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.
Resultado
—
Constante de rigidez da junta
A constante de rigidez de uma junta aparafusada é C = k_b ÷ (k_b + k_m), a partir da rigidez do parafuso k_b e da rigidez dos membros (peças unidas) k_m. A constante C (também chamada fração de carga do parafuso) é o coração da análise de uniões aparafusadas: ela diz qual fração de uma carga externa de tração é suportada pelo parafuso, sendo o restante (1−C) suportado pela descompressão dos membros. O valor de C revela o comportamento elegante e protetor da junta pré-carregada: como os membros (maciços) costumam ser muito mais rígidos que o parafuso (fino), k_m ≫ k_b, e portanto C é pequeno (tipicamente 0,2 a 0,4). Isso significa que, quando uma carga externa P é aplicada, apenas uma pequena parcela C·P se soma à tração do parafuso — o grosso da carga, (1−C)·P, é absorvido pelo alívio da compressão entre as peças. É por isso que a variação de tensão no parafuso é pequena (boa resistência à fadiga) e por que a pré-carga é tão benéfica. Quanto menor C (peças rígidas, parafuso flexível), melhor a proteção do parafuso. A constante C aparece em todas as fórmulas subsequentes: carga no parafuso, força residual nos membros, carga de separação e fator de segurança à fadiga. Informe a rigidez do parafuso e a rigidez dos membros.
Related Tools
Bolt Load under External Load
Calculate the total tensile force in the bolt when an external load is applied to the joint, F_b = F_i + C·P, from the preload F_i (N), the joint stiffness constant C and the external tensile load P (N). This is one of the most important — and most surprising to the uninitiated — relations of bolted joints: when you apply an external load P trying to 'separate' the parts, the bolt tension does NOT rise from F_i to F_i + P (as intuition suggests), but only to F_i + C·P, where C is typically 0.2-0.4. That is, the bolt only 'feels' a FRACTION of the external load! The reason: most of the external load (1−C)·P merely RELIEVES the compression between the parts (which were compressed by the preload), rather than stretching the bolt more. This is the genius of the preloaded joint — it 'hides' the external load from the bolt. So a well-tightened joint, under a CYCLIC external load (causing fatigue), exposes the bolt to a very small stress variation (proportional to C·ΔP, not ΔP), making it extremely fatigue-resistant. This formula holds while the joint does NOT separate (P below the separation load); above that, the bolt carries the whole load. Enter the preload, stiffness constant and external load.
Bolt Stiffness
Calculate a bolt's stiffness (spring constant), k_b = (A_t·E) ÷ L, from the tensile area A_t (mm²), the material elastic modulus E (MPa) and the grip length L (mm, the effective length under tension between head and nut). When tensioned by the preload, the bolt behaves as a very stiff SPRING: it stretches an amount proportional to the force (Hooke's law), and its stiffness is force per unit elongation. This stiffness is one of two essential ingredients of bolted-joint analysis — the other is the stiffness of the clamped PARTS (members). The ratio between these two stiffnesses (the joint stiffness constant C) determines how an external load splits between the bolt and the parts. Typically the parts (massive, with large effective compression area) are MUCH stiffer than the bolt (thin and long), which is the DESIRED situation: stiff parts absorb most of the external load, protecting the bolt from stress variation and fatigue. Long, thin bolts have low stiffness (good for sharing load), while short, thick bolts are stiff. Knowing k_b is the starting point of fatigue and joint-separation analysis. Enter the tensile area, elastic modulus and grip length.
Joint Separation Load
Calculate the external load that causes a bolted joint to separate (open), P_0 = F_i ÷ (1 − C), from the preload F_i (N) and the joint stiffness constant C. The separation load is the external tensile load at which the compression between the clamped parts fully vanishes — the point where the joint starts to OPEN. Below it, the parts stay compressed and the joint behaves 'smartly' (the bolt feels only C·P of the external load, with small stress variation); ABOVE it, the parts separate, and from then on ALL additional external load goes straight to the bolt (which then takes the whole load, with severe fatigue and failure risk). Joint separation is thus a condition the design must AVOID with margin: a safety factor against separation is applied (the separation load must be well above the maximum expected external load). The formula shows the separation load grows with preload (well-tightened joints separate later) — another reason to use high preloads. Separation also causes leaks (in sealed joints), loss of stiffness and loosening. Ensuring the joint never separates under service load is a fundamental bolted-joint design criterion. Enter the preload and the stiffness constant.
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.