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# Stress - cantilevered plate with hole and point force2

## Stress - cantilevered plate with hole and point force

(OP)
Hello

I have a plate 152mm long, 45mm wide and 30mm height (thick). The plate has a 22mm diameter hole through it, hole is 50mm from fixed end. One end is fixed and the other end has a point load of 500N.

I just want to find out what the stress is next to the hole due to bending?

Is it simply σ = (W*l)/(Z)? Where l is distance from the force to the point next to the hole. And I is based only on the dimensions of the sectioned material on either side of the hole, ie Z = ((width - hole diameter)*(height^2))/6.

Or due to the presence of the hole are stress concentration factors needed?

Kind Regards

### RE: Stress - cantilevered plate with hole and point force

Thank you for including a "drawing" with your question, even if I can't open it, yet.
I'll have to do some finagling to open that *.ipt" file. *.ipt" is from Autodesk Inventor, I presume ?

From your description I'd expect a significant stress concentration due the hole.

What is the nominal stress you solved for already?

http://www.amesweb.info/StressConcentrationFactor/...

### RE: Stress - cantilevered plate with hole and point force

if you want the "stress next to the hole" then it sounds like you want to include stress concentration effects. Note, Kt due to bending is not quite the same as Kt due to tension; there are many texts with this in them (like Petersen).

### RE: Stress - cantilevered plate with hole and point force

(OP)
Thank you very much for the feedback.

The axial stress I compute without stress concentration factors is σ = 95 MPa and my allowable is S = 141.6 MPa.

The only problem I see with the stress calculator is that my plate does not satisfy the requirements needed, ie. d/D < 0.3 and 1 < d/t < 7. I eventually found a text by Roark also with these conditions, so not sure what to do still.

There is some wriggle room in the design but not enough to meet the conditions necessary to use the formula.

### RE: Stress - cantilevered plate with hole and point force

so you have a large hole (undimensioned). Kt effects could be relevant, though limited to the material adjacent to the hole. Using Fty as a net section allowable (ie not including Kt) is reasonable. Else FEA it.

### RE: Stress - cantilevered plate with hole and point force

(OP)
Thank you very much, will go with the assumption that the stress is reasonably low enough.

Will also use inventor FEA, just to make sure.

Was hoping to find out the equation behind it as if I had to run a full FEA, it would have to go to the FEA department therefore increasing the cost of the design.

Once again thank you both very much.

### RE: Stress - cantilevered plate with hole and point force

it gets complicated with bending and finite width effects.

you might get somewhere with a crude FEA (like Inventor) looking at three or four hole diameters to get a curve. Make sure to use the stress at the node on the bore of the hole (and not the element stress).

### RE: Stress - cantilevered plate with hole and point force

There are several good reference texts on this type of stress concentration problem. Many of the better Strength of Materials and Theory of Elasticity books give some good general info. on the topic. A fairly low/reasonable nominal/net stress level, due to bending and shear, with the increase factors for hole size vs. plate width, etc. should then be applied. You should consider fatigue and vibration or cyclical loading if they are an issue, because they will have a significant affect on the problem. But, just as important to this somewhat nebulous (exact?) stress level, is good detailing in the area of the hole. I would radius the hole edge all the way around (its circumference) at the top and bot. surfaces of the plate; and I would do the same small radius at the four edges (corners, sides to top and bot. surfaces of the plate) for an inch or so fore and aft of the hole. I would clean up the outer sides of the plate and the inner circumferential surface of the hole, removing any significant tooling or cutting marks. You do not want any nicks, gouges, tooling marks (additional stress raisers or crack starters) transverse to the stress flow direction, particularly in an area where you have this type of stress concentration too.

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