# Question on reducing how a beam bends under load



## dave_r_1 (Apr 21, 2018)

This is the frame for the mowing deck on a large walk behind mower I have (mow and deck have been removed, and it's upside down):


The chain is just on it because I used it to straighten that leg (it's 1" x 2" square tubing, likely 1/8" thick but I can't say for sure as I'd have to cut into it to find out).

Last year, I mounted a bagger on it.  Here's how it's attached to the frame:


And the overall unit:



From use, the leg on each side as bent downwards about 1/4" (as in, using a straightedge, when it's flat on one end, there's about 1/4" gap between the other end of the leg and the straightedge).

The bagger unit and mount weight about 75 lbs and the vast majority of the time, the bags are empty or have very little in them, but sometimes they can have upto to about 150 lbs of stuff in them.

My question is, would a good way to reduce this bending be to weld a strip of angle iron to the bottom outside edge of that leg?  I've got 1"x 1/8" and 1" x 1/4" angle iron that I could weld along that edge, with a cutout around that flat piece of steel with the slot in it.  Or is there something else that would do a better job of stiffening those 2 legs?

I can also weld something to the outside of the legs (there's 2 brackets that I'd have to weld around), but I can't weld something bulky to the bottom of it (more than 1/2") as it would limit how high the mowing deck can be raised.  The top of the legs have a number of mounting points on them, so I don't think anything useful can be done welding to the top, and welding to the inside of it would interfere with the mowing deck pulley cover.


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## benmychree (Apr 21, 2018)

Replace the tube with one with a thicker wall.


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## Ray C (Apr 21, 2018)

Weld a flat piece along the side.  Partially overlay it as shown.   Don't weld the full length of the piece.   Just a 1" long weld every couple inches along the full length at the top and bottom of the piece.  It's cheap, dirty and will work.







Ray


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## BtoVin83 (Apr 21, 2018)

We have an old saying "deeper is cheaper"


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## JCByrd24 (Apr 21, 2018)

I’m guessing that tubing is thinner than 1/8” wall if it’s bending under that load. I bet a 1/8”x2” flat bar as simply sistered on one side of each leg would stiffen it up sufficiently. Or as ray suggested I’d you can make the assembly deeper that would be even better.


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## extropic (Apr 21, 2018)

Very hard question to understand. The second and third pictures are postage stamp size. Three different configurations AND three different orientations pictured.
A clear description of the problem will be more likely to get you cogent replies.

FWIW, your tube bends in the vertical plane. Correct? I'm assuming that the bend is toward the ground and between the bagger mount and the front casters. If that's not correct, disregard the following comments except the comment that clarification of the issue might help.

Obvious solution = increase vertical dimension of the tube. You say no room, many mounting points. Is there any way to add stiff struts from high on the bagger mount, forward to the front caster mounts?
A lesser effective option (but maybe good enough) would be to weld a length of .500" diameter rod on the bottom of the frame tube.

Best for me to stop there.


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## Ray C (Apr 21, 2018)

If you were to weld a piece of flat bar or even a piece of that angle iron to the side that it protrudes past the bottom as shown in the illustration in post 3, that would stiffen that up a good bit.

The problem you'd have with that 1/4" wall angle iron, is that it's it sounds like it's 2-3 times thicker than the tube.   Prime candidate for blowing holes thru the tube if you're heavy handed and hot-headed with the welder.




Ray


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## Ray C (Apr 21, 2018)

If you use the angle iron, you could stick it on like this.




Or like this but the above picture would be easier to weld and grass clippings won't get stuck under the lip.




Ray


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## dave_r_1 (Apr 21, 2018)

Sorry, those were the pictures I have of it assembled, so you could get an idea of the overall setup, I don't have the original image files to generate larger ones.  They do bend in the vertical plane.  In the first image, of the frame on the sawhorses, the middle bends slightly upwards (because it's upside down).

I made a small hole in one of the legs, and it is 1/8" thick.  It also has a mowing deck hanging from it, I would guess it's maybe 100-125 lbs (52" fabricated deck).

There aren't any good spots for supports going to the front casters, as they would prevent the removal of the bags when they are full.

I'll give the second suggestion a try (the one in post #3).  I've got some 1" x 3/16" flat steel that I can weld to it.

After this summer, when I remove it to put on a plow attachment I made, I'll check if/how much it has bent.  If it has noticeably bent, I'll attempt to recreate the frame using 2x1x3/16" thick tubing if I can find a local supplier.  Otherwise I'll see if the support arms for the mowing deck would interfere with a wider tubing ( maybe 2x1.5x1/8?).

I'd like to thank everyone for their input & help with this.


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## Downunder Bob (Apr 22, 2018)

In keeping with most consumer devices like this, they are generally made only just strong enough to do the job as intended. As soon as you start adding weight to them they bend or even fail completely. A number of solutions have been offered and each in their own way will work.

