Unit load Fictitious force Support reaction Torque Strain energy Shear force Unit weight Total weight Coordinate Coordinate Deflection Slope, torsional deflection An integral An integral | CHAPTER 50 DEFLECTION Joseph E. Shigley Professor Emeritus The University of Michigan Ann Arbor Michigan Charles R. Mischke . . Professor Emeritus of Mechanical Engineering Iowa State University Ames Iowa STIFFNESS OR SPRING RATE DEFLECTION DUE TO BENDING I PROPERTIES OF BEAMS I COMPUTER ANALYSIS ANALYSIS OF FRAMES GLOSSARY OF SYMBOLS a Dimension A Area b Dimension C Constant D d Diameter E Young s modulus F Force G Shear modulus I Second moment of area J Second polar moment of area k Spring rate K Constant e Length M Moment M J Moment relation MIEIf N Number STANDARD HANDBOOK OF MACHINE DESIGN q Q R T U V Unit load Fictitious force Support reaction Torque Strain energy Shear force w W Unit weight Total weight X Coordinate y 8 e 0 V Coordinate Deflection Slope torsional deflection An integral An integral STIFFNESS OR SPRING RATE 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 - d Gy i r F d G no f sdw hus 501 where D mean coil diameter d - wire diameter N number of active turns In a round bar subject to torsion _ GJG dT GJ n T thus 4 35- 502 and the tensile force in an elongating bar of any cross section is thus k If k is constant as in these cases then displacement is said to be linear with respect to force torque . For contacting bodies with all four radii of curvature finite the approach of the bodies is proportional to load to the two-thirds power making the spring rate proportional to load to the one-third power. In hydrodynamic film bearings the partial derivative would be evaluated numerically by dividing a small change in load by the displacement in the direction of the load. DEFLECTION DEFLECTION DUE TO BENDING The relations involved in the bending of beams are well known and are given here for .
