What are all the limit states to check in a steel connection?

A complete AISC 360-22 bolted connection check covers 12 limit states across three categories: BOLT LIMIT STATES (6): (1) Bolt shear — phi=0.75, Rn = Fnv x Ab. For A325-N (threads included): Fnv = 54 ksi. (2) Bolt bearing — phi=0.75, Rn = 1.2Lc x t x Fu per bolt, with upper bound 2.4d x t x Fu. (3) Bolt tearout — same equation, governs when edge distance is small. (4) Bolt tension — phi=0.75, Rn = Fnt x Ab = 90 ksi for A325. (5) Combined shear-tension — F'nt = 1.3Fnt - (Fnt/phiFnv) x frv per J3.7 interaction. (6) Slip resistance (if slip-critical) — phi=1.0 STD/0.85 OVS, Rn = mu x Du x hf x Tb x ns. CONNECTING ELEMENT LIMITS (4): (7) Gross yielding — phi=0.90, Rn = Fy x Ag. (8) Net rupture — phi=0.75, Rn = Fu x Ae. (9) Block shear — phi=0.75, Rn = 0.60Fu x Anv + Ubs x Fu x Ant. (10) Plate flexure (for extended shear tabs). WELD LIMITS (2): (11) Fillet weld shear — phi=0.75, Rn = 0.60FEXX x throat. (12) CJP/PJP weld — per J2. Column-side adds web yielding, crippling, panel zone. Every state must satisfy DCR <= 1.0.

How do you calculate a demand-to-capacity ratio (DCR)?

DCR = Ru / (phi x Rn), where Ru = required strength (factored demand from analysis), phi = resistance factor (from AISC Chapter J tables), Rn = nominal strength (from AISC equations). The connection passes when DCR <= 1.0 for every limit state. The governing DCR is the highest ratio — it identifies the controlling limit state. Example for a shear tab with 45 kip factored reaction: Bolt shear DCR = 45 / (0.75 x 54 x 0.442 x 4) = 45/71.5 = 0.63. Bolt bearing DCR = 45/154 = 0.29. Plate shear DCR = 45/97 = 0.46. Block shear DCR = 45/128 = 0.35. The governing DCR = 0.63 (bolt shear). This means the connection is at 63% capacity with bolt shear controlling — it could take 1/0.63 = 1.59x the load before failure. A DCR pattern reveals connection efficiency: multiple DCRs near 0.9-1.0 = efficient design. One DCR at 0.95 and all others at 0.3 = overdesigned everywhere except one limit state. A DCR > 1.0 in one state and < 0.5 in others = fix the weak limit state, the rest has reserve.

How does block shear failure work in steel connections?

Block shear is a failure mode where a block of plate material tears out — shear failure on one plane combined with tension rupture on a perpendicular plane. Per AISC 360 J4.3: Rn = 0.60Fu x Anv + Ubs x Fu x Ant <= 0.60Fy x Agv + Ubs x Fu x Ant. Anv = net area in shear (bolt holes deducted from shear plane). Ant = net area in tension (bolt holes deducted from tension plane). Agv = gross area in shear. Ubs = 1.0 when tension stress is uniform (most gusset/coped beam cases), Ubs = 0.5 when tension stress is non-uniform. The 0.60Fu x Anv term is shear rupture on the net section. The Ubs x Fu x Ant term is tension rupture on the net tension plane. The upper bound 0.60Fy x Agv prevents the equation from predicting a higher strength than gross shear yielding can provide. Block shear is the #1 governing limit state for: coped beam webs at connections, gusset plates at bolt groups, and tension member end connections. It is often the governing limit state because the shear + tension combination consumes less material area than pure tension would.

When should a connection be slip-critical vs bearing-type?

