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Calculating stress induced in a plate from pin located in it

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meyeal

meyeal

Mechanical
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Firstly, hello to all. I found this forum whilst searching for help and it seems many good answers have been previously provided - hopefully someone can do the same for me.

My problem is this: I have a large, flat plate which is to be lifted parallel to the floor, by 4 pins located in the corners. The 4 corners can be approximated to each bear the same load. The pins lie on the same plane as the large face of the plate i.e. are mounted horizontally by means of drilling and tapping.

The pins are forged bar and by assuming them to be a simple cantilevered beam, fixed at the point of entry into the plate, I have calculated the maximum stress in them to be +/- 137 N/mm^2 and shear stress to be +/- 69 N/mm^2. Yield stress for the material is 435 N/mm^2 so I am satisfied there, and deflection tends to zero.

The plate is made of cast iron, with Youngs Modulus of 69 GN/m^2.

I would really appreciate further advice about how to develop this and analyse the stresses in the plate.
 
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so you're lifting a (very heavy) plate with 4 eye-bolts threaded into the thickness (side) of the plate.

in calculating your stresses did you include an inertia factor on the weight ? or a safety factor (for lifting something presumably over the heads of people/workers) ?

one concern i'd have would be the strength of the thread (reacting the moment) ... though i don't think it'd be a deal-breaker. how long is the thread ? how long is the off-set (distance between the lift and the edge of the plate) ? dia. of the pins ?
 
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Hi prex

Good spot thanks!

Ignore my reference meyeal the reference I gave you was all edges simply supported and it should be the one prex posted.

desertfox
 
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desertfox, prex; thanks for the links. I actually found my way to the 4 corner supported plate but I had previously not encountered that site so it is another useful resource, thank you. I should have been more precise and stated that my concern was rather calculating stresses in the area where the pin locates within the plate.

rb1957; yes I am lifting a heavy plate, approx 43 tonnes. The bolts are actually simple pins, not eye bolts, threaded into the side of the plate. They have a rope sheave mounted on them which is held in place by a washer and retaining pin. A rope eye locates on these sheaves for lifting. I did not include an inertia factor in the original calculation but the yield stress:maximum stress value ratio is 3.17; I would have assumed 4 to be desired.

The thread is M100 and 156mm long, with a further 215mm of unthreaded bar going deeper into the plate. The lifting point can be assumed to be 66mm from the edge of the plate. The dia. of the pin protruding from the plate is 80mm but, as I said, the forged bar is not my concern, rather the cast plate.

Thanks for your quick replies, this is most helpful.
 
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"The bolts are actually simple pins, not eye bolts, threaded into the side of the plate. They have a rope sheave mounted on them which is held in place by a washer and retaining pin." ... is this normal practice for restraining 43 tons ?

"the forged bar is not my concern ..." ... that's not quite the same thing as saying "i'm pretty sure that there isn't a problem with the pins", but then that's probably due to ESL (no slight implied or intended).

i don't think it's a problem with the thread ... 156mm of thread, dia 100mm, sounds penty for what you're doing, i'm just not sure of the strength of a thread in cast iron ...

it's fine to apply factors after your calc ... but it helps us understand your stresses if we know they're unfactored. a factor of 3 would not be unreasonable and this increases your stress to 400MPa, close to yield.

have you checked your calc with the xcalc reference provided ?



 
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rb1957, the lifting point items are rather heavily engineered; there are no lateral forces at work and the steel rope used is regulated as with any other lifting gear. The pins were actually a modification - the trunnion used to be part of the cast plate but a couple broke off when dropped so they were modified.

I assume ESL is english second language which made me laugh as I am currently trying to learn a second language... but it's spanish!

I didn't apply factors before the calculation as I was trying to calculate the existing conditions before I ascertain whether the design is sufficient or not.

I agree with you regarding the strength of a thread in cast but I believe with the loading characteristics they will not see any significant lateral force.

I suspect maximumum stress values in the plate will occur in the thread region but even with FEA modelling this would be very long-winded so I was thinking if I approximate it to be a simple press fit would I be able to develop my calculations?
 
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"there are no lateral forces at work" ... there may be none intended, but the real world has a way of surprising you.

