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Bolted plate on a gusset: AISC 360-16 bolt shear, bearing and tearout, effective bolt-group strength, tension and block shear (Purdue CE 470 Example 3.1)
| Tool | AISC Connection Checks |
| Source | Varma, A. H. (2017). CE 470: Design of Steel Structures, Chapter 3 Fasteners, Bolts and Welds. Lecture notes, Purdue University, West Lafayette, IN. Example 3.1; American Institute of Steel Construction (2016). Specification for Structural Steel Buildings. ANSI/AISC 360-16, Chicago, IL. Sections J3.6, J3.10, J4.1, J4.3; American Institute of Steel Construction (2017). Steel Construction Manual, 15th ed. AISC, Chicago, IL. Tables 7-1, 7-4 and 7-5. |
| Level | Undergraduate |
Problem
A 5 × 1/2 in ASTM A36 plate (F_y 36 ksi, F_u 58 ksi) is bolted to a 3/8 in A36 gusset with four 3/4 in A325-N bolts in standard holes, two lines at a 2.5 in gage with two bolts per line at 2.5 in spacing, 1.25 in end and edge distances, single shear. Is the connection adequate for a factored load of 60 kips (LRFD), and which limit state governs?
Inputs to Enter
- Plate A36, t 0.5 in, W 5 in; gusset t_g 0.375 in, F_u 58 ksi; connecting element (J4.1), U = 1.0
- Bolts 3/4 in Group A threads included (F_nv 54, F_nt 90 ksi), standard holes, n_r 2, n_c 2, s 2.5 in, g 2.5 in, l_ev 1.25 in, l_eh 1.25 in, n_s 1, deformation considered, U_bs 1.0
- LRFD, P = 60 kips
Answers
- Bolt shear: φr_n = 0.75 · 54 · 0.4418 = 17.9 kips per bolt, φR_n = 71.6 kips (Manual Table 7-1)
- Plate bearing / tearout: end holes l_c = 1.25 − 0.8125/2 = 0.844 in, φr_n = 0.75 · 1.2 · 0.844 · 0.5 · 58 = 22.03 kips (tearout) ≤ 39.15 kips; interior holes l_c 1.688 in, 44.06 → capped at 39.15 kips (bearing); φR_n = 2 · 22.03 + 2 · 39.15 = 122.36 kips (Tables 7-5 / 7-4: 44.0 and 78.3 kips/in × 0.5)
- Gusset bearing / tearout: 16.52 and 29.36 kips per hole, φR_n = 91.76 kips; the notes' connection strength is the least of 71.6, 122.36 and 91.76 = 71.6 kips > 60 kips
- Effective bolt-group strength (Manual Part 7, lesser of shear and bearing at each bolt in every element): end bolts 22.02 kips (gusset tearout), interior bolts 23.86 kips (bolt shear), φR_n = 0.75 · 91.76 = 68.82 kips — governs, ratio 0.872, M.S. +0.15
- Plate tension: A_n = 2.5 − 2 · 0.875 · 0.5 = 1.625 in² (≤ 0.85 A_g), φP_n yielding 81.0 kips, rupture 70.69 kips; block shear (L block, shear yielding governs) R_n = 0.6 · 36 · 1.875 + 58 · 1.219 = 111.2 kips, φR_n = 83.39 kips
Notes
The tool's default inputs are this example; press Submit. The lecture notes print the bolt shear and the bearing strengths of both elements; the effective-strength, tension and block-shear values are the tool's, checked against the AISC equations and an independent numpy implementation (test_aisc_connection.php, References/AISC-Connection/connection_check.py).