Slip-critical connections (SC) are required per AISC 360 Section J3.8 when: (1) Slip would impair the serviceability of the structure — connections with oversized holes, slotted holes with load perpendicular to the slot, connections subject to load reversal (fatigue), or connections where slip would cause misalignment of equipment. (2) Per AISC 341, SCBF brace connections and certain SMF connections. (3) Connections with combined shear + tension where the faying surface compression from bolt pretension is needed for fatigue resistance. Bearing-type connections: the default for most building connections. Slip is accepted at ultimate load — the bolts bear against the hole wall. The key difference: slip-critical checks slip at SERVICE loads using factored slip resistance Rn = mu x Du x hf x Tb x ns. The bolt shear check at ultimate load still applies even to slip-critical connections. SC connections use fully pretensioned bolts (snug-tight is not sufficient). Class A faying surfaces (clean mill scale): mu = 0.30. Class B (blast-cleaned): mu = 0.50 — nearly doubles slip resistance. Specifying Class B surfaces adds cost but is often cheaper than adding bolts.

What column-side limit states must be checked at bolted connections?

When a beam connects to a column, the column must also be checked per AISC 360 J10: (1) Web local yielding — the beam flange force (tension or compression) spreads into the column web: Rn = Fy x tw x (5k + lb). This prevents the column web from crushing under the beam flange. (2) Web crippling — if the beam flange is in compression: Rn = 0.80 x tw^2 x [1 + 3(lb/d)(tw/tf)^1.5] x sqrt(E x Fy x tf/tw). (3) Web panel zone shear — the column web panel at the joint resists shear from the beam moment couple: phi Rn = 0.90 x 0.60Fy x dc x tw x (1 + 3bftf^2/(db dc tw)) per J10.6. Panel zone yielding is a ductile energy dissipation mechanism in SMF. (4) Flange local bending — if the beam flange is welded to the column flange, the column flange bends: Rn = 6.25 x tf^2 x Fy. (5) Web compression buckling — for heavy compression forces at beam bottom flange. These column-side checks are often overlooked because they appear in Chapter J (Connections) rather than Chapter H (Combined Forces). A connection that passes all beam-side checks but fails column web crippling is not adequate.

Connection Checks — Engineering Reference

Q: How do you calculate a demand-to-capacity ratio (DCR)?

DCR = Ru / (phi x Rn), where Ru = required strength (factored demand from analysis), phi = resistance factor (from AISC Chapter J tables), Rn = nominal strength (from AISC equations). The connection passes when DCR <= 1.0 for every limit state. The governing DCR is the highest ratio — it identifies the controlling limit state. Example for a shear tab with 45 kip factored reaction: Bolt shear DCR = 45 / (0.75 x 54 x 0.442 x 4) = 45/71.5 = 0.63. Bolt bearing DCR = 45/154 = 0.29. Plate shear DCR = 45/97 = 0.46. Block shear DCR = 45/128 = 0.35. The governing DCR = 0.63 (bolt shear). This means the connection is at 63% capacity with bolt shear controlling — it could take 1/0.63 = 1.59x the load before failure. A DCR pattern reveals connection efficiency: multiple DCRs near 0.9-1.0 = efficient design. One DCR at 0.95 and all others at 0.3 = overdesigned everywhere except one limit state. A DCR > 1.0 in one state and < 0.5 in others = fix the weak limit state, the rest has reserve.

Q: How does block shear failure work in steel connections?

Block shear is a failure mode where a block of plate material tears out — shear failure on one plane combined with tension rupture on a perpendicular plane. Per AISC 360 J4.3: Rn = 0.60Fu x Anv + Ubs x Fu x Ant <= 0.60Fy x Agv + Ubs x Fu x Ant. Anv = net area in shear (bolt holes deducted from shear plane). Ant = net area in tension (bolt holes deducted from tension plane). Agv = gross area in shear. Ubs = 1.0 when tension stress is uniform (most gusset/coped beam cases), Ubs = 0.5 when tension stress is non-uniform. The 0.60Fu x Anv term is shear rupture on the net section. The Ubs x Fu x Ant term is tension rupture on the net tension plane. The upper bound 0.60Fy x Agv prevents the equation from predicting a higher strength than gross shear yielding can provide. Block shear is the #1 governing limit state for: coped beam webs at connections, gusset plates at bolt groups, and tension member end connections. It is often the governing limit state because the shear + tension combination consumes less material area than pure tension would.

