Springs in Parallel

Two or more springs are said to be in parallel when they are connected side-by-side so as to act as a single spring.The extension of the combination of springs is their common extension, and the total force is the sum of the forces in the individual springs.k_eq = k₁ + k₂In a parallel arrangement the springs hang side by side from the same support and are joined at the bottom by a bar that carries the load. If the bar stays level, every spring has the same extension Δx, and the load is shared between them, so the total force is the sum of the forces in the individual springs:F = F₁ + F₂ = k₁Δx + k₂Δx = (k₁ + k₂)ΔxComparing this with F = k_eqΔx gives k_eq = k₁ + k₂. For more springs, add every spring constant.The combination is stiffer than any single spring, the opposite of springs in series.Worked exampleSprings of stiffness 200 N m^-1 and 300 N m^-1 are connected in parallel and support a load of 25 N.k_eq = 200 + 300 = 500 N m^-1Δx = F ÷ k_eq = 25 ÷ 500 = 0.050 mThe forces in the springs are 200 × 0.050 = 10 N and 300 × 0.050 = 15 N, which add up to the 25 N load. The stiffer spring carries the larger share.Two identical springs in parallel have twice the stiffness of one spring, so under the same load they extend half as much.