Machinery's Handbook, 31st Edition
1668 Bolts and Nuts . W S A d 025 t = − ^ h In this formula, W , S t , and d are as previously given, and A = area at the root of the thread, square inches. Example: What is the working strength of a 1-inch bolt that is screwed tightly in a packed joint when the allowable working stress is 10,000 psi? . . W 10,000 0 55 1 0 25 1 3000pounds approx. 2 # # = − = ^ h Formulas for Stress Areas and Lengths of Engagement of Screw Threads.— The criti- cal areas of stress of mating screw threads are: 1) The effective cross-sectional area, or tensile-stress area, of the external thread; 2) the shear area of the external thread, which depends principally on the minor diameter of the tapped hole; and 3) the shear area of the internal thread, which depends principally on the major diameter of the external thread. The relation of these three stress areas to each other is an important factor in determining how a threaded connection will fail, whether by breakage in the threaded section of the screw (or bolt) or by stripping of either the external or internal thread. If failure of a threaded assembly should occur, it is preferable for the screw to break rather than have either the external or internal thread strip. In other words, the length of engagement of mating threads should be sufficient to carry the full load necessary to break the screw without the threads stripping. If mating internal and external threads are manufactured of materials having equal tensile strengths, then to prevent stripping of the external thread, the length of engagement should be not less than that given by Formula (1): (1) In this formula, the factor of 2 means that it is assumed that the area of the screw in shear must be twice the tensile-stress area to attain the full strength of the screw (this value is slightly larger than required and thus provides a small factor of safety against stripping); L e = length of engagement, in inches; n = number of threads per inch; K n max = maximum minor diameter of internal thread; E s min = minimum pitch diameter of external thread for the class of thread specified; and A t = tensile-stress area of screw thread given by Formula (2a) or (2b) or the thread tables for Unified threads, Table 4a through Table 5h . 31416 . 2 1 057735 2 A t # + max min max K n − L K n E ^ e n s = h : D
starting on page 1978, which are based on Formula (2a) . For steels of up to 180,000 psi ultimate tensile strength,
. 31416 2 16 3 E H − a
.
2
2
or
. 0 7854 0 9743 D n − a
A
A
(2a)
k
k
=
=
t
t
For steels of over 180,000 psi ultimate tensile strength,
min
E
2
. 016238
(2b) In these formulas, D = basic major diameter of the thread, E = basic pitch diameter, and the other symbols have the same meanings as before. Stripping of Internal Thread: If the internal thread is made of material of lower strength than the external thread, stripping of the internal thread may take place before the screw breaks. To determine whether this condition exists, it is necessary to calculate the factor J for the relative strength of the external and internal threads given by Formula (3): (3) J A A tensile strength of internal thread material tensile strength of external thread material n s # # = . 31416 2 A n t s = − a k
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