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Bolted cast-iron pressure-vessel cover: stiffnesses, joint constant, preload and the number of bolts for a load factor (Shigley Example 8-4)

Tool	Bolt Preload and Torque
Source	Budynas, R. G., and Nisbett, J. K. (2015). Shigley's Mechanical Engineering Design, 10th ed. McGraw-Hill Education, New York. Example 8-4 (Sections 8-4 to 8-9: eqs. 8-17, 8-22, 8-23, 8-24, 8-27 to 8-31).
Level	Undergraduate

Problem

A grade 25 cast-iron pressure-vessel cover (E = 14 Mpsi) is held by 5/8 in-11 UNC SAE grade 5 bolts over a grip of 1.50 in against a total separating force of 36 kip. Find the bolt and member stiffnesses and the joint constant, the preload for a reusable connection and its torque, the number of bolts for a load factor of 2, and with that number the load, yielding and separation factors.

Inputs to Enter

Thread 5/8-11 UNC (A_t = 0.226 in²), grade SAE 5 (S_p = 85 ksi), bolt modulus 30 Msi, bolt length blank (standard 2.25 in), joint type bolt and nut
Members 0.75 + 0.75 in cast iron, E = 14 Msi each, no washer or gasket; member stiffness by the conical frusta
Preload 0.75 F_p, nut factor K = 0.20, torque scatter ±25 %; static total load 36 kip on 6 bolts; required load factor 2.0

Open the Bolt Preload and Torque tool (loaded with this example)

Answers

l_d = l_t = 0.75 in → k_b = 5.21 Mlbf/in; k_m = 8.95 Mlbf/in by the frusta (8.81 by the Wileman fit); C = 0.368
F_p = 19.21 kip, F_i = 0.75 F_p = 14.4 kip (σ_i = 63.7 ksi); T = K F_i d = 1,801 lb-in (friction equation with f = f_c = 0.15: 1,767 lb-in)
N = C n_L P_total/(S_p A_t − F_i) = 5.51 (book 5.52 with rounded inputs) → six bolts
Six bolts, P = 6 kip each: n_L = 2.18, n_p = 1.16, n_0 = 3.80 (book 2.18, 1.16, 3.80); P_0 = 22.8 kip per bolt; M.S. proof +0.16, separation +2.80

Notes

The tool's default inputs are this example; press Submit. Example 8-5 of the same chapter (cap screws, 0 to 5 kip fluctuating load) is reproduced by choosing the cap-screw joint, a 1/16 in washer, 5/8 in steel and cast-iron (16 Msi) members and the fluctuating load type: Goodman 2.32, Gerber 3.48, ASME-elliptic 2.91.