Dam Sliding Safety Factor
Calculate the sliding safety factor of a gravity dam, FS = (μ·W) ÷ F_h, from the base friction coefficient μ (tan of the concrete-foundation friction angle, typically 0.6-0.75), the effective self-weight W (dam weight minus uplift, kN/m) and the destabilizing horizontal force F_h (hydrostatic thrust, kN/m). This factor compares the forces resisting the dam sliding on its foundation (mobilized base friction, proportional to the effective normal force) with those pushing it downstream (the reservoir thrust). It is one of the two fundamental gravity dam stability checks — the other being overturning. Codes typically require sliding FS ≥ 1.5 for normal loading. The simplified form uses friction only; fuller analyses add interface cohesion (c·B). Note how decisive uplift is: it reduces W and thus the numerator — hence the importance of foundation drainage. Enter the friction coefficient, effective weight and horizontal force.
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Fator de segurança ao deslizamento (barragem)
O fator de segurança ao deslizamento de uma barragem de gravidade é FS = (μ·W) ÷ F_h, comparando as forças que resistem ao escorregamento da barragem sobre sua fundação com as que tendem a empurrá-la a jusante. No numerador, o atrito mobilizado na base: o coeficiente de atrito concreto-fundação μ (tipicamente 0,6 a 0,75) vezes o peso próprio efetivo W (o peso da barragem menos a subpressão). No denominador, a força horizontal desestabilizadora F_h — essencialmente o empuxo hidrostático da água represada. Essa é uma das duas verificações fundamentais de estabilidade de barragens de gravidade; a outra é o tombamento (rotação em torno do pé de jusante). As normas exigem FS ao deslizamento tipicamente ≥ 1,5 para o carregamento normal de operação (admitindo-se valores menores para combinações excepcionais raras, como sismo de projeto ou cheia extrema). A formulação simplificada usa só o atrito; análises mais completas somam a coesão da interface concreto-rocha (c·B), que pode ser significativa em fundações sãs. Observe o papel decisivo da subpressão: como ela reduz W, reduz diretamente o numerador e o fator de segurança — é por isso que a drenagem da fundação, que combate a subpressão, é tão crucial para a estabilidade. Informe o coeficiente de atrito, o peso efetivo e a força horizontal.
Related Tools
Hydrostatic Thrust on Dam
Calculate the horizontal hydrostatic thrust per metre of length on a dam face, E = ½·γ·H², from the unit weight of water γ (≈ 9.81 kN/m³) and the water depth H (m) at the upstream face. Since hydrostatic pressure grows linearly with depth (p = γ·h), its diagram is triangular and the resultant is its area, ½·γ·H², applied at one third of the height from the base. This thrust is the main action tending to overturn and slide the dam, and the starting point of gravity dam stability analysis: it generates the overturning moment (about the downstream toe) and the horizontal force resisted by base friction. Dam stability depends on its self-weight (providing the stabilizing moment and normal friction force) exceeding these with adequate margin, also accounting for foundation uplift. Enter the unit weight of water and the depth.
Gear Tooth Bending Safety Factor
Calculate the bending safety factor of a gear tooth, FS = σ_perm ÷ σ, from the material's allowable (permissible) bending stress σ_perm (MPa, the bending fatigue strength with its factors) and the acting bending stress σ (MPa, from Lewis/AGMA from the load). It is the final bending-design check: the material strength must exceed the demand with adequate margin. Gears run for millions to billions of cycles, so the allowable stress is the material's bending FATIGUE strength (at the design-life cycle count), adjusted by reliability, temperature and life factors. Required safety factors depend on criticality and uncertainty (typically 1.5-3 for bending). If FS is insufficient, the module is increased (bigger, stronger teeth), the face width, or a better material/heat treatment used. A tooth breaking by bending fatigue is a CATASTROPHIC, sudden failure (unlike pitting, which gives progressive signs), since the broken tooth comes loose and can damage the whole drive — so bending is designed with generous margins. With the pitting (contact) safety factor, it defines the gear's robustness. Enter the allowable stress and the acting stress.
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.
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.