Equivalent Stiffness (Springs in Parallel)
Calculate the equivalent stiffness of two springs in parallel, k_eq = k₁ + k₂, by adding the individual stiffnesses. The result, in the same unit (N/m), is always larger than the largest stiffness — springs in parallel are stiffer, since they share the load under the same displacement and the forces add. This is the case of mounts, isolators and supports placed side by side carrying the same component. Reducing spring assemblies to an equivalent stiffness is the first step to compute a vibrating system's natural frequency. Enter the two stiffnesses.
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Rigidez equivalente — molas em paralelo
Quando duas molas são dispostas em paralelo, lado a lado, suportando o mesmo componente, elas compartilham o mesmo deslocamento, mas cada uma contribui com sua força, e as forças se somam. O resultado é um conjunto mais rígido que qualquer das molas isoladas: k_eq = k₁ + k₂ (simples soma, a mesma forma de resistores em série ou capacitores em paralelo). Duas molas iguais de 100 N/m em paralelo dão 200 N/m — o dobro. A regra geral: a rigidez equivalente em paralelo é sempre maior que a maior das rigidezes. Essa é a configuração mais comum em apoios reais: os quatro coxins que sustentam um motor, os vários isoladores sob uma máquina, as molas paralelas de uma suspensão, os apoios de neoprene de uma ponte — todos trabalham em paralelo, dividindo a carga. Saber a rigidez equivalente total é essencial porque ela, junto com a massa do equipamento, define a frequência natural do sistema montado. E aqui há uma tensão de projeto interessante: para bom isolamento de vibração queremos rigidez baixa (frequência natural baixa, bem abaixo da frequência de excitação da máquina), mas para estabilidade e capacidade de carga queremos rigidez alta — o projeto dos isoladores equilibra os dois. Informe as duas rigidezes.
Related Tools
Equivalent Stiffness (Springs in Series)
Calculate the equivalent stiffness of two springs in series, 1 ÷ k_eq = 1/k₁ + 1/k₂, from the individual stiffnesses k₁ and k₂. The result, in the same unit (N/m), is always smaller than the smallest stiffness — springs in series are more flexible, since each deforms under the same force and the displacements add. It is the fundamental calculation to reduce suspension systems, isolators and structures with elastic elements in sequence to a single-degree-of-freedom model, the basis for finding the natural frequency. Enter the two stiffnesses.
Joint Stiffness Constant
Calculate a bolted joint's stiffness constant, C = k_b ÷ (k_b + k_m), from the bolt stiffness k_b (N/mm) and the members' (clamped parts) stiffness k_m (N/mm). The constant C (also called bolt load fraction) is the heart of bolted-joint analysis: it tells what FRACTION of an external tensile load is carried by the BOLT, the rest (1−C) being carried by decompression of the MEMBERS. The value of C reveals the elegant, protective behavior of a preloaded joint: since the (massive) members are usually much stiffer than the (thin) bolt, k_m >> k_b, so C is SMALL (typically 0.2-0.4). This means that when an external load P is applied, only a small portion C·P adds to the bolt tension — most of the load (1−C)·P is absorbed by RELIEF of the compression between the parts. That is why the bolt stress variation is small (good fatigue resistance) and why preload is so beneficial. The smaller C (stiff parts, flexible bolt), the better the bolt protection. The constant C appears in all subsequent formulas: bolt load, residual member force, separation load and fatigue safety factor. Enter the bolt stiffness and the members' stiffness.
Natural Frequency from Static Deflection
Calculate a system's natural frequency from its static deflection, f_n = (1 ÷ 2π)·√(g ÷ δ), where δ is the static deflection caused by self-weight and g the gravitational acceleration (9.81 m/s²). The result, in Hz, is a practical and elegant way to estimate the natural frequency without separately knowing mass and stiffness — you just measure how much the system sags under its own weight. Larger deflections (more flexible systems) give lower natural frequencies, desirable in vibration isolators. It is widely used in spring and mount design. Enter the static deflection (in metres).
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.