Q: When should a connection be slip-critical vs bearing-type?

Slip-critical connections (SC) are required per AISC 360 Section J3.8 when: (1) Slip would impair the serviceability of the structure — connections with oversized holes, slotted holes with load perpendicular to the slot, connections subject to load reversal (fatigue), or connections where slip would cause misalignment of equipment. (2) Per AISC 341, SCBF brace connections and certain SMF connections. (3) Connections with combined shear + tension where the faying surface compression from bolt pretension is needed for fatigue resistance. Bearing-type connections: the default for most building connections. Slip is accepted at ultimate load — the bolts bear against the hole wall. The key difference: slip-critical checks slip at SERVICE loads using factored slip resistance Rn = mu x Du x hf x Tb x ns. The bolt shear check at ultimate load still applies even to slip-critical connections. SC connections use fully pretensioned bolts (snug-tight is not sufficient). Class A faying surfaces (clean mill scale): mu = 0.30. Class B (blast-cleaned): mu = 0.50 — nearly doubles slip resistance. Specifying Class B surfaces adds cost but is often cheaper than adding bolts.

Q: What column-side limit states must be checked at bolted connections?

When a beam connects to a column, the column must also be checked per AISC 360 J10: (1) Web local yielding — the beam flange force (tension or compression) spreads into the column web: Rn = Fy x tw x (5k + lb). This prevents the column web from crushing under the beam flange. (2) Web crippling — if the beam flange is in compression: Rn = 0.80 x tw^2 x [1 + 3(lb/d)(tw/tf)^1.5] x sqrt(E x Fy x tf/tw). (3) Web panel zone shear — the column web panel at the joint resists shear from the beam moment couple: phi Rn = 0.90 x 0.60Fy x dc x tw x (1 + 3bftf^2/(db dc tw)) per J10.6. Panel zone yielding is a ductile energy dissipation mechanism in SMF. (4) Flange local bending — if the beam flange is welded to the column flange, the column flange bends: Rn = 6.25 x tf^2 x Fy. (5) Web compression buckling — for heavy compression forces at beam bottom flange. These column-side checks are often overlooked because they appear in Chapter J (Connections) rather than Chapter H (Combined Forces). A connection that passes all beam-side checks but fails column web crippling is not adequate.

AISC 360 demand-to-capacity checks for steel connections: bolt shear, bearing, block shear, weld throat, and tearout limit states explained.

Overview

Every steel connection must be checked against a series of limit states to confirm that the demand-to-capacity ratio (DCR) does not exceed 1.0 for any failure mode. A DCR = R_u / (phi x R_n), where R_u is the required strength (factored demand) and phi x R_n is the design strength (factored capacity). The connection is adequate when every DCR <= 1.0. The governing DCR (the highest ratio) identifies the controlling limit state and the remaining reserve in the connection.

AISC 360-22 Chapter J provides the limit state equations for bolts (J3), welds (J2), and connecting elements (J4). A typical bolted shear connection requires checking 6-10 limit states; a moment connection may require 12-15 checks including column-side verifications.

Complete limit state checklist

Bolted connection checks

#	Limit State	AISC Section	Equation	phi
1	Bolt shear	J3.6, Table J3.2	R_n = F_nv x A_b x n_s	0.75
2	Bolt bearing	J3.10	R_n = 1.2 x L_c x t x F_u (per bolt)	0.75
3	Bolt tearout	J3.10	R_n = 1.5 x d x t x F_u (upper limit)	0.75
4	Bolt tension	J3.6, Table J3.2	R_n = F_nt x A_b	0.75
5	Combined shear-tension	J3.7	F'_nt = 1.3F_nt - (F_nt/(phi x F_nv)) x f_rv	0.75
6	Slip resistance	J3.8	R_n = mu x D_u x h_f x T_b x n_s	1.00 or 0.85

