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

[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.

 

[john101]

Interesting set of choices.

I've found two 3/4" strips long enough to fit snugly into the tube.

 

[JBA]

I assume you are still going to cut the tubing to allow welding the strips directly to the lifting arms.

 

[john101]

Yes. And if I understand correctly : then weld the tube onto the arms then weld on the strips and the u piece. ?

 

[JBA]

The top ends of the lifting arms and "U" slot plates should be cut 1 1/2" wide and 3" deep to fit closely to the 1 1/2" X 3" crosspiece bar set.

The crossbar tube should be cut to a length such that when one end of the the 1 1/2" plate set is inserted through the lifting arms there will be enough space between the ends of the tube and the inside of the lifting arms to be able to make a solid strong weld of the bar set to the inside face of the lifting arms inside "U" plates before welding the tube end to that assembly.

Finally, since the crosspiece 1 1/2" bar set should be long enough to extend at least 1/4" or more beyond the face of the "U" plate on the outside of each lifting arm, then a full around fillet weld between the exposed end of the plate set, the outside face of the "U" plate and outer edge of the lifting arm top cap should finish the weld.

Basically the crosspiece two plate set should be welded to the lifting arms as though the 2x3 tube did not even exist and then the ends of the tube should be welded around its ends to the exposed bars fillet welds to the lifting arms.

I am not saying that the whole assembly should not be fitted and tacked together before any welding is done. I am just trying to give a clear description of the type of crosspiece welded end connections I am looking for.

The primary strength of the crosspiece is the from the 1 1/2" by 3" two bar assembly, the 2 x 3 tubing is simply a cover piece that will add needed strength to that bar assembly.

If you have any questions just let me know

 

[JBA]

Disregard the the above post; in error, I wrote it as though the crosspiece slots were in the 2" faces of the 2"x 3" lifting arms. See the below for a correct procedure with the crosspiece slots in the 3" reinforced faces of the lifting arms and that the crosspiece bars are 3/4" x 2 5/8" which reduces the slots' depth to 2 5/8" to make the top of the bars flush with the cut top edge of the 2x3 lifting arm tubes.

Note: Before proceeding with any of the below material cutting and fabrication, I recommend addressing the design and attachment of the piston axle connections on the bottom of the lifting arms to insure that the arms and their reinforcing strips are cut to the correct lengths for the overall assembled arms.

The top end slots of the lifting arms with their 3" x 1/4" longitudinal reinforcing straps should be cut 1 1/2" wide and 2 5/8" deep to fit closely to the 1 1/2" X 2 5/8" crosspiece bars.

(from this point on the term "lifting arm" refers to the lifting arm 2x3 tube complete with its attached inside and outside 3" x 1/4" thick reinforcing straps).

The crossbar tube should be cut to a length such that when one end of the the 1 1/2" bar set is inserted through the lifting arms there will be enough space between the each end of the 2x3 tube and the inside face of each lifting arm to allow making a strong weld of the cross bars to the inside face of the lifting arm and its top end 1/4" thick cover plate before welding the tube end to that assembly.

Finally, since the crosspiece bars should be long enough to extend at least 1/4" or more beyond the the outside face of each lifting arm, then a full around fillet weld between the exposed end of the bars, the outside face of the lifting arm and outer edge of the lifting arm top cap plate should finish the crosspiece to lifting arm connection.

Basically the crosspiece bars should be welded to the lifting arms as though the 2x3 crosspiece tube did not even exist and then the ends of that tube should be welded to the exposed bars fillet weld to the lifting arms.

This does not mean that the whole assembly should not be fitted and tacked together before any finish welding is done. I am just trying to give a clear description of the type of crosspiece to lifting arm welded end connections I am looking for.

The primary strength of the crosspiece is the from the 1 1/2" by 3" two bar assembly, the 2 x 3 tubing is simply a cover piece that will add needed strength to that bar assembly.

Let me know your thoughts and/or any questions on all of this.