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where Nt is the total number of coils in the spring When a spring is compressed to its minimum length, it is said to have bottomed out At the point where a spring bottoms out, the spring rate increases greatly, since further compression requires deformation in the packed spring wires This characteristic is sometimes exploited to create progressive springs in which the spring rate increases as the spring is compressed Figure 1112a illustrates a compression spring with varying pitch Unlike the constant pitch spring, where all coils bottom out at once, the more closely spaced coils on a variable pitch spring bottom out at a lower spring de ection than the more widely spaced coils When a coil bottoms out, the effective number of coils is reduced, so the spring displays a stiffening characteristic in compression, as illustrated in Fig 1112b Note that the bottoming out effect only occurs in compression, since the coils continually move further apart when a coil spring is placed in tension 1142 Compliance of Other Mechanical Elements Spring rates for any element in the system can be obtained through experimental testing of the force-displacement relationship or, for simple geometries, from basic results from mechanics of materials A few common force-de ection relationships for simple geometries and their corresponding spring rates are listed in Table 111; many more can be found in engineering handbooks or textbooks on the mechanics of materials (Popov, 1976, Chen, 1982, Relvas, 1985, Ungar, 1985) If the desired relationship is not readily available, spring



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1 A review of the fundamentals of analysis is presented here Knowledge of applied mechanics can be utilized by applying laws of equilibrium, compatibility, strain displacement relations and boundary conditions Whether it is the nite element method or partial differential

Summary

F Last coil bottoms Next coil bottoms d (compression)

.

d (tension)





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equations approach, it is mathematically convenient to assume Cartesian coordinates in three dimensions 2 By performing analysis, we translate the physical concept into a mathematical procedure which serves as the basis of sizing the member or nalizing its design It determines external force effects on the structure, which for equilibrium is resisted by internal forces within the material 3 Stress resultants on a structural member can be idealized as bending moments acting in two planes at right angles and a torsion in the third plane Out of the three moments, one is torsion and the other two are bending moments, all acting at right angles to each other and located in planes at right angles Similarly, the shear forces acting in two planes at right angles and an axial force in the third plane are complementary to each other Out of the three forces, one is axial force and two are shear forces, all acting at right angles to each other and located in planes at right angles This reference system in setting up a mathematical model is widely used in structural mechanics due to its simplicity in locating moments and forces in a structural member It may be further noted that axial force can be compressive or tensile Compressive force may result in global or local buckling when compressive stress is very high Tensile stress may result in tearing of material due to direct tensile stress Magnitude and distribution of forces and moments can be analyzed by the following approaches: 1 Idealizing or selecting a structural behavior Such as representing a straight line for a beam, a convex curve for an arch, or a concave curve for a cable The line element, whether straight or curved, in each case can be assumed to act at the centroid of the cross section 2 Mathematical model Such as a thin plate as compared to a thick plate 3 Reference system for measurements Such as rectangular (cartesian x, y, z coordinates) or curvilinear (r, coordinates) 4 Analytical tools Such as stiffness methods, strain energy method, or differential equations 5 Numerical model Such as solving a system of algebraic equations using matrix inversion, iteration, or the step-by-step Gaussian elimination method 6 Computational model Such as programming computers with high speed, large storage capacities, and virtual memory, which would enable solving a large number of unknowns resulting from multiple load combinations or post-processing of results 7 Manual computation methods Such as checking computed results by empirical methods A designer is also an analyst and must have a clear concept about the fundamentals of the subject Hence, to keep up with technological advancements, the knowledge base for applying the principles and theorems of statics and dynamics to structural behavior needs to be supplemented by continuing education or training courses.

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jPDFViewer - Java PDF Reader / PDF Renderer for Java
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rates can be easily derived from a basic stress analysis First, choose a simpli ed geometry that approximates the shape of the element in question Next, calculate the stress arising in the element as a result of the applied load If it is assumed that the element is acting in the region of elastic deformation (a reasonable assumption for the systems in question here since they must be designed to survive cyclic motion and loading), the stress can then easily be related to strain Finally, the de ection can be calculated from the strain and the spring rate determined from this relationship between force and de ection This procedure is illustrated by a simple example

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Displaying PDF files on browser (Servlets forum at Coderanch)
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