Connecting element checks

#	Limit State	AISC Section	Equation	phi
7	Gross section yielding	J4.1(a)	R_n = F_y x A_g	0.90 (tension), 1.00 (shear)
8	Net section rupture	J4.1(b)	R_n = F_u x A_e	0.75
9	Block shear rupture	J4.3	R_n = 0.6F_u x A_nv + U_bs x F_u x A_nt	0.75
10	Plate flexure	F11 or J4	M_n = F_y x Z (compact)	0.90
11	Plate buckling	E3 (Thornton)	P_n = F_cr x A_whitmore	0.90

Weld checks

#	Limit State	AISC Section	Equation	phi
12	Fillet weld shear	J2.4	R_n = 0.60 x F_EXX x t_e x L	0.75
13	Base metal at weld	J2.4	R_n = 0.60 x F_u x t x L (shear)	0.75
14	CJP weld (tension)	J2.3	Same as base metal	per base metal

Column-side checks (moment connections)

#	Limit State	AISC Section	Equation	phi
15	Column flange bending	J10.1	Yield line / T-stub	0.90
16	Web local yielding	J10.2	R_n = F_yw x t_w x (5k + l_b)	1.00
17	Web crippling	J10.3	Per AISC Eq. J10-4	0.75
18	Web panel zone shear	J10.6	R_v = 0.60 x F_y x d_c x t_w	0.90

Worked example — DCR summary for a shear tab

Given: W21x44 beam, R_u = 55 kip, 3/8 in. x 9 in. A36 shear tab, three 3/4 in. A325-N bolts at 3 in. spacing, 5/16 in. fillet weld (E70XX) to W14x48 column.

Check	phi x R_n (kip)	R_u (kip)	DCR	Status
Bolt shear (3 bolts)	53.7	55	1.02	NG — need 4 bolts
Bearing on tab (3 bolts)	58.2	55	0.94	OK
Block shear (beam web)	112	55	0.49	OK
Block shear (tab)	98	55	0.56	OK
Tab gross shear yielding	72.9	55	0.75	OK
Tab net shear rupture	66.7	55	0.82	OK
Weld (2 x 9 in. lines)	111.5	55	0.49	OK
Column web yielding	185	55	0.30	OK

Revised with 4 bolts (12 in. tab): Bolt shear = 4 x 17.9 = 71.6 kip. DCR = 55/71.6 = 0.77. All checks pass. Governing limit state: bolt shear at DCR = 0.77.

Demand-to-capacity ratio interpretation

DCR Range	Interpretation
0.00 - 0.50	Significantly over-designed — consider reducing plate/bolt size
0.50 - 0.85	Efficient design — good balance of economy and reserve
0.85 - 0.95	Tight design — acceptable but limited reserve for field changes
0.95 - 1.00	Marginally adequate — reconsider if loading assumptions change
> 1.00	Fails — must revise connection

Code comparison — connection check approach

Feature	AISC 360	AS 4100	EN 1993-1-8	CSA S16
Bolt shear check	Table J3.2 (F_nv tabulated)	Clause 9.2.2 (V_f)	Table 3.4 (alpha_v x f_ub x A)	Clause 13.12.1
Block shear model	Combined shear + tension planes	Clause 9.1.9	Not explicit (use Annex)	Clause 13.11
Bearing model	1.2 L_c t F_u per bolt	3.2 d t f_up	k_1 x alpha_b x f_u x d x t	3 x phi x n x t x d x F_u
Weld directional strength	1.0 + 0.50 sin^1.5(theta)	Not permitted	k_w directional factor	Not permitted
Base metal check required	Yes (J2.4)	Yes (implicitly)	Yes (Table 4.1)	Yes

