How to Calculate Pressure Exerted by C in a Lever and Fulcrum Configuration?

[john101]

 

[JBA]

Using the 1/4" angle on lid to supply some reinforcement at the top of the side plate will not be effective because it will not provide any longitudinal reinforcement support to the lower region of the side plate or along its bottom edge.

Because of the inability to add any longitudinal horizontal stiffening bars across the outside face of the side, because they would interfere with the pulling links movements, the only alternative is to use a sufficient side plate thickness to provide the necessary bending resistance for the side plates and my selected 1" thickness is actually pushing the limits of an A36 plate material and counting on the fact that the what appears to be 1" plate use on the above mentioned observed machine would indicate that the transverse pressure load factor could be closer to .30 rather than the .55 value I found in my study of other forms of soil compaction.

At the same time, since my last post, I have done a bit more investigation of laminated plate structures and their shearing stresses and found an analysis that indicates that, if getting the 1' plate is impossible but you can get some 1/2" plate, then a time consuming alternative to the 1" plate would be to use one full size 6" x 12" piece of the 1/2" plate and then, cut three 12" long strips of that 1/2" plate material at a width that will allow full depth welds between the strips for their full length to both the base plate and to each other. In this manner those longitudinal welds plus the outer edge perimeter welds will provide the shearing strength needed between the base plate and strips and the strips plus the full depth welds will provide an laminated plate equivalent to the solid 1" thick plate. The main risk with this process is the possible (probable?) warping of the plate assembly due to all of the welding.

The 1/2" plate alone will be sufficient for use for the 6" long end plates.

Even with the use of the 1" plate, the one place where adding thee 1/4" angles will be of definite benefit will be as reinforcement on the vertical joints between the side and end plates.

 

[john101]

All right. Thank you for that detailed explanation. I can see there is no way around it. I'll widen my search. That is ok. It'd be no good to be in full swing making bricks and have a failure because I was in a hurry now.

 

[john101]

I got two pieces 1" plate 6x13 in the city this morning. $80 cut. (In the off time I've been building a hand cranked concrete mixer to mix the soil with.)

 

[JBA]

Congratulations on your find.

 

[john101]

It's a good fit. I feel confident about that part now.

I plan to add a rib to the 3/8" end pieces (in blue).

The lift arms are not long enough. I'll upgrade those to the thicker rectangular tubes. They are 2" x 3" od , 3/16" walls. ? with the cross piece on edge.

 

[JBA]

I like the web idea, probably locating that web 4" from the top would be best because that will form a web box around the region where all of high loading will occur.

Obviously, make sure to get a full fillet weld on the ends of the 1" plates.

 

[john101]

It didn't occur to me that only the top plate and the slot the c axle runs in and the case walls are needed to guide the piston in the case. I'm rebuilding the piston as a result. I'm using the same materials but off cutting bevel sections in the upright plates and the square tubes.

Can you confirm that the rectangular tubes for the lifter arms (dimensions given above) are good as is.

I'll fit the cross piece into the arms, then bolt and weld them.

 

[JBA]

I need to see a clearer picture of what you are doing to the piston to make sure I understand all of the changes you describe; and I also don't quite understand what you are showing me in the above illustration, is that the crossbar at the top end of the arms?

Meanwhile I will check the tubes to see if they need any of the same longitudinal bar reinforcement that I specified for the prior arm tubes. I thought the prior sq tubes had 5/16 wall thickness.

 

[JBA]

Your new 2 x 3 x 3/16" tubing is much weaker in tension than the original 1 15/16 Sq x 5/16". The total wall area for the new 2x3 is only 85% of that of the 1 15/16 sq with the 1/8" thicker wall.

 

[john101]

Yes that's the crossbar. I'll post a pic as soon as I have made parts.My apologies. I've rechecked the square tubing and they are 3/16. (I must have misread the vernier or mistyped, damned careless of me).

That mistake by me is no good. Where does that leave us.

 

[JBA]

I will have to do a new calculation but you are still going to need reinforcing straps. I will let you know the size after I do the calc.

 

[john101]

Ok, thank's.

here's what I mean re beveling.

When the plates were square I kept jamming the piston in the case with the slightest of misalignment.

