entire frame.1973 Lincoln SA 200, Already replaced shunt coils, Idle board (SOLD)1984 Miller Dialarc 250HF, Miller water cooler, 250 AMP water cooled torch, you know the worx.
Reply:I have no idea but I must say your welding table is cool!!!Torchmate 2x2 CNC with Flashcut CNC controlsHypertherm Powermax45 Esab ET220i Razorweld 195 MigRazorweld 200ac/dc TigTormach 770, Tormach xstechRazorweld, Vipercut/Vipermig, SSC Foot Pedal Dealer
Reply:Engineer here.    Based on 1 inch outside square and .072 wall, the area momement of inertia for that cross section is 0.03859 in.^4.Since there's three beams each 78 inches long, we take 200 lbf / 78 in / 3 to get 0.8547 lbf / in.  Plug that into efunda's beam calculator for a simply supported, uniformly distributed load beam and you get a deflection of 0.368 inches in the center, a maximum bending stress of 8420 psi, and a max shear of 33.3 lbf.  With a cross-sectional area of 0.2673 in.^2, the max shear stress is ~125 psi.Looking at the properties of standard A36 low carbon steel, you'd have to get that bending stress up 36,000 psi to hit yield and the shear stress would have to reach 21,000 psi before you'd have problems in that area.  Keep in mind, this is for a simply supported condition, which allows one end to pivot and the other end to pivot and translate, which doesn't account for real-world end conditions such as welding or bolting the ends to something.  Analyzing the stresses in your weld joints would be a whole 'nother ball of wax, but they're close to the ends, so there shouldn't be a lot of bending stress in them.  Also, the real-world center deflection with welded or bolted-down ends should be somewhat lower than the simply supported number given above.Nice table BTW.  Hope you're TIG'ing it - I'd hate to get spatter on that table.  Last edited by dbotos; 04-05-2012 at 01:17 PM.
Reply:thanks a lot of the analysis.  can I get away with only two sticks of 1x1, like in the picture?  and if i used 3 sticks, but the middle stick was .063 (16 gauge)?  I'll absolutely be tigging it.  Usually I tack on this table and bring it to another table to do the welding, even if it's tig.
Reply:I'm an engineer as well, but i'm piggybacking off dbotos moment of inertia because I don't feel like doing the math right at the moment.Short answer for your question about 2 sticks of 1 x 1 I would say No.You won't be overstressed by any means, redoing dbotos analysis with 2 beams instead of 3, I get about 12,000 psi max stress, which is still well below yield, but you are looking at 0.53" of deflection at the center, which I would consider unacceptable.  switching the middle stick to 0.063" wall tube will leave you with something closer to dbotos original answer, but slightly more deflection and stress due to the thinner wall.Like dbotos said, your end connections and the shelf material will influence the deflection numbers given above, and they will probably be lower than the numbers we specified.  Use of alloy steel with a higher yield stress will have no effect since the modulus of elasticity is the same for just about all steel.  Higher strength would only allow you to use less material.Anything you can do to increase the height of the beam helps alot.  Just as an example, if you used 1x2 tube oriented vertically, with 2 beams you'd drop your deflection to 0.03" and your maximum bending stress to 1570 psi, holding everything else constant.Good luck!If it doesn't fit, you aren't hitting it hard enough!Miller AerowaveMiller Radiator 1A4.5" DeWalt (with the paddle switch!)Jackson NexGen Helmet
Reply:wow, thanks a lot dbotos and GT Steve.  That gives me a very good idea on what i should do...but... let me squeek in just one last engineer question.  if i use 1.5x1 inch and orient the tubing vertically... would 2 sticks work?  I'd be pretty satisfied with 3 sticks of 1x1.  2 sticks of 1.5x1 will only save me a little weight and less welding.  but down side is a thicker shelf.
Reply:The area moment of inertia is much better for 1.5 x 1 x 0.072 - it jumps up to 0.1034 in.^4.  Resulting numbers with two sticks of that are:-deflection of 0.2 inches in the center-max bending stress of 7070 psi-50 lbf max shear, which gives a shear stress of 147 psi (divide shear by cross sectional area to get shear stress)For as long of a span as it's covering, I'd say that's pretty good.  Also, each stick would weigh about 7.5 pounds.  That 15 pounds is a 7.5% increase in your distributed load, which bumps the numbers up a little:0.22 inch deflection7600 psi bending stress54 lbf shearNothing major, but usually a good a idea to "remember the weight of the bridge".