Common mistakes to avoid

Checking bolt shear but skipping bearing/tearout — bearing on thin plates (shear tabs, gussets) with short edge distances frequently governs over bolt shear. This is the single most commonly missed check in practice.
Not checking block shear on the beam web — at coped beams, the beam web block shear capacity can be 30-50% lower than the bolt group shear capacity. This check must be performed for every coped beam connection.
Using gross area for net section rupture — the net area deducts bolt holes (nominal diameter + 1/16 in. per AISC B4.3). Forgetting hole deductions overestimates the rupture capacity.
Ignoring base metal capacity at welds — the weld may be stronger than the base metal it connects to. Both the weld throat and the base metal at the weld must be checked. For thin plates with large welds, base metal shear rupture often governs.
Not presenting a DCR summary — a well-organized DCR table is essential for peer review and building permit approval. Presenting only the governing check without showing all limit states makes it impossible for the reviewer to verify completeness.

AISC Chapter J connection design checklist

AISC 360-22 Chapter J governs the design of all steel connections. The chapter is organized by connection element type, and each section contains the limit state equations that must be satisfied. The following checklist summarizes the key sections and the checks required for each connection type.

Chapter J Section	Scope	Primary Checks	Typical Application
J1.1	Joint terminology	Definitions	All connections
J2	Welds	Fillet weld throat, CJP strength, PJP effective throat, base metal at weld	Welded shear tabs, moment connections, brace gussets
J3	Bolts	Shear, tension, combined shear-tension, bearing, tearout, slip resistance	Bolted shear tabs, moment end plates, base plates
J4	Connecting elements	Gross yielding, net rupture, block shear, compression buckling	Gusset plates, shear tabs, angle clips, tee stems
J5	Filler plates	Thicker filler requirements, filler contribution	Bolted splices with different member depths
J10	Flanges and webs	Flange local bending, web local yielding, web crippling, web panel zone shear	Moment connections, concentrated forces on columns

A complete connection design must address every applicable section of Chapter J. For a typical simple shear connection (single-plate shear tab), Sections J2, J3, and J4 cover the majority of limit states. For a fully welded moment connection, Sections J2 and J10 are the primary references, with J4 for the end plate or flange plate.

Connection design workflow

Determine the required strength from the structural analysis (R_u for LRFD or R_a for ASD).
Select a preliminary connection configuration (bolt count, plate size, weld size).
Check all applicable bolt limit states (shear, bearing, tearout, tension, combined loading, slip).
Check all applicable weld limit states (fillet weld throat capacity, base metal capacity).
Check all connecting element limit states (gross yielding, net rupture, block shear, plate buckling).
Check the supported member (beam web block shear, coped section capacity).
Check the supporting member (column web yielding, web crippling, panel zone shear).
Tabulate DCR values for all limit states and confirm the governing DCR is less than or equal to 1.0.

Bolt limit states in detail

Bolt shear (AISC J3.6)

Bolt shear capacity is the most fundamental bolt check. The nominal shear strength per bolt is:

R_n = F_nv * A_b * n_s

where F_nv is the nominal shear stress from AISC Table J3.2, A_b is the nominal bolt area (pi * d^2 / 4), and n_s is the number of shear planes (1 for single shear, 2 for double shear).

Bolt Grade	F_nv (ksi) Single Shear	F_nv (ksi) Double Shear	Thread Condition
A325-N	54	54	Threads in shear plane
A325-X	68	68	Threads excluded from shear plane
A490-N	68	68	Threads in shear plane
A490-X	84	84	Threads excluded from shear plane
A307	27	27	N/A (no X condition)

The phi factor is 0.75 for bolt shear. Note that double shear does not change Fnv — it simply provides two shear planes, doubling the total capacity per bolt. For example, a 3/4 in. A325-N bolt in double shear: phi * Rn = 0.75 * 54 _ 0.4418 _ 2 = 35.8 kip per bolt.

