Punch Capacity: Max Hole or Thickness
The inverse of the punch-force tile: the largest round hole (or the thickest material) a press of a given tonnage can punch, max thickness = F / (pi x D x shear) or max diameter = F / (pi x T x shear), with F = capacity_tons x 2000 lb. A 9.8 ton press punches a 0.5 in hole in 0.25 in of 50 ksi-shear steel - or a half-inch hole in that same quarter-inch plate. Answers 'what can my press punch' instead of the force for one hole. Shear strength ~0.8 x UTS; keep press and tooling margin. First-principles shear; the press and tooling govern.
Formula and source
F = capacity_tons x 2000; max thickness = F / (pi x D x shear strength); max round diameter = F / (pi x T x shear strength). The inverse of F = perimeter x thickness x shear strength.
Punching force as sheared area times shear strength solved for capacity - first-principles as in Machinery's Handbook (Industrial Press), by name; public domain.
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