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Assessing shear force in combined profile?

Assessing shear force in combined profile?

Assessing shear force in combined profile?

(OP)
I've made a simplified example, see attachment.
A profile of 20mm wide, 100mm high, cantilevered, carries a shear force.
The profile has a through hole in it (diamater 80mm), so that the remaining section is composed of two small rectangles (20 wide x 10 high) as per the attached document.

I'm doing something wrong there, as my shear stress values absolutely do not add up.

The shear force I've chosen is 250 kN, which is a factor 20 higher than reality, but that's only to have reasonable/readable results in the excell chart. Values are for illsutration only.

I've tried Jouravski, but I guess I cannot use it without defining certain conditions, as the average shear stress is noticably higher.
How do I define these conditions, in order to obtain results that are actually worth something?

Note: the dimensions I used in the attachment are all either mm, mm^4, N and MPa (N/mm²).

I'm looking for some guidelines, not for actual results... so if someone would be so helpful of telling me where I'm going off-track with this?

RE: Assessing shear force in combined profile?

What's the question?

Max vertical shear in section?
Max load at tip of cantilever?
Max horizontal shear?

tg

RE: Assessing shear force in combined profile?

(OP)
actual (vertical) shear in the weakened section.

I have taken my textbooks at hand, it is agreed Jouravski does not apply here but none of the books I have cover this situation.

RE: Assessing shear force in combined profile?

i think the question is why is the shear stress calc so different to the average shear stress (625MPa).

i think, FWIW, that you shouldn't consider both rectangles in calculating Sx ... this gives you an unrealistic shear stress on the inner surface. i think you need to consider the two reactangle acting independently, each carrying 1/2 the applied shear.

Quando Omni Flunkus Moritati

RE: Assessing shear force in combined profile?

(OP)
Here is an overview of the situation: it's a curved lever that pivots over an (way to big) bearing.

There is one original force, F, that I have "divided" in the Free Body Diagram (attachment) into a parallel and perpendicular force, and two forces because of the applied moment.

Problem is, FEA gives a result that is about 4x the value I get by hand. Which means either I do not understand how the forces are applied into the section I am evaluating, or something's wrong with the computer analysis.

I tried to apply the shear stress over both sections, and even multiplying them by 1.5 (as Jouravski also gives 50% higher stresses for rectangles when comparing to average shear stress), but I don't get even close to the FEA.

All insights much appreciated...

RE: Assessing shear force in combined profile?

i suspect that your stress peak is very narrow ... i'd consider curved beam effects and stress concentration.

I'm sure you recognise that your FBD is a very simple solution to the problem, linearising and averaging out the peaks.

Quando Omni Flunkus Moritati

RE: Assessing shear force in combined profile?

(OP)
All are very generous radii, so I'd say stress concentration is rather limited.

and yes, I'm aware I am simplifying, but I'm just looking for a 2nd opinion because I do not use FEA regularly, so I don't rely blindly on the results (bad input => bad output, and I make mistakes as well as the next person).
But having a 4x difference seems too large in my opinion, even when examining a simplified situation.

I'll have a read this weekend about curved beams...

Thanks for your insights.

RE: Assessing shear force in combined profile?

but if it it a highly localised peak, your (reasonable) simplifing assumptions have smoothed out the peak (in reality highly localised yielding).

try modelling a straight beam, constant-ish area, under axial load with a big hole in it ... i think there'll still be a stress concentration.

is the hole just a hole, or a boss (that this link is rotating about) ?

Quando Omni Flunkus Moritati

RE: Assessing shear force in combined profile?

(OP)
The lever has a hole in it, with a ball-bearing (press fit) over an axis.

You are probably right about the stress concentration, I'll have another look at it this weekend.
and I'll read up on curved beams.

If I come up with something interesting, I'll update this thread.

I do still wonder about how to analyse shear stress over a "combined" cross section (for possible future cases as well).
I've browsed through Roark's, read the appropriate chapters in J.M. Gere's "Mechanics of Materials", I've got a German similar handbook, I've got Blodgett's books (design of structures and design of weldments), I've got Srinath's "Advanced mechanics of Solids" and my uni textbooks, and none of those mention this case. This cannot be that exceptional? see all the holes that are drilled in beams? (although there, shear almost never defines the profile, but deflection does), ... Oh how little do we know...