Bolt bearing and tearout (AISC J3.10)

Bolt bearing capacity depends on the clear distance between the edge of the hole and the adjacent hole or material edge (L_c). When deformation at the bolt hole is a design consideration (which is the usual case), the nominal bearing strength per bolt is the lesser of:

R_n = 1.2 * L_c * t * F_u    (bearing deformation limit)
R_n = 2.4 * d * t * F_u      (upper bound — tearout limit)

where L_c is the clear distance in the direction of force, t is the connected material thickness, F_u is the tensile strength of the connected material, and d is the nominal bolt diameter.

For a bolt at the edge of a plate with edge distance L_e and standard hole diameter d_h = d + 1/16 in.:

L_c = L_e - d_h / 2 = L_e - (d + 1/16) / 2

For interior bolts at spacing s:

L_c = s - d_h = s - (d + 1/16)

Bearing often governs for thin plates (shear tabs, gussets) with large bolts and close spacing. The phi factor is 0.75 for both bearing and tearout.

Bolt tension and combined loading (AISC J3.6, J3.7)

When bolts are loaded in tension only (e.g., anchor bolts, hanger connections), the nominal tensile strength per bolt is:

R_n = F_nt * A_b

Bolt Grade	F_nt (ksi)
A325	113
A490	141
A307	60

When a bolt is simultaneously loaded in shear and tension (e.g., prying action in a moment end plate, bracket connections), the interaction equation applies:

F'_nt = 1.3 * F_nt - (F_nt / (phi * F_nv)) * f_rv <= F_nt

where f*rv is the required shear stress in the bolt. The modified tensile capacity is then phi * F'_nt _ A_b. This interaction check prevents the bolt from failing simultaneously in both shear and tension.

Slip resistance (AISC J3.8)

Slip-critical connections use pretensioned bolts to clamp the connected plies together, preventing slip under service loads. The nominal slip resistance is:

R_n = mu * D_u * h_f * T_b * n_s

where mu is the slip coefficient (0.30 for Class A, 0.50 for Class B surfaces), D_u is a factor reflecting the ratio of mean installed pretension to minimum pretension (1.13 per the AISC Commentary), h_f is a factor for fillers (1.00 for no filler), T_b is the minimum bolt pretension from AISC Table J3.1, and n_s is the number of slip planes.

Bolt Diameter (in.)	A325 Min. Pretension T_b (kip)	A490 Min. Pretension T_b (kip)
5/8	19	24
3/4	28	35
7/8	39	49
1	51	64
1-1/8	64	80
1-1/4	81	102

The resistance factor for slip is 1.00 at the service load level (LRFD) or 0.85 at the factored load level (when slip is checked at the strength limit). Slip-critical connections are required for connections subject to fatigue, connections with oversized holes, connections with slotted holes loaded perpendicular to the slot, and connections where slip would compromise the structural integrity.

Weld limit states in detail

Fillet weld shear (AISC J2.4)

The nominal shear strength of a fillet weld per unit length is:

R_n = 0.60 * F_EXX * t_e * L

where F_EXX is the weld electrode tensile strength (70 ksi for E70XX), t_e is the effective throat thickness (0.707 * w for equal-leg fillet welds with leg size w), and L is the weld length.

For E70XX fillet welds, the capacity per inch of weld per sixteenth of leg size is approximately:

phi * R_n per inch = 0.75 * 0.60 * 70 * 0.707 * w = 22.3 * w (kip/in., w in inches)

Or equivalently, 1.39 kip per inch per sixteenth of leg size. A 5/16 in. fillet weld (5 sixteenths) has a capacity of 5 * 1.39 = 6.95 kip per inch of weld.

