AISC Connection Checks: Method

AISC Connection Checks

The tool evaluates the limit states of ANSI/AISC 360-16 Chapters D and J for a bolted connection of a plate, gusset, splice plate or tension-member end, and the fillet-welded alternative. Every limit state is reported as the Specification writes it: a nominal strength R_n with the resistance factor φ (LRFD) or the safety factor Ω (ASD), so the available strength is φR_n or R_n/Ω and is compared with the required strength P (the factored load under LRFD, the service load under ASD). The demand-to-capacity ratio of each limit state is tabulated, the largest one governs, and the margin of safety is the available strength over the required strength less one.

Geometry and conventions

The load P acts along the connected element toward its loaded end. The bolt group has n_r bolts in each line along the load, at spacing s, and n_c lines across the load at gage g. The end distance l_ev is measured from the centre of the end bolt to the loaded edge along the load; the edge distances l_eh (and l_eh2 on the other side) from the outer bolt lines to the side edges. The plate width across the load is W; for a plate whose edges sit at the entered edge distances W = (n_c − 1) g + l_eh + l_eh2, and the tool says so when the entered width differs (the edge distances then govern block shear and tearout, the width the gross and net areas). Each bolt has n_s shear planes: one for a lap or single-plate connection, two for a double-shear splice. The figure draws the plate in plan with the bolts, the dimensions and the governing block-shear path.

The Specification's tables are written in inches and kips, so SI inputs are converted to those units for the lookups (hole sizes of Table J3.3, pretensions of Table J3.1, edge distances of Table J3.4) and the results converted back; the metric Tables J3.3M and J3.4M differ by a millimetre or so from the converted imperial values.

Bolt shear and tension (J3.6)

The nominal shear strength of one bolt is F_nv A_b per shear plane, the nominal tensile strength F_nt A_b, with A_b = πd²/4 the nominal (unthreaded) area and F_nv, F_nt the stresses of Table J3.2: Group A (ASTM A325, F1852) 54 ksi in shear with the threads included in a shear plane (N) or 68 ksi with the threads excluded (X), 90 ksi in tension; Group B (A490, F2280) 68 / 84 and 113 ksi; Group C (F3043, F3111) 90 / 113 and 150 ksi; A307 27 and 45 ksi. The grade dropdown fills the two stresses and the fields stay editable. φ = 0.75 and Ω = 2.00. The Specification's shear values already carry the length-reduction factors for connections up to 38 in long; longer connections take a further 0.833 that the tool does not apply.

Combined tension and shear in bearing-type connections (J3.7)

When a bolt tension T is entered together with the shear P, the nominal tensile stress is reduced for the shear stress f_rv = P/(n_b n_s A_b): F′_nt = 1.3 F_nt − F_nt f_rv/(φ F_nv) ≤ F_nt (Eq. J3-3a, LRFD) or 1.3 F_nt − Ω F_nt f_rv/F_nv ≤ F_nt (Eq. J3-3b, ASD). The Specification allows the interaction to be ignored when the required stress is at or below 30 % of the available stress in either direction; the tool shows the reduced value in every case and states the percentage.

Bearing and tearout at bolt holes (J3.10)

At each hole the strength is the lesser of tearout, 1.2 l_c t F_u, and bearing, 2.4 d t F_u, when deformation at service load is a design consideration, or 1.5 l_c t F_u ≤ 3.0 d t F_u when it is not; long-slotted holes with the slot perpendicular to the load take 1.0 l_c t F_u ≤ 2.0 d t F_u. l_c is the clear distance in the direction of the load between the edge of the hole and the edge of the material (end bolts: l_ev − d_h/2) or the next hole (interior bolts: s − d_h), with d_h the nominal hole dimension along the load from Table J3.3 (standard holes d + 1/16 in up to 7/8 in bolts and d + 1/8 in from 1 in; oversized and slotted holes as tabulated). The connection strength is the sum over the holes (φ = 0.75, Ω = 2.00). A second connected element (the gusset or the other splice plate) is checked with the same hole geometry when its thickness is entered. The bolt group's effective strength follows the Manual's Part 7 method: each bolt carries the lesser of its shear strength and the bearing / tearout strength at its hole in every connected element, and the group strength is the sum; this row, not the separate bolt-shear and bearing rows, enters the governing comparison.

Slip-critical connections (J3.8, J3.9)

With the slip-critical option the nominal slip resistance is R_n = μ D_u h_f T_b n_s per bolt: μ = 0.30 for Class A faying surfaces (unpainted clean mill scale, Class A coatings) or 0.50 for Class B (unpainted blast-cleaned, Class B coatings); D_u = 1.13, the ratio of the mean installed pretension to the specified minimum; h_f = 1.0 with no filler or one filler, 0.85 with two or more; T_b the minimum pretension of Table J3.1 (Group A: 28 kips for a 3/4 in bolt, 51 kips for 1 in; Group B: 35 and 64 kips), which the tool looks up by size and group or takes as entered. φ = 1.00 and Ω = 1.50 for standard holes and short slots perpendicular to the load, 0.85 and 1.76 for oversized holes and short slots parallel to the load, 0.70 and 2.14 for long slots. An applied tension T reduces the clamping force by k_sc = 1 − T/(D_u T_b n_b) (LRFD) or 1 − 1.5 T/(D_u T_b n_b) (ASD), J3.9. A slip-critical connection must also satisfy the bearing-type limit states, so those stay in the table.

