Tools › Mechanical Design › Fasteners and Power Screws › Thread Engagement and Strength › Example
1/2-13 UNC-2A bolt in a 2B nut: H28 limits of size, thread shear areas, stripping strengths and the required length of engagement
| Tool | Thread Engagement and Strength |
| Source | National Bureau of Standards (1969). Screw-Thread Standards for Federal Services, Part I. NBS Handbook H28, Tables 2.8 and 2.21 and Appendix A5; Barrett, R. T. (1990). Fastener Design Manual. NASA Reference Publication 1228, p. 21. |
| Level | Undergraduate |
Problem
A 1/2-13 UNC-2A steel bolt (F_tu 120 ksi, proof strength 85 ksi) is engaged 0.5 in in a class 2B nut of the same material and carries 8 kip in tension. Find the basic thread dimensions and the tensile stress area, the class 2A / 2B limits of size from the H28 tolerance formulas, the shear areas of the bolt and nut threads over the engagement, the bolt tensile strength and both stripping strengths, the length of engagement that makes the bolt break before either thread strips, and the margins against the load.
Inputs to Enter
- Thread 1/2 in - 13 UNC, classes 2A / 2B, engagement 0.5 in
- Bolt F_tu 120 ksi, nut F_tu 120 ksi, shear strengths blank (0.6 F_tu, NASA RP-1228 p. 21), proof strength 85 ksi
- Load 8 kip, design factor 1.0, nut factor 0.20; joint type bolt in a nut
Answers
- Basic profile: p = 0.07692 in, E = 0.4500, K_n = 0.4167, K_s = 0.4056 in, lead angle 3.11° (3° 7′), A_t = 0.7854 (0.5 − 0.9743/13)² = 0.1419 in² (Table 2.8 prints 0.4500 / 0.4056 / 0.4167 / 0.1419)
- Class 2A tolerance 0.0015 ∛0.5 + 0.0015 √0.5 + 0.015 ∛(1/13)² = 0.004965 in → 0.0050; allowance 0.0015; limits D_s 0.4985 / 0.4876, E_s 0.4485 / 0.4435; 2B: K_n 0.417 / 0.434, E_n 0.4500 / 0.4565 (Table 2.21 p. 2.27, every value)
- Shear areas over 0.5 in: A_ss = π n L_e K_n,max [1/(2n) + 0.57735 (E_s,min − K_n,max)] = 0.3912 in², A_sn = 0.5617 in² (0.4909 and 0.6872 in² at basic dimensions); fractions of the shear cylinders 0.574 and 0.733
- Strengths: P_t = 0.1419 × 120 = 17.03 kip, P_ss = 0.3912 × 72 = 28.16 kip, P_sn = 0.5617 × 72 = 40.45 kip; bolt breaks first (ratios 1.65 and 2.38, margins +0.65 and +1.38)
- Engagement: equal strengths 4 A_t/(πE) = 0.4015 in; H28 2 A_t / (A_ss per inch) = 0.3628 in, 2 A_t / (A_sn per inch) = 0.2526 in; J = 0.696 so the bolt thread governs, required L_e = 0.3628 in (0.5 in entered, M.S. +0.38); proof load 12.06 kip, torque for 0.75 P_p 905 lb-in; load margins +1.13 (tension), +2.52, +4.06, +0.51 (proof)
Notes
The tool's default inputs are this case; press Submit. The bolt, the strengths and the load are illustrative (stated on the page); every thread dimension and limit is the printed H28 value, and test_thread_strength.php (1,699 checks) reproduces 23 rows of Tables 2.8-2.10 and 33 class rows of Table 2.21 to the printed digits, integrates the thread form numerically against the Appendix A5 shear-area formulas, and checks the default against the numpy script in References/Thread-Strength/checks/. The M12 × 1.75 twin (827 MPa, 12 mm engagement) gives A_s 84.27 mm², P_t 69.69 kN and a required engagement of 7.08 mm.