I think that to replace the beam with one of thicker section is the way it should have been done when it was  made, but to rebuild it like that is a big job. Some of the next best solutions suggest extending the beam down deeper, a very good way of stiffening a beam is to make it deeper, but there appears to be some space limitations here.

I'd like to suggest a variation on replacing the beam with one of thicker section, don't replace it, just plate it up. Once you've straightened the beam weld a strip of 2"x 3/16" strip on the front and rear face, then take a strip of 1" x 3/8 " and weld it to the top and bottom. you now have a heavy section tube that won't bend and fairly easy to do. 

You could use 1/8" thick and it would most likely be enough, but considering your planning to add even more weight to it I'd go the 3/16". Pay attention to cutting in around the various fittings on the beam and welding right up to them. Also make sure the front and rear plates extend out to the vertical tubes that carry the wheels, maybe even add a couple of gussets to them.


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## dave_r_1 (Apr 22, 2018)

Downunder Bob said:


> In keeping with most consumer devices like this...
> ...but considering your planning to add even more weight to it...



This is a 52" Snapper Pro Hydro walk behind commercial mower model, not a consumer model.  I don't plan on adding anything more to this mower deck.  I have made a plow attachment for this mower, but it uses a separate frame.  The frame (and deck hanging from it) are unbolted from the drive unit, and a frame made specifically for the plow is bolted on.  Here's a pic of the plow/frame attached to the drive unit(it's currently attached to the drive unit):


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## ACHiPo (Apr 22, 2018)

BtoVin83 said:


> We have an old saying "deeper is cheaper"


Yep--increase the moment of inertia.  Think I-beam.  Your angle iron idea is good, anything that increases the vertical height of the tube/member will reduce the tendency to deflect.


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## BGHansen (Apr 22, 2018)

ACHiPo said:


> Yep--increase the moment of inertia.  Think I-beam.  Your angle iron idea is good, anything that increases the vertical height of the tube/member will reduce the tendency to deflect.


As ACHiPo mentions, increase the moment of inertia.  For a rectangular section, the formula is "Base x Height cubed" or "B x H^3".  Think of a 2 x 4 flat vs. on edge.  Moment of inertia for 1 1/2" and 3 1/2" dimensions would be 11.8 in^4 for a flat 2 x 4, 64.3 in^4 for one on the edge or roughly 5.5 times stiffer on the edge.

Stress in a simply support beam is "sigma = (Moment x distance from the neutral axis) / Moment of inertia".  So the bigger the moment of inertia, the less stress in the beam at a given load/torque.

Another formula (last one, been 39 years since I had my mechanics class in college) is "deflection = Force x Length / (cross section area x Young's modulus).  Stress is force per unit area (head is starting to hurt . . .), so "deflection = stress x Length / Young's modulus".  Young's modulus is a material property, use 30,000,000 psi for steel. 

I'm sure more than anyone wants to know and I'm afraid to go further as it's been a long time since I had the class(es)!  There are tables out there for the moment of inertia for a rectangular tube section; just plug in the wall thickness and OD's.  Then do the "b x h^3" add on for your reinforcement and compare the ratios between the two.  The 1/8" tubing with a piece of 1/4" stock of the same height welded vertically with just about double the stiffness of your beam (Two 1/8" thick vertical walls on the tube vs. an added on 1/4" wide bar of the same height).  If you have the real estate to double the height of the add on, your make it stiffer by a factor of 8 (2 times taller ^3).

Bruce


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## RJSakowski (Apr 22, 2018)

The horizontal leg of a piece of angle iron will contribute little to stiffness in a horizontal plane.  A piece of 3/16" x 3" or 4". flat stock welded to the vertical sides will stiffen your frame up considerably.


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## dave_r_1 (Apr 23, 2018)

Welded on strips of 3/16 x 2, with some cutouts to go around existing bits on each leg.





One thing I forgot about was the mounting plate holes (the triangular piece on the end, that bolts to the main drive unit).  The strip I welded on partially covered up that hole, and I didn't notice it until after everything was assembled and I was bolting it to the drive unit.  Ground a small semi-circle for clearance and it's done.

Hopefully this works, as those two round bushings/mounts need to be located pretty precisely for the deck to stay level as it's raised/lowered, which I'm not particularly good at yet.


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## Ray C (Apr 23, 2018)

That's not going to bend anymore!


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## ACHiPo (Apr 23, 2018)

dave_r_1 said:


> Welded on strips of 3/16 x 2, with some cutouts to go around existing bits on each leg.
> 
> 
> One thing I forgot about was the mounting plate holes (the triangular piece on the end, that bolts to the main drive unit).  The strip I welded on partially covered up that hole, and I didn't notice it until after everything was assembled and I was bolting it to the drive unit.  Ground a small semi-circle for clearance and it's done.
> ...


That'll do!


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## Groundhog (Apr 23, 2018)

Now you can put a seat on it and ride.


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