Tension of the connecting element or member (B4.3, D2, D3, J4.1)

Tensile yielding on the gross section, R_n = F_y A_g (φ = 0.90, Ω = 1.67), and tensile rupture on the effective net section, R_n = F_u A_e (φ = 0.75, Ω = 2.00). The gross area is W t unless the member's A_g is entered; the net area deducts the holes of one line across the load at the nominal hole width plus 1/16 in for damage (B4.3b). For a connecting element A_e = A_n ≤ 0.85 A_g (J4.1(b)). For a tension member A_e = U A_n with the shear-lag factor of Table D3.1: case 1 (all elements connected) 1.0; case 2, U = 1 − x̄/l with x̄ the connection eccentricity and l the length between the first and last bolt of a line (entered, or taken as (n_r − 1) s); case 4 (plates with longitudinal welds, 2016 form) U = 3l²/(3l² + w²)(1 − x̄/l); case 7 for W, M, S and HP shapes connected by the flanges, 0.90 when b_f ≥ 2/3 d and 0.85 otherwise, or 0.70 by the web; case 8 for angles, 0.80 with four or more fasteners per line and 0.60 with two or three. For cases 7 and 8 the Specification permits the larger of the tabulated value and the case 2 value, which the tool uses when x̄ is entered. Staggered holes are not handled: enter the controlling net area through A_g and the equivalent width if needed.

Block shear rupture (J4.3)

R_n = 0.60 F_u A_nv + U_bs F_u A_nt ≤ 0.60 F_y A_gv + U_bs F_u A_nt (φ = 0.75, Ω = 2.00): tension rupture on the net tension plane with the lesser of shear rupture on the net shear planes and shear yielding on the gross shear planes. U_bs = 1.0 where the tension stress is uniform (plates, angles, single-row beam-end connections) and 0.5 where it is not (multiple-row coped beams). The tool tries every block bounded by the bolt lines and the plate edges: the U block with shear planes along both outer lines from the last bolt to the loaded edge and the tension plane between them, and the L blocks with one shear plane and the tension plane running from that line across the other lines to the far side edge. Along a shear plane the holes count n_r − 1/2 (the end hole is split by the tension plane); across the tension plane the holes between the lines count whole and the one at the shear line counts half. The block with the smallest R_n governs and is drawn in red on the figure; every block is tabulated.

Whitmore section

For a gusset the load spreads from the first bolt row at 30° to both sides over the length of the bolt group (Whitmore 1952; Manual Part 9), giving an effective width l_w = (n_c − 1) g + 2 (n_r − 1) s tan 30°, limited to the plate width. The section is checked in tensile yielding (φ = 0.90, Ω = 1.67) and, with the holes of the last row deducted, in tensile rupture (φ = 0.75, Ω = 2.00). Gusset buckling in compression is not covered.

Shear of the connecting element (J4.2)

When a shear V across the element (a shear tab or a plate loaded transversely) is entered, shear yielding 0.60 F_y A_gv (φ = 1.00, Ω = 1.50) and shear rupture 0.60 F_u A_nv (φ = 0.75, Ω = 2.00) are checked on the gross section W t and the net section through one line of holes.

Welded alternative (J2.4, J4.2)

Fillet welds of leg w and total length L_w carrying P have the nominal strength F_nw A_we with F_nw = 0.60 F_EXX (1.0 + 0.50 sin^1.5 θ) and A_we = 0.707 w L_w (φ = 0.75, Ω = 2.00), θ the angle between the load and the weld axis (0 for longitudinal welds, 90° for transverse; the directional increase is written for a linear weld group loaded through its centroid and may be switched off). For E70 electrodes this is the Manual's 1.392 D l kips per sixteenth of leg (LRFD) or 0.928 D l (ASD). The base metal of the plate along the welds is checked in shear yielding 0.60 F_y t L_w (φ = 1.00, Ω = 1.50) and shear rupture 0.60 F_u t L_w (φ = 0.75, Ω = 2.00), J4.2. The Table J2.4 minimum size (1/8 in up to 1/4 in material, 3/16 to 1/2 in, 1/4 to 3/4 in, 5/16 above) and the J2.2b maximum along an edge (t − 1/16 in for t ≥ 1/4 in) are reported, as is the 4 w minimum effective length. The welded rows are an alternative to the bolt group and are summarised with their own governing limit state and margin.

Checks and limits of the tool

The tool reports an edge distance below the Table J3.4 minimum (with the Table J3.5 increment for oversized and slotted holes) and a spacing below 2-2/3 d or above the J3.5 maximum, but does not change the strengths for them. Not covered: eccentrically loaded bolt groups (see the Bolt Group Loads tool), prying action, staggered holes, long-connection and filler reductions on bolt shear, plug and slot welds, complete-joint-penetration welds, gusset buckling, and beam-end connections with copes (U_bs = 0.5 is offered for the block-shear equation only). The default case is Example 3.1 of the Purdue CE 470 lecture notes (A. H. Varma): a 5 × 1/2 in ASTM A36 plate and a 3/8 in gusset with four 3/4 in A325-N bolts at 2.5 in spacing and 1.25 in edge distances under P_u = 60 kips, whose printed bolt shear (71.6 kips) and bearing strengths (122.4 kips for the plate, 91.8 kips for the gusset) the page reproduces; the test script also reproduces the printed values of AISC Design Examples D.1 to D.5 (tensile yielding and rupture with shear lag), the Manual Table 7-1 to 7-5 bolt values and the Purdue block-shear and weld examples.