Making a 2D Problem into a 1D Problem

[chessguy103]

TL;DR

How can I take a 2D pressure problem and then it into a 1D beam problem?

Hi,

Forgive me for the crowded drawing, but please reference the attached screenshot. Let’s say I have 2 plates bolted together by some bolts (red), and on the inside is a pressure w pushing the top plate up, in psi (lb/in^2). In order to get an estimate for the maximum distance between bolts, I want to take the circled part and treat it as a 1D problem.

My question is, how do I take that w, and convert it into q in lb/in?

Thanks

 

[Tom.G]

It is rather unclear just what "W" and "Q" are, could you give their definition?

For a simplified approach, take the area in square inches that is exposed to pressure and multiply by the pressure.
Total_Force (on plate) = Area(sq.in.) x Pressure (psi)

To find the force on each bolt, divide Total_Force by number_of_bolts.
force_per_bolt = (Total_Force) / (number_of_bolts)

Then you have to decide if the bolts you want to use are strong enough to hold the thing together. (don't forget a safety factor! You don't want it to take someones arm off if it fails.)

Also decide if the plates are stiff enough so they don't deform like a balloon under pressure; and strong enough that they don't tear through at the bolt heads.

For more details, we need one of the Mechanical Engineers to chime in.

Cheers,
Tom

 

[chessguy103]

W is the pressure on the inside surface of the plate in psi, and q is the distributed load (lb/in) when looking at the problem from a 1D point of view, with 2 of the bolts acting as simple supports. The exact values don’t really matter. But let’s say I wanted to prescribe a certain deflection of that beam, and need to solve for L, the distance between the supports (aka bolts). That’s my goal.

So in order to go from psi to lb/in, would I multiply w by the “thickness” of the 1D beam that I’m considering to get to q?

I’m not sure if I’m thinking about this correctly, but that’s what I’m trying to get to.

 

[Lnewqban]

An uniformly loaded plate deforms in

Summary: How can I take a 2D pressure problem and then it into a 1D beam problem?

Hi,

Forgive me for the crowded drawing, but please reference the attached screenshot. Let’s say I have 2 plates bolted together by some bolts (red), and on the inside is a pressure w pushing the top plate up, in psi (lb/in^2). In order to get an estimate for the maximum distance between bolts, I want to take the circled part and treat it as a 1D problem.

My question is, how do I take that w, and convert it into q in lb/in?

Thanks

A plate bolted all around like that deforms very different from a beam supported by hinges.

Anyway, you could just imaginarily remove two rows of bolts on the longer side of the plate, and use the same value of pressure for uniformly distributed load and consider only the width of the plate supporting that load.

The remaining two rows of bolts will function more like two solid embedments at each end of the beam than hinges, but considering hinges would give you a higher value of safety factor.

 

[T1m0]

A plate bolted all around like that deforms very different from a beam supported by hinges.

Anyway, you could just imaginarily remove two rows of bolts on the longer side of the plate, and use the same value of pressure for uniformly distributed load and consider only the width of the plate supporting that load.

The remaining two rows of bolts will function more like two solid embedments at each end of the beam than hinges, but considering hinges would give you a higher value of safety factor.

If this is a real problem and not a purely academic one, you should consult Chapter 8 in Shigley's Design book (or a similar Machine Design book) to arrive a a proper bolt design that accounts for preload, tensile stress area, etc.