Stress Intensity Factor (K)
Calculate the stress intensity factor, K = Y × σ × √(π·a), from the geometry factor Y (dimensionless), the applied stress σ (MPa) and the crack size a (m). The result, in MPa·√m, quantifies the intensity of the stress field at a crack tip, the central concept of fracture mechanics. When K reaches the material's fracture toughness (K_IC), the crack propagates unstably and failure occurs — even at stresses well below the yield strength. It is the basis of damage-tolerant design. Enter the geometry factor, the stress and the crack size.
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Fator de intensidade de tensão (K)
A mecânica da fratura nasceu de uma constatação inquietante: estruturas falhavam a tensões muito abaixo do limite de escoamento do material, por causa de trincas e defeitos. A explicação está na concentração de tensões na ponta da trinca, quantificada pelo fator de intensidade de tensão: K = Y × σ × √(π·a). Aqui σ é a tensão nominal aplicada (MPa), a é o tamanho da trinca (m, metade do comprimento para trinca interna, ou o comprimento total para trinca de borda), e Y é um fator geométrico adimensional que depende da forma da peça e da trinca (≈1 para uma trinca pequena num corpo grande). O resultado, em MPa·√m, descreve a severidade do campo de tensões na ponta da trinca. A falha ocorre quando K atinge um valor crítico, a tenacidade à fratura K_IC, que é uma propriedade do material: aí a trinca propaga de forma instável e a peça rompe. Esse critério (K ≥ K_IC) é a base do projeto tolerante a danos: em vez de supor o material perfeito, admite-se que há trincas e calcula-se o tamanho máximo aceitável e os intervalos de inspeção. Informe o fator geométrico, a tensão e o tamanho da trinca.
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Sling Tension Factor
Calculate the tension (load) factor of a sling leg, k = 1 ÷ cos α, from the leg angle from vertical α (degrees). The tension factor is the MULTIPLIER showing how much a sling leg's inclination INCREASES its tension versus a vertical leg. For a vertical leg (α = 0°), the factor is 1 (the leg supports exactly its share of the weight); as the angle opens, the factor grows: 1.04 at 15°, 1.15 at 30°, 1.41 at 45°, 2.0 at 60°, and shoots to infinity approaching 90° (horizontal legs, physically impossible to support). This factor is the quick, standardized way to assess the angle 'penalty' in lifting: just multiply the load per leg (weight ÷ number of legs) by the tension factor to get the real tension. Rigging tables and sling safety labels carry these factors precisely for the operator to adjust capacity. The golden rule of safe rigging is to keep leg angles CLOSED (near vertical, below 45° from vertical whenever possible) — very open legs are a frequent cause of overload accidents. Knowing the tension factor is essential for any lift with inclined sling legs. Enter the leg angle from vertical.
Number of V-Belts
Calculate the number of V-belts needed in a drive, N = P_design ÷ P_belt, from the design power P_design (the power to transmit times the service factor, kW) and the power each individual belt can transmit P_belt (kW, corrected by the wrap-angle and length factors). When a single V-belt lacks capacity to transmit the needed power, SEVERAL belts are used in parallel, running in parallel grooves of the same pulleys (multi-groove pulleys). The belt count is the design power divided by one belt's capacity. The design power includes the SERVICE FACTOR (1.0 to 2.0+), amplifying the nominal power to cover real operating conditions — shocks, frequent starts, hours of daily use, type of driving and driven machine (a crusher has a high factor, a fan a low one). The power per belt comes from the maker's tables for each profile and speed, corrected by the wrap angle (less wrap → less capacity) and belt length. When several belts are used, they should be a MATCHED SET (with identical lengths) to share the load equally — belts of different lengths overload some and idle others. This is the final step of selecting a V-belt drive. Enter the design power and the power per belt.
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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