TABLE OF CONTENTS Joseph E. Shigley
Professor Emeritus
The University of Michigan
Ann Arbor, Michigan
Charles R. Mischke, Ph.D., PE.
Professor Emeritus of Mechanical Engineering
Iowa State University
Ames, Iowa
| a | Dimension | |
| A | Area | |
| b | Dimension | |
| C | Constant | |
| D, d | Diameter | |
| E | Young s modulus | |
| F | Force | |
| G | Shear modulus | |
| J | Second moment of area | |
| J | Second polar moment of area | |
| k | Spring rate | |
| K | Constant | |
| ? | Length | |
| M | Moment | |
| N | Number | |
| q | Unit load | |
| Q | Fictitious force | |
| R | Support reaction | |
| T | Torque | |
| U | Strain energy | |
| V | Shear force | |
| w | Unit weight | |
| W | Total weight | |
| x | Coordinate | |
| y | Coordinate | |
| ? | Deflection | |
| ? | Slope, torsional deflection |
The spring rate (also called stiffness or scale) of a body or ensemble of bodies is defined as the partial derivative of force (torque) with respect to colinear displacement (rotation). For a helical tension or compression spring,
| (37.1) |  |
where D = mean coil diameter
d = wire diameter
N = number of active turns
In a round bar subject to torsion,
| (37.2) |  |
and the tensile force in an elongating bar of any cross section is
| (37.3) |  |
If k is constant, as in...
