Resulting force when bending plywood My sister and I are working on a thesis in interior design on a plywood chair similar to the picture, where the red part bends. We are trying to work out how much the plywood would push back when a force F (human sitting on it) is applied on a distance d from the fixture. We have found a formula for bending strength of plywood: Mr = cMpd, where c is a known constant and Mp is the bending strength of the wood that is used. We find this confusing because Mp is in Newton, but the result, Mr is something in Newton*m. We also have no idea how to find the force with which the wood pushes back.

Any help is welcome!
Edit: (to make the question more clear)
What we know:
F, the weight of a person (his mass times g)
d, the distance the person is sitting from the fixture
Mp, something in N about the bending strength of the wood (we got it from  a table)
What we want to know:
The force that the wood aplies on the person.
 A: The units you mention, N*m, are units of energy and torque.  That equation is determining the amount of torque applied to the red portion of your diagram.  You want to figure out how much torque you can apply before the chair breaks.  
Torque is a measure of a time-varying change in angular momentum, which is fancy words for a force applied to a lever arm in your case.  The magnitude of the torque is equal to the magnitude of the force, $F = m \ g$ ($g$ = acceleration of gravity here and $m$ = mass), times the length of the lever, $d$, arm times the angle between the direction of the applied force and a line through the lever arm (in your case, this should be ~$90^{\circ}$ unless the chair bends appreciably or breaks).
Since $d$ is presumably a constant (i.e., the chair seat length doesn't change), then the only variable is the mass of the object placed on the chair.  Since gravity is roughly constant across Earth's surface, the force applied from sitting down is just proportional to the mass times a constant (i.e., the acceleration of gravity ~ 9.8 m/$s^{2}$).
One of Newton's laws states, in slightly different wording than I will state here, that unless the system is accelerating, the force applied will equal the force returned.  Meaning, the force you apply to the chair will equal the force of the chair pushing back on you.  This must be so, otherwise something (either the person or the chair) would be accelerating.
Side Note
Mass is not the same as weight.  Weight is a measure of force.  The reason people often interchange mass and weight is because $g$ ~ constant at all places on Earth's surface.  Thus, the difference between mass and weight is merely a multiplicative constant.  This is why people often approximate 1 lb ~ 2.2 kg, when really that is wrong because kg are units of mass and lbs are units of force (like Newtons).
A: I would guess that you are interested in achieving a comfortable springingness, a comfortable deflection under weight. Calculating it is just a tool to get you there. It may be easier to try different things out until you find the right feel. 
After all, the calculation you are looking for assumes a person sits at a point. That point is their center of mass. For a standing person that is about at your butt. But for a sitting person, it changes if you lean forward or lean back. Also the calculation assumes they sit still. And if you did calculate it and got an answer of 1 cm, would that tell you if the deflection was right? 
If this is true, some rules about deflection might be more helpful that how to calculate it. Since you have used d for something else, I will use x for deflection. 

Wood is like a spring. Deflection depends on the mass (or weight) of the person sitting on it. Assume two people have the same size and shape, but different weights. Assume they sit exactly the same way, and they sit still. Then deflection is proportional to their mass. $x \sim m$
This means if one person weighs 10% more than the other, the chair will deflect 10% more. 

Deflection depends on length of the wood. In your diagram, you have shown a length d for the top. $x \sim d^2$
This means if you increase d by 10%, x will increase 21%. 
Here is how to show this 
You have two chairs. One has $d_1$. The other has $d_2 = d_1 * 110$% $ = d_1 * 1.1$
$x_2 = (d_2)^2 * $ (other stuff) 
$= (d_1 * 1.1)^2 *$ (other stuff) 
$= 1.21 * (d_1)^2 *$ (other stuff) 
$= 1.21 * x_1$

Deflection gets smaller as the wood gets thicker. $x \sim 1/t^2$
1/4" plywood deflect 4 times more than 1/2", and 9 time more than 3/4"

You have shown a diagram where the top piece bends. Keep in mind all the pieces may bend. 
Also safety. A chair that is comfortably springy for a light person may break when a heavy person sits on it. 
A: As long as the chair does not break, the force exerted on the person is equal to the force the person exerts on the chair. 
