In
mechanics
Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects ...
, two or more
springs
Spring(s) may refer to:
Common uses
* Spring (season), a season of the year
* Spring (device), a mechanical device that stores energy
* Spring (hydrology), a natural source of water
* Spring (mathematics), a geometric surface in the shape of a he ...
are said to be in series when they are connected end-to-end or point to point, and it is said to be in parallel when they are connected side-by-side; in both cases, so as to act as a single spring:
More generally, two or more springs are ''in series'' when any external
stress applied to the ensemble gets applied to each spring without change of magnitude, and the amount strain (deformation) of the ensemble is the sum of the strains of the individual springs. Conversely, they are said to be ''in parallel'' if the strain of the ensemble is their common strain, and the stress of the ensemble is the sum of their stresses.
Any combination of
Hookean (linear-response) springs in series or parallel behaves like a single Hookean spring. The formulas for combining their physical attributes are analogous to those that apply to
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of a ...
s connected in
series or parallel in an
electrical circuit
An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sour ...
.
Formulas
Equivalent spring
The following table gives formula for the spring that is equivalent to a system of two springs, in series or in parallel, whose
spring constants are
and
.
[Keith Symon (1971), ''Mechanics.'' Addison-Wesley. ] (The
compliance
Compliance can mean:
Healthcare
* Compliance (medicine), a patient's (or doctor's) adherence to a recommended course of treatment
* Compliance (physiology), the tendency of a hollow organ to resist recoil toward its original dimensions (this is a ...
of a spring is the reciprocal
of its spring constant.)
Partition formulas
Derivations of spring formula (equivalent spring constant)
:
:
:
:
See also
*
Truss
A truss is an assembly of ''members'' such as beams, connected by ''nodes'', that creates a rigid structure.
In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assembla ...
*
Duality (mechanical engineering) In mechanical engineering, many terms are associated into pairs called duals. A dual of a relationship is formed by interchanging force (stress) and deformation (strain) in an expression.
Here is a partial list of mechanical dualities:
* force & ...
References
{{reflist
Springs (mechanical)