NapkinCalc

Mechanics of Materials — Stress & Strain

Shear stress — forces that slice, not stretch

continues from lesson 3 — values defined earlier in the course stay live here

ELI5: a bolt holding two plates feels a force trying to shear it across, not pull it apart. Shear stress τ = V / A uses the same force-over-area idea, but the area is the cross-section being sliced.

Vshear:=20kNV_{shear} := 20 kN = 20 kN sideways force on a bolt
dbolt:=12mmd_{bolt} := 12 mm = 12 mm bolt diameter
Abolt=π⋅(dbolt2)2A_{bolt} = \pi \cdot \left(\frac{d_{bolt}}{2}\right)^{2} = 113.1 mm^2 bolt cross-section
τbolt:=Vshear/AboltinMPa\tau _{bolt} := V_{shear} / A_{bolt} in MPa = 176.84 MPa shear stress ≈ 177 MPa
✓ pass τbolt>0MPa\tau _{bolt} > 0 MPa a real shear stress the bolt must survive