I need help dimensioning a screw-beam system of a press. I built one prototype but the beam is bending too much.

Below is a sketch of my press. In the middle it has a fixing screw which presses downwards on a beam (3D printed plastic) that presses down my Device Under Test (DUT). The problem is that the beam bends too much so it doesn’t apply pressure evenly downwards on the DUT.

(I used plastic instead of a harder material because I have access to a 3D printer but no access to a workshop)

[![Sketch of beam in press](https://i.stack.imgur.com/Pltvh.jpg)](https://i.stack.imgur.com/Pltvh.jpg)

I did some research and found in the book “Mechanics of Materials” of Gere and Timoshenko following formulae for displacement $\delta$:

$$
\delta = \frac{F\cdot L^3}{48 \cdot E \cdot I}
$$
F = Force downward
L = Length of beam
E = Young's Modulus
I = Moment of inertia

And for the moment of inertia:

$$
I = \frac{b \cdot h^3}{12}
$$

So that I have

$$
\delta = \frac{F\cdot L^3}{4 \cdot E \cdot b \cdot h^3}
$$

I believe I can specify a maximum displacement $\delta$ of let’s say 0.1 mm and the compute the necessary beam height $h$ or choose another material with a higher Young’s modulus E

* My first question is: How do I compute the force F that the screw is foing downwards? I tried looking in Shigley’s “Mechanical engineering Design” Chapter about screws but couldn’t find anything.
* My second question is: Is my dimensioning approach (to specify a maximum bending) correct?

Thanks in advance!
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You are on track with your beam calculations, but I doubt you will be happy with the results, just because a 3-D printed part is unlikely to act the way a cast or milled solid plastic part would. You would be well served to just buy aluminum bar stock and cut it with a hack saw.

As to the screw force produced, I doubt you will be happy with that either. Much of the torque will go to thread friction instead of down into the beam. Without friction, a screw is modeled as an simple inclined plane, so force exerted would be given by dividing the force produced by the sine of the thread angle (not the angle of the threads, but of the pitch, in metric threads the arctan of pitch/diameter). The force would be the torque divided by the radius, to the mid-point of the threads. Greased threads would be appropriate, and you could use a scale to calculate your friction losses.

I recommend using something like a beam that you can place weights on to give you a force driving downward onto your testing beam. It can then act directly without worry of friction. Loosely anchor the beam on one side of your press, have a connector going down to your testing device, and extend the beam over the other side. Known weights will then produce a known force, and you could also change the lever by placing weights on different notches along the beam.
Force F is related to torque and the pitch of the screw:

let's call the radius of your screw r and the tread pitch N and torque t.

$ F= \frac{\tau/r}{(2\pi r/N )} $

And the answer to the 2nd part is the numbers are ok, but these are for very small angles of deformation, things around a few degrees, and L should bee the distance between the supports as Jko said.