RE: Assessing shear force in combined profile?

Kingnero:
That’s a nasty little problem, I’ve never seen a detail where the hole (for the press fit bearing) was such a dominant part of the whole cross section, and the two outer flanges were so small. That’s kinda akin to having a simple span WF beam and removing the entire web section and leaving just the t&b flanges at mid-span. The flgs. must then transit any shear across the web hole opening by means of a secondary bending action; two shallow, but wide beam elements, fixed at each end of the web hole. You might even want to be careful how hard you press fit that bearing into the hole or you will be adding another tensile force field around that hole. For the sake of discussion, let’s assume that 12 o’clock is on your x axis, through the pivot center, and at the hole edge on block A1; and 6 o’clock is on the x axis and hole edge at block A2. The center of curvature for the whole crank is up toward your x-y coordinate marking.

I expect your max. stress is in flange A1 at about 12 o’clock, but I’m not sure off the top of my head where in the 10mm depth of A1. My first guess would be near the top edge of A1. Does your FEA show a von Mises stress as the max.? This is not directly comparable to the way you and I might combine forces (stresses) in your FBD. I would want a very fine mesh in my FEA model in the region of the bearing hole to capture better what is really happening there. And, there is nothing about your structure which confines a small stress max./spike, within surrounding low stressed regions, so this could be critical and more likely to yield and grow. I certainly would not want any nicks or rough spots in the top surface or the top corners of that top flg. If it was advantageous, could you make the bearing and bearing hole a smaller dia.? Could you shift the bearing hole a bit to the compressive side of the crank; thus A1 might be 12mm deep and A2 only 8mm deep? Could you increase the radius of curvature of the crank, moving the center of curvature nearer your x-y axis coordinate marking? These would all likely improve the stress picture.

What I think is happening is that in the top flange you have shear and axial tensile and normal tensile bending stresses combining in the worst possible way. Whereas, in the bottom flange you will have the compressive normal bending stresses tending to confine or cancel the shear stresses. The curved beam aspect of the problem adds a couple more layers of complexity to a long hand analysis. The normal stresses due to bending and axial loads, moving around their curved path, induce a radial stress component perpendicular to the curved path of the normal stresses. This radial component is inversely proportional to the radius of curvature of that flg., thus larger on the top flg. On the top flange this will tend to pull the flange away from the hole and toward the center of curvature, out near your x-y coordinate marking. This radial component will also increase the tensile stress in the top edge of the top flg., as though it was a beam fixed to the left and right of the hole by the full depth section (20x100). In the bot. flg. this radial component will tend to push the flg. away from the hole or center of curvature. Then, the second aspect of the curved beam theory is that the curved beam tends to draw the N.A. of the section toward the center of curvature, so, while you have a solid flg. section and a given I (mm^4), you have a smaller section modulus at the top fiber of the top flg., because the distance to that fiber is reduced. Finally, I suspect that the stress concentration affect that rb1957 is thinking about relates to the condition where the normal stresses flow around a bolt hole in a plate loaded in tension, and cause some stress increases. I also agree with him that you should probably not be using the full section properties to do your long hand analysis.

I’ve never seen a nice closed form, simple solution to this problem. I would split shear and the axial forces btwn. the t&b flange blocks (10x20mm in your sketch) probably in proportion to their relative areas. I would take the (moment)/(90mm lever arm) and apply these couple forces as normal forces/stresses to each flg. This looks essentially like what you are going to do in your latest sketch (FBD). Then I would treat each flg. as an independent element carrying these forces, and make some attempt at applying some of the secondary effects I’ve mentioned.

Who the heck is Jouravsk? This problem is a real head scratcher, I would have to fiddle with it for a while. Could you post some of your FEA work, so we could see some of the stresses that it shows and their locations? In pdf format if you can, since I can see and print that best. Does any of the above correlate with or explain you FEA results?

RE: Assessing shear force in combined profile?

How about a FBD of the complete lever? Is the bearing's axis fixed?

tg

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