Vessel Allowable Stress (ASME)
Calculate the design allowable stress of a pressure-vessel material by the ASME criterion, S = σ_uts ÷ n, from the material minimum tensile strength σ_uts (MPa) and the safety factor n (3.5 in the current ASME VIII Div. 1 edition for tensile strength). The allowable stress S is the MAXIMUM stress permitted in the vessel material in service, and is the basis of all thickness and MAWP calculations — it embeds the safety margin against failure. The ASME code sets the allowable stress as the SMALLEST among several criteria: a fraction of the TENSILE strength (σ_uts/3.5 in the current edition — formerly /4.0, reduced as materials and inspection advanced), a fraction of the YIELD strength (2/3 of σ_yield), and, at high temperatures, criteria based on CREEP and creep rupture (since at high temperature the material deforms slowly under constant load). For each material and temperature, the code TABULATES the S value — this formula shows the tensile-strength criterion, often governing at moderate temperatures. Using the correct allowable stress (from the code, for the right material and temperature) is absolutely essential: it is the safety margin protecting against vessel explosion. Enter the tensile strength and the safety factor.
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Tensão admissível de vaso (ASME)
A tensão admissível de projeto de um material de vaso de pressão, pelo critério ASME, é S = σ_rup ÷ n, a partir da resistência à tração mínima σ_rup e do fator de segurança n (3,5 na edição atual da ASME VIII Div. 1 para a resistência à tração). A tensão admissível S é a tensão máxima permitida no material em serviço, e é a base de todos os cálculos de espessura e de MAWP — ela embute a margem de segurança contra a falha. O código ASME determina a tensão admissível como a menor entre vários critérios: uma fração da resistência à tração (σ_rup/3,5 — antes era /4,0, reduzido com o avanço dos materiais e da inspeção), uma fração do limite de escoamento (2/3 de σ_esc), e, em altas temperaturas, critérios baseados na fluência e na ruptura por fluência. Para cada material e temperatura, o código tabela o valor de S — esta fórmula mostra o critério da resistência à tração, frequentemente o governante em temperaturas moderadas. Usar a tensão admissível correta (do código, para o material e a temperatura certos) é absolutamente essencial: ela é a margem de segurança que protege contra a explosão do vaso. Informe a resistência à tração e o fator de segurança.
Related Tools
Cylindrical Shell MAWP
Calculate the maximum allowable working pressure (MAWP) of a pressure-vessel cylindrical shell, MAWP = (S·E·t) ÷ (r + 0.6·t), from the allowable stress S (MPa), the joint efficiency E, the available thickness t (mm, corrosion-deducted) and the internal radius r (mm). The MAWP is the MAXIMUM pressure a vessel can safely operate at the top, in the operating position, at the design temperature — one of a pressure vessel's most important numbers, stamped on its nameplate. It is the INVERSE of the thickness calculation: given the REAL available thickness (supplied, minus corrosion suffered), the maximum pressure it withstands is computed. MAWP is fundamental for several reasons: it sets the SAFETY-VALVE setting (which must open before pressure reaches MAWP, protecting the vessel from overpressure — the cause of explosions); it establishes the vessel's operating limit; and, recomputed periodically with the REMAINING thickness (measured by ultrasound at inspection, decreasing with corrosion), it monitors the vessel's 'health' over life — when MAWP drops below the operating pressure, the vessel must be repaired or retired. Each component (shell, heads) has a MAWP, and the vessel's is the smallest (the weakest component). Enter the allowable stress, efficiency, thickness and radius.
Hydrostatic Test Pressure
Calculate the hydrostatic test pressure of a pressure vessel by the (simplified) ASME rule, P_test = 1.3 · MAWP, from the maximum allowable working pressure MAWP (MPa). Before entering service (and periodically, at revalidations), every pressure vessel undergoes a HYDROSTATIC TEST: it is filled with WATER (not gas!) and pressurized ABOVE the operating pressure, to verify structural integrity and tightness before entrusting it with a hazardous fluid. ASME VIII Div. 1 (rule UG-99) requires a test pressure of 1.3 times MAWP (corrected by the allowable-stress ratio at test and design temperatures, simplified here). Using WATER is a fundamental safety matter: water is practically incompressible, so it stores very little energy when pressurized — if the vessel ruptures during the test, the failure is localized and relatively safe (it leaks, not explodes); whereas a compressed gas stores enormous energy and a rupture would be EXPLOSIVE, possibly lethal. The 1.3×MAWP test subjects the vessel to higher-than-operating stresses, revealing defects (cracks, bad welds, insufficient thickness) with margin, without reaching general yielding. Passing the hydrostatic test is a condition for the vessel's certification and operation. Enter the MAWP.