Because only the top plate edges and the slot/shaft ( red lines) are needed to align the piston in the case I cut the sides down so now it moves easily.

 

[JBA]

If you can place the strips on the 3" wide sides then you will require a 3" wide x 1/4" thk strip on both sides welded across each end and 1" up both edges of the strip from the end.
If you place them on thee 2" sides then the strips will you will require a 2" wide x 3/8" thk strip on both sides welded across each end and 1" up both edges of the strip from the end.

 

[JBA]

OK, now that I see what you were saying on the piston that all looks good to me.

 

[john101]

All right. Thank you for that.

I'll do the 3" wide x 1/4" thk strips. I've got plenty of the 1/4" plate to use. A popular size for large bbq plates.

 

[JBA]

When I was working in the oil field, 26" dia x 1/4" x 30" lg sections of well casing pipe cut in half and hinged was what the welders used for making bbq units.

 

[JBA]

On an additional note about the arms. I like for you to send me more details about your new top bar and its connections to the arms

 

[john101]

My idea is to recess the crossbar into the arms, bolt them on and then weld all around.

Then add the strips.

 

[JBA]

Because of the relatively thin tubing walls it would also help to extend the crossbar ends sufficiently beyond the outside of the arms and to allow adding a "U" shaped plate the crosses below the bar between the bar sides and the welds to the reinforcing strips on the sides of arms on both the inside and outside of the arms to transfer some of the shear loading of the bar form the thin 3/16 tubing walls to those side reinforcing strips (i.e. creating a band around the arms in the area of the crossbar).

With regard to the bolting, any support from the bolts to reduce the loading on the welds is going to be a trade off of material strength, the bolt material that you add with the bolt reduces the area of material on the arm wall and reinforcing strips on each side of the bolt holes that is there resist the tensile loading and the holes cause stress concentrations on the sides of the holes. The smaller the bolt, the less it helps; but the larger the bolt, the more it weakens the arms. (If you were pushing with the arms then the bolts would help but since you are pulling, the holes for them are a problem.)

 

[john101]

As previously mentioned 3" wide x 1/4" thk strips are going on the outside and inside of the long arms. I'm not sure what you mean in the first paragraph.

Ok, I get what you mean about the bolts. I'll leave them out.

 

[JBA]

Between the latest drawing in post #159 and the previous drawing in post # 148 I am a bit confused about the orientation of the joining of the crossbar bar and the tubes. Is the top bar flat and notched with the tubing in the notch; or, is the crossbar on edge and the tubing notched as in the drawing in post #148.

 

[john101]

The blue is the crossbar, on edge. It's 2" wide to fit centrally, on the angleiron, over b.

"crossbar on edge and the tubing notched"

 

[JBA]

OK then I will try to give you a picture of the added pieces I am suggesting.

 

[JBA]

I am suggesting that the crosspiece be extended enough beyond the outer face of each arm to allow the above piece to slip around its end from the bottom, with the sides of this piece also being wide enough to be welded to the edges of the reinforcing straps and welded all around to the crosspiece and to the arms and side reinforcing plates; and, that the same type of piece be installed on the inside faces of the arms as well.

 

[john101]

You mean :

Instead of the outer and inner strip (with the outer capping the end of the cross piece.) the outer strips are cut to accommodate an extension of the cross piece and an inverted u piece is welded on to that. ? like what is shown on the right arm here

 

[JBA]

OK, we need more clarification, if the 2" x 3" arms are notched on the 3" sides then forget the above pieces and just notch the 3" wide reinforcing straps at the top along with the tubing and add rectangular plates 2" wide x the height of the crosspiece on the 2" sides to form a band around the top of the arm.

If the 2" sides are notched then add the above "U" pieces as described with the full length 1/4" thk reinforcing straps on the 3" faces of the tubing. If you move the full length straps to the 2" sides then the specified thicker material must be used for them and the same type of rectangular plates as described should be added to the 3" sides to band the top region of the arm.

Either way, the top ends of the arms should be capped.

PS It is actually very fortunate that you decided to make the tubing change because it revealed the error in the wall thickness of the original tubing and those arms would not have been nearly strong enough.