"I didn't apply factors before the calculation as I was trying to calculate the existing conditions before I ascertain whether the design is sufficient or not." ... would caution you alitle, you've calculated a low unfactored stress and concluded things are ok. but there really isn't much reserve in the plate ... i wouldn't have thought a FS of 3 was unreasonable for lifting a 43 ton (100,000 lbs) plate.

"I believe with the loading characteristics they will not see any significant lateral force." ... consider how the thread reacts the moment (due to the off-set lift) ... i'm not saying it's a problem, just something to be aware of.

is this standard with you guys (threading into cast iron) ? is it a bunch of work ? would a cross-bolt work as well, and be easier to build (and analyze) ?

 
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If you are mainly concerned with the stresses in the plate near the lifting point (so presumably almost only shear), you'll have to analyze the local weakening in the plate due to the pin holes, but you don't tell us much about this. How much is the pin hole diameter with respect to plate thickness?

prex
: Online engineering calculations
: Magnetic brakes for fun rides
: Air bearing pads
 
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Just an idle thought. If you are lifting the thing with the load split 'equally' between the 4 threads, and they are arranged roughly as a square, then in practice 2 will be carrying most of the load. So your safety factor of 4 is actually 2.




Cheers

Greg Locock

SIG:Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
 
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"is this standard with you guys (threading into cast iron) ? is it a bunch of work ? would a cross-bolt work as well, and be easier to build (and analyze) ?" ...The plates are already in service (and have been so in this repaired state for around 5 years). At the moment the plate weighs 25 tonnes and is lifted by just 2 pins to tip it over and empty the waste material from the previous ingot casting process. So, each lifting pin is effectively bearing a load of 12.5t already. We actually had an FEA analysis done of the plate in this orientation and this indicated a maximum principal stress value of 26MPa tensile, and Mises stress not exceeding 38MPa.

What we now propose to do is to lift the plate horizontally with additional ironware on (namely, a centre stone and 8 cobbles - distributed equally). I have been asked to ascertain whether the plates are sufficiently engineered to operate in this new configuration. It is assumed that they will be but obviously some evidence is necessary.

"If you are mainly concerned with the stresses in the plate near the lifting point (so presumably almost only shear), you'll have to analyze the local weakening in the plate due to the pin holes, but you don't tell us much about this. How much is the pin hole diameter with respect to plate thickness?" ... The plate is 250mm thick, and the centreline of the pin is located 20mm above the centreline of the plate i.e. there is 105mm material between hole and bottom surface of plate and 65mm between hole and top surface.
 
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meyeal

Just reading your latest post do I understand correctly that prior to what you wish to do now, the plate wasn't lifted parallel to the floor but tipped up on one edge (presumeably one edge rotating on the floor)by lifting the other edge on two pins? if that is the case then those pins would not see anything like 12.5tonnes each.
If this lifting is to be done frequently then not only are you putting greater stress on the cast iron threads but also a much greater range of stress from a fatigue point of view. As you are no doubt aware cast iron is a brittle material and very poor in tension even if you load it in pure shear you will have tensile and compressive stresses acting with the threaded area ie principle stresses acting at approximately 45 deg to the shear stress, I think people here are just trying to warn you that what you appear to be doing doesn't sound very safe.

desertfox

desertfox
 
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It is clearly unfortunate that the hole is closer to the top face of the plate, instead of being near the bottom, but of course I assume this was due to geometric constraints.
A few more comments on the information you provided:
1)38 MPa of Mises stress is quite high for cast iron, possibly quite beyond allowable, though it depends on grade: what kind of allowable stress do you intend to assume for the plate?
2)If an inertia factor was not included in that figure, you already were beyond the edge.
3)As you have a FEM analysis of the plate in its former state, supposedly with a close 3D modeling of the pin hole, why not use it for the new state? You just have to scale the stresses with the new load.
4)As the maximum shear stress is clearly in the ligament above the pin (your 65 mm) at plate edge, this stress critically depends on an assumption to be done on the distribution of pressure along the length of the pin inserted in the hole. This assumption in turn should be based on the more or less close fit of the pin in the hole and would also be more comfortable with a ductile material (and we know that cast iron isn't that much ductile).

prex
: Online engineering calculations
: Magnetic brakes for fun rides
: Air bearing pads
 
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