Weld length limitations

AISC J2.2b imposes the following limits on fillet welds:

Minimum effective length: 4 times the weld size (w). If the length is less than 4w, the effective weld size is reduced to L/4.
Maximum effective length for longitudinal welds: For flat-bar-to-plate connections loaded in tension, the effective length is limited to 70w (to account for nonuniform strain distribution along very long welds). Transverse welds do not have this limit.
Minimum weld size: Per AISC Table J2.4, the minimum fillet weld size depends on the thinner connected part: 1/8 in. for material up to 1/4 in. thick, 3/16 in. for material 1/4 to 1/2 in., 1/4 in. for material 1/2 to 3/4 in., and 5/16 in. for material over 3/4 in. thick.
Maximum single-pass weld size: 5/16 in. for flat position, 1/2 in. for horizontal/vertical. Larger welds require multiple passes.

Directional strength increase (AISC J2.4)

When the load on a fillet weld is not parallel to the weld axis, the weld capacity increases due to the directional strength effect. The nominal strength becomes:

R_n = 0.60 * F_EXX * t_e * L * (1.0 + 0.50 * sin^1.5(theta))

where theta is the angle between the weld axis and the line of force. For a transverse weld (theta = 90 degrees), the increase factor is 1.0 + 0.50 * sin^1.5(90) = 1.50, giving a 50% increase in capacity. This is a significant advantage when using transverse fillet welds instead of longitudinal welds.

Limit state priority table

The following table ranks the most common limit states by how frequently they govern in practice, based on typical building connection configurations:

Priority	Limit State	Frequency of Governing	Common Scenario
1	Bolt shear	Very High	Shear tabs, double-angle connections, end plates
2	Bearing on connected material	High	Thin shear tabs, gusset plates with close bolt spacing
3	Block shear rupture	High	Coped beam webs, gusset plates, angle legs
4	Net section rupture	Moderate	Angles with multiple bolt lines, plates with many holes
5	Fillet weld shear	Moderate	Welded shear tabs, bracket connections
6	Slip resistance	Moderate	Slip-critical connections, connections with slotted holes
7	Gross section yielding	Low	Thick plates, stocky gussets
8	Tearout	Low	Connections with short edge distances
9	Column web yielding	Low	Light columns with heavy connections
10	Panel zone shear	Low	Moment connections in seismic frames

Worked example: simple shear connection for W18x50 beam

Given: W18x50 beam (t_w = 0.355 in., d = 18.0 in., F_y = 50 ksi, F_u = 65 ksi) framing into a W14x61 column. Required shear R_u = 45 kip. Use a single-plate shear tab (A36, F_y = 36 ksi, F_u = 58 ksi) with 3/4 in. A325-N bolts and 5/16 in. fillet weld (E70XX) to the column flange.

Step 1 -- Preliminary configuration: Select a 3/8 in. x 8 in. shear tab with three 3/4 in. A325-N bolts at 3 in. spacing. Edge distance at top and bottom = 1.0 in. Weld length = 8 in. (two vertical lines, one each side of tab).

Step 2 -- Bolt shear: phi _ R_n = 0.75 _ 54 _ 0.4418 _ 3 bolts = 53.7 kip. DCR = 45 / 53.7 = 0.84. OK.

Step 3 -- Bolt bearing on shear tab: Standard hole diameter d*h = 3/4 + 1/16 = 13/16 in. Clear distance at edge bolt: L_c = 1.0 - 13/32 = 0.594 in. Bearing at edge bolt: R_n = 1.2 * 0.594 _ 0.375 _ 58 = 15.5 kip. phi _ R_n = 11.6 kip. Clear distance at interior bolts: L_c = 3.0 - 13/16 = 2.188 in. Bearing at interior bolt: R_n = 1.2 _ 2.188 _ 0.375 _ 58 = 56.9 kip. phi _ R_n = 42.7 kip. Check tearout at edge bolt: R_n = 2.4 _ 0.75 _ 0.375 _ 58 = 39.2 kip. phi _ R_n = 29.4 kip. Total phi * R_n = 11.6 + 42.7 + 42.7 = 97.0 kip. DCR = 45 / 97.0 = 0.46. OK.

Step 4 -- Block shear on shear tab: Gross shear area Anv = 2 * (1.0 + 2 