what is the force required to seat a staple? i understand the staple needs to overcome the friction force and also push material out to completely seat. how would i go about finding the force required to seat a particular guage thickness? There are formulas out there for withdrawal force, but i think the push force would be higher. 
 A: At least three main forces are relevant to the seating of a staple (also see figure below):


*

*The force required for the leading points of the staple to make a
hole in each layer of paper.

*The force required to overcome friction on the sides of the staple as it slices through successive layers of paper. 

*The force required to bend the staple as it exits the successive layers of paper, contacts the smooth (stainless steel) guiding grooves at the bottom, and bends inwards.


To pierce the paper requires that the force per unit area $F/A$ at the staple leading point, be in excess of the shear strength $\tau$ of the paper, or $F > \tau A$.
As the staple enters the paper stack, the friction coefficient between the staple and the paper, multiplied by the force exerted on the staple trunk sides by the paper it has pierced, gives you the force required to push the stapler down the pile of papers against friction:
$F_{friction} = \mu N_{sideways}$
As the staple exits the paper stack at the bottom, contacting the groove, with a friction coefficient $\mu$ between the stapler and groove surface, the vertical force $F$ must be enough to result in enough stress to cause the outer surface of the staple just exiting the paper, stack to yield in bending. The equation for this stress is:
$\sigma_x = {{My}\over I_x},\qquad$ where M is the bending moment applied, y is the perpendicular distance from the neutral axis, and $I_x$ is the second moment of area about the neutral axis x. of the staple's trunk. The bending moment is $Ftan\theta$, where $F$ is the vertical force applied. To overcome friction between the staple point and the groove, we must add $\mu F$, giving a total requirement
$F(tan\theta + \mu) > \sigma_x$.
After the staple tip exits the bottom of the stack, apart from the initial piercing force, the forces act concurrently.

