ABSTRACT
It may be instructive here to ponder those elementary cases where individual fasteners behave as conventional structural beams in tension, bending, or shear. As stated in Chapter I, the elementary case of a fastener shown in Fig. 2 may have a variable cross-section. The total change in length under the axial load F follows then from the application of the well-known Hooke's law, which, in the analysis of the fastener given in Fig. 2, yields:
In the formula given by Eq. (1) E denotes the conventional modulus of elasticity expressed in psi (using English units) while L and A (values as indio cated in Fig. 2) are the length and cross-sectional dimensions in linear and square inches, respectively. For a constant cross-section A and the total length L equal to L1 + L2 + L3 +~ + Ls , Eq. (1) reduces to the familiar elementary expression:
L\L= FL AE
(2)
This formula leads to the important definition of a spring constant, Kr, often used in the analysis of mechanical joints held by fasteners:
F AEKr = -=-~L L (3)
Although the calculations of a spring constant using Eqs. (1-3) appear to be simple, the exact dimensions, mechanical properties, and the fabrication techniques may be of some importance in the measurement of bolt stretch (~L) or a spring constant as an indication of preload.. The nominal axial stress in tension is, of couse;
(4)
Here D denotes the nominal fastener diameter, so that the corresponding cross-sectional area becomes:
(5)
The general symbol A refers here only to the nominal cross-section. The actual areas of interest in stress calculations can be estimated on the basis of nominal, major diameter of thread, or root diameter. These are usually called tensile stress and thread root areas, respectively. In inch series these parameters are expressed in terms of the nominal diameter D and the number of threads per inch is denoted by n, as shown in Chapter 7. Similarly, these areas are given as a function of D and p for the metric series, where thread pitch is p.