OK, now let me know what you think about all of the above.

 

[JBA]

One last item, what are the height and width dimensions of the crosspiece bar?

 

[john101]

ok, It's paragraph no1 of post 167: 'the 2" x 3" arms are notched on the 3" sides' and therefore 'notch the 3" wide reinforcing straps at the top along with the tubing and add rectangular plates 2" wide x the height of the crosspiece on the 2" sides to form a band around the top of the arm.' ok, I got it.

the cross piece is of the same tubing.

 

[JBA]

If you remember, I previously recommended reinforcing the given 5/16" walls on the original sq tubing,; so actually I had hoped you had switched to a heavy rectangular bar for the crosspiece so here I am going to suggest another change because I am very concerned about the very high loading that is going to be on the even thinner 3/16" bottom face of that beam and the bending moment on the beam at those two edge points, plus the risk of buckling of the thinner 3/16" tube sidewalls.

As a result I am now recommending that you fabricate your own welded 2"x 3" x 1/4" wall rectangular tubing crosspiece using your available 1/4" plate; and, if you have available thicker plate I recommend using that for the fabrication.

By doing this you will keep your current tube outside dimensions while adding additional beam bending strength, better bearing strength at the contact points at the ends of your crosspiece lifting plate and needed increased buckling strength to the tube sidewalls.

Also if you will give me the end clearance between thr inside of the two lifting arms and the ends of the crosspiece lifting plate I will run a new stress analysis on the proposed new crosspiece.

 

[john101]

How about using the 1/4" plate to cut six 2 10/16" pieces the length of the crosspiece and inserting/jamming them/welding in place into the crosspiece tube?

The case is now at a welder (I'm having the important pieces welded professionally). I'll pick it up in the morning.

'clearance between the inside of the two lifting arms and the ends of the crosspiece lifting plate' is 1 5/8" on both sides. The lifting plate is 3x3x1/4" angle iron 4 3/4" wide. The cross piece is bolted on to that. not welded.

The whole thing is getting very heavy. It will be in about 4 parts to be assembled on site.

 

[JBA]

The multiple plates is a good idea but it will be better to use (7) 3" x 1/4" full length strips and eliminate the tubing entirely. These vertical strips do not need to be welded together for their full lengths, only for a couple of inches of stitch welds at their midpoint and ends. These welds are not stress critical because the sum of the individual strips will be carrying the load like a group of individual beams regardless of the welds.

I have analyzed the above and the resulting composite 3" h x 1/3/4" w beam with the 7 strips will be within the normally accepted stress limits for A36 mild steel.

Apart from that the end connections should be as already planned with the "U' shaped plates, end caps on the arm tops, etc.

As an alternative to the plates' edge stitch welds, about 1/2" dia through holes on mid-height of the strips at the center of the span and near the ends with sections of rod inserted through and welded at each end will work just as well as the 2" edge welds to hold the strips aligned.

The reason I want to eliminate the tubing is that it simply interferes with getting good strong welded end connections between the composite strips and the lifting arms that are critical to transferring the loading between those parts.

 

[JBA]

Alternative variations on the above:

If you need the 2" width then obviously you can just add one more plate to the above set.

If you still want the tubing, then the best arrangement would be to cut the tubing short enough to allow a sufficient gap on each end for welding the plate stack directly to the arms with the "U" plates, arm caps, etc and the ends of the tubing to the plate stack and arms.

 

[john101]

Hmmm... I have to remind myself of the amount of forces involved. My instincts don't really encompass the enormity.

I'll go with the 1/4" stack to get 2" wide bar (while looking out for a foot long 2x3" bar.)

If solid how thick would it need to be?

 

[JBA]

It would need to be a minimum of 3" x 1 3/4" (the equivalent of 7 of the 3" x 1/4" thk bars), the effective strength is the same for either the horizontally stacked strips or a solid bar.

My calculations show that one alternative to the above would be to make a 4" x 1" crossbar by stacking four 4" x 1/4" plates or by using a solid bar or cut 1" plate strip. You could put a couple of 1/2" spacers between that narrower plate and the back of the lifting plate angle to keep the lifting point centered 1" from the angle back face.