Thin-Wall Pressure Vessel Hoop and Longitudinal Stress
The stress a pressure vessel's wall carries, around it and along it.
Example
You enter
- Internal pressure P (psi) 150
- Diameter D (in, mean/inner) 12
- Wall thickness t (in) 0.25
- Allowable stress S (psi, optional) 15000
You get
- Hoop (circumferential) stress 3600 psi
- Longitudinal stress 1800 psi (half the hoop)
- Demand/capacity (hoop) 0.24
Details, formula, and sources
Hoop stress sigma_h = P D/(2t) and longitudinal sigma_l = P D/(4t) = half the hoop (why cylinders split lengthwise), valid for D/t >= 20. A 12 in tank, 0.25 in wall, 150 psi -> 3,600/1,800 psi. Not a substitute for the ASME BPVC or the engineer of record.
sigma_h = P D/(2 t); sigma_l = P D/(4 t); D/t (thin-wall if >= 20); DCR = sigma_h / S_allow.
The thin-wall pressure-vessel membrane-stress relations (Barlow / mechanics of materials), by name.
The thin-wall hoop and longitudinal stress formulas (Barlow's) are published free in any mechanics-of-materials reference. The ASME BPVC and the engineer of record govern.
Estimate. AHJ and licensed professional govern.
Field names used by the API: P_psi, D_in, t_in, S_allow, sigma_h_psi, sigma_l_psi, DCR
- Membrane stress sigma_h = P D/(2 t), sigma_l = P D/(4 t) = half the hoopthin-wall / Barlow
- Thin-wall validity valid for D/t >= 20; below that use a Lame thick-wall checkmechanics of materials
- Not a code check no external pressure, discontinuity/nozzle stress, joint efficiency, or corrosion allowancescope of this tile