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Chapter 4 Outline - long as the deformations are not larger...

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SECTION 4.1: SPRING ELEMENTS Main Principle: All physical objects deform somewhat under the action of externally applied forces. We see this in the obvious example of a spring. However, other mechanical elements can be described in the same way. Force-Deflection Relations The spring consists of: - free length, L - displacement, x (which is L-final – L) - spring constant, k o k = (Gd^4)/(64nR^3) o G= shear modulus of elasticity o R= radius of the coil o d= diameter of the wire o n= number of coils Linear Force-Deflection Model: - f = kx - units of k: lb/ft or N/m - sign convention: if x>0 corresponds to extension, a positive force represents the spring pulling against whatever is causing this extension Mechanical Elements Spring Constants - can be described by the linear law f= kx for both compression and tension as
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Unformatted text preview: long as the deformations are not larger than the elastic limit-k is the slope of the Tension Force vs. Elongation graph when the elongation is below the elastic limit-Spring Constants of common elements Table 4.1.1 (page 186) Torsional Spring Elements-torsion: resulting twist on the object-“curly symbol” used to denote a torsional spring element-T = k -k units: lb-ft/rad or N-m/rad-Common torsional spring constants are found in Table 4.1.2 (page 187) Spring Elements in Series and Parallel-the relationship is the opposite to that found in circuits-Parallel: f = x(k 1 +k 2 )-Series: k e = (1/k 1 ) + (1/k 2 )-These are only true if system is in static equilibrium...
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