#round 3 "Thin Wall Pressure Vessel Analysis 'This calculator determines hoop and longitudinal stresses in a thin-walled cylindrical pressure vessel under internal pressure, with a von Mises equivalent stress check against an allowable stress derived from material yield strength and a factor of safety. "References 'Ref 1: Young, W.C. and Budynas, R.G., 2002, Roarks Formulas for Stress and Strain, 7th Edition, McGraw-Hill "Inputs '

Vessel Geometry

' Internal diameter -'D = ? {1000}mm ' Wall thickness -'t = ? {10}mm '

Loading

' Internal gauge pressure -'p = ? {2}MPa '

Material Properties

' Yield strength -'f_y = ? {250}MPa '

Design Parameters

' Factor of safety -'FoS = ? {1.5} "Calculations '

'Click to expand/collapse detailed calculations '

Diameter to Thickness Ratio

R_Dt = D/t ' Diameter to thickness ratio -'R_Dt '

[Thin wall validity check, D/t greater than 20]

Hoop Stress

σ_h = p*D/(2*t)|MPa ' Hoop stress -'σ_h '

[Ref 1, Table 13.1]

Longitudinal Stress

σ_l = p*D/(4*t)|MPa ' Longitudinal stress -'σ_l '

[Ref 1, Table 13.1]

Von Mises Equivalent Stress

σ_vm = sqr(σ_h^2 + σ_l^2 - σ_h*σ_l)|MPa ' Von Mises equivalent stress -'σ_vm '

[von Mises yield criterion]

Allowable Stress

f_allow = f_y/FoS|MPa ' Allowable stress -'f_allow '

Utilization

util = σ_vm/f_allow ' Utilization ratio -'util '

"Results 'Diameter to Thickness Ratio: R_Dt 'Hoop Stress: σ_h 'Longitudinal Stress: σ_l 'Von Mises Equivalent Stress: σ_vm 'Allowable Stress: f_allow 'Utilization: util '

Assessment - Thin Wall Assumption

#if R_Dt ≥ 20 '

VALID - Thin Wall Assumption

D/t ratio = 'R_Dt' is greater than or equal to 20

Thin wall theory is applicable for this vessel.

#else '

WARNING - Thin Wall Assumption

D/t ratio = 'R_Dt' is less than 20

Thin wall assumption may not be valid. Consider a thick wall analysis.

#end if '

Assessment - Stress Check

#if util ≤ 1 '

PASS - Pressure Vessel Stress Check

Utilization = 'util' is less than or equal to 1.0

Von Mises stress of 'σ_vm' is within the allowable stress of 'f_allow'

#else '

FAIL - Pressure Vessel Stress Check

Utilization = 'util' is greater than 1.0

Von Mises stress of 'σ_vm' exceeds the allowable stress of 'f_allow'

Increase wall thickness, reduce vessel diameter, or use higher strength material.

#end if "Conclusion 'The thin-walled cylindrical pressure vessel with internal diameter 'D' and wall thickness 't' under an internal pressure of 'p' has been analyzed. The D/t ratio is 'R_Dt'. Hoop stress is 'σ_h' and longitudinal stress is 'σ_l', giving a von Mises equivalent stress of 'σ_vm'. With an allowable stress of 'f_allow' the utilization is 'util'.

Thin Wall Pressure Vessel Analysis

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