IntroductionSprings are load bearing elastic objects that are used to store and transfer mechanical energy. They are usually made from a low alloy, medium or high carbon steel. Their relatively high yield strength allows them to return to their original shape and size after a temporary deformation. There are several types of springs, including helical springs, flat springs and torsion springs among others. Each of these types is suited to its own specific application, however there are all constructed from a pliable / resilient material that can withstand a certain degree of deformation without fracture or failure. In engineering applications springs are often used for their compression or load-bearing ability, as well as for dampening out the effects of shock or impact loads.
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1 - Under Axial Load, W
- As the angle of the helix is small, the action on any cross section is approximately a pure torque and the effects of bending and shear can be neglected. The value of the torque is given by:
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2- Under Axial Torque Load, T
- This will produce approximately a pure bending moment of magnitude T at all cross sections. The total strain energy is therefore given by: 9)
Example - Helical Spring Under An Axial Torque T
Open-coiled Helical Spring.Let be the angle of the helix, then the length of the wire
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Example - Axial extension of spring subjected to a load
Leaf SpringsThis type of spring was universally used on cars, lorries, and railway trucks. Whilst the introduction of independent suspension has reduced the automotive use, leaf springs are still in common use. The spring is made up of a number of leaves of equal width but varying length, placed in laminations and loaded as a beam. There are two main types. The "Semi-elliptic" is simply supported at both ends and loaded at it's centre whilst the quarter-elliptic is arranged as a cantilever. Semi-Elliptical Type In order to develop a simplified theory, it is assumed that the ends of each leaf (where they extend beyond their neighbour)are tapered uniformly to a point. It is also assumed that the "pack" is complete and that the shortest leaf is diamond shaped. These assumptions are not realised in practice. The main leaf must by necessity retain it's full width where it is supported. These slight departures from design do not seriously affect the the theory.
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- l = span ( assumed constant)
- b = width of leaves
- t = thickness of leaves
- W = central load
- y = rise of crown above the level of the ends
- n = The number of leaves in the spring
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- The analysis is similar to to that used above. In this case the equivalent plan section varies from zero to nb at the fixed end, and the other values at this end are: 34)
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Example - Leaf Springs