Torispherical Head Thickness (ASME)
Calculate the minimum thickness of a torispherical (standard flanged-and-dished) pressure-vessel head, t = (0.885·P·L) ÷ (S·E − 0.1·P), from the internal pressure P (MPa), the spherical crown radius L (mm), the allowable stress S (MPa) and the joint efficiency E. The TORISPHERICAL head is the most COMMON and economical head type in medium-pressure vessels (and universal in shallow tanks): it combines a central spherical crown (radius L) with a toroidal knuckle transition at the edge, joining the cylindrical shell — a form easier and cheaper to stamp than the hemispherical, and more compact (lower height). The 0.885 factor and formula hold for the standard ASME geometry with L ≈ D (crown radius equal to diameter) and the knuckle radius of 6% of the diameter. The price of the economy is a GREATER thickness than the hemispherical (the toroidal transition concentrates stress) and a critical knuckle region, where high bending stresses can arise. The torispherical head is the practical 'middle ground' between the costly hemispherical and the flat (which needs enormous thicknesses). This formula is essential in designing vessels with this head type. Enter the pressure, crown radius, allowable stress and joint efficiency.
Cylindrical Shell Thickness (ASME)
Calculate the minimum wall thickness of a pressure-vessel cylindrical shell by the ASME Section VIII Division 1 formula, t = (P·r) ÷ (S·E − 0.6·P), from the internal design pressure P (MPa), the internal radius r (mm), the material allowable stress S (MPa) and the welded-joint efficiency E (0-1). The pressure vessel — used in boilers, chemical reactors, heat exchangers, compressed-air and LPG tanks, autoclaves — is a CRITICAL safety component: a failure under pressure can be explosive and catastrophic. So its design is rigorously codified, the ASME BPVC (Boiler and Pressure Vessel Code) being the world's most used. This formula gives the minimum cylindrical-shell thickness to safely resist the circumferential (hoop) stress. The '−0.6·P' term refines the thin-wall formula for moderately thick walls. The joint efficiency E (0.70 to 1.0, per weld type and radiographic-inspection degree) penalizes strength at the welded region — fully radiographed welds have E=1.0, uninspected welds lower E. The corrosion allowance is added to the calculated thickness. This is the central pressure-vessel design calculation, and underestimating is inadmissible. Enter the design pressure, internal radius, allowable stress and joint efficiency.
Hemispherical Head Thickness (ASME)
Calculate the minimum thickness of a pressure-vessel hemispherical head by the ASME Section VIII formula, t = (P·r) ÷ (2·S·E − 0.2·P), from the internal pressure P (MPa), internal radius r (mm), allowable stress S (MPa) and joint efficiency E. Heads close the ends of a pressure vessel's cylindrical shell, and their shape is decisive for structural efficiency. The HEMISPHERICAL (half-sphere) head is the MOST EFFICIENT of all: since the sphere distributes pressure equally in all directions (uniform membrane stress), the hemispherical head needs only about HALF the thickness of the cylindrical shell of the same radius and pressure (compare the '2·S·E' in the denominator with the shell's 'S·E'). So it is the choice for high-pressure vessels. The drawbacks are costlier fabrication and greater height (more space). For moderate pressures and costs, elliptical (2:1) or torispherical heads, intermediate, are used. The head-type choice is a trade-off among thickness/material (cost), space and fabrication ease. This formula is fundamental in the complete vessel design, combining shell and heads. Enter the pressure, internal radius, allowable stress and joint efficiency.
Vessel Head Axial Force
Calculate the total axial force the internal pressure exerts on a pressure vessel's cover (or head), F = P · (π·D²/4), from the internal pressure P (MPa) and the internal diameter D (mm); the result is in N. A vessel's internal pressure acts on the ENTIRE internal surface, and on the cover (or closure flange) it generates an axial force tending to PUSH the cover outward — equal to pressure times the cross-sectional area. This force can be ENORMOUS: a modest 1 MPa (10 bar) pressure in a 1-metre-diameter vessel generates a force of nearly 800 kN (80 tonnes!) trying to blow off the cover. This force is what the closure-flange BOLTS (or the head weld) must resist — so flanged pressure vessels have many robust bolts, and computing this force is the starting point of sizing the flange, bolts and gasket. The force also explains why one must NEVER open a still-pressurized vessel: the cover can be hurled with lethal force (serious accidents happen this way, especially with autoclaves and filters). Knowing the cover force is essential for safe closure design and operating procedures. Enter the internal pressure and the diameter.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.