NapkinCalc

Mechanics of Materials — Stress & Strain

Pressure vessels — the hoop stress that ties to this app's roots

continues from lesson 5 — values defined earlier in the course stay live here

A pressurised cylinder: internal pressure stretches the wall around its circumference (hoop) twice as hard as along its length.
A pressurised cylinder: internal pressure stretches the wall around its circumference (hoop) twice as hard as along its length.

ELI5: pressure inside a cylinder pushes the wall outward everywhere. The seam running around the circumference (hoop stress, σ = P·r / t) carries twice the stress of the seam running along it. That factor of two is why pressure tanks split lengthwise.

Pinternal:=2MPaP_{internal} := 2 MPa = 2 MPa internal pressure
rtank:=0.5mr_{tank} := 0.5 m = 0.5 m tank radius
twall:=10mmt_{wall} := 10 mm = 10 mm wall thickness
σhoop:=Pinternal∗rtank/twallinMPa\sigma _{hoop} := P_{internal} * r_{tank} / t_{wall} in MPa = 100 MPa hoop stress = 100 MPa
σlong:=Pinternal∗rtank/(2∗twall)inMPa\sigma _{long} := P_{internal} * r_{tank} / (2 * t_{wall}) in MPa = 50 MPa longitudinal stress = 50 MPa
✓ pass abs(σhoop−2∗σlong)<1e−6MPaabs(\sigma _{hoop} - 2 * \sigma _{long}) < 1e-6 MPa hoop stress is exactly twice the longitudinal

Real-world hook: this very formula sizes scuba tanks, propane cylinders, boilers, and the FRP storage tanks NapkinCalc was first built to design.

Where next: Beams & Columns bends these materials — turning a load into the bending stress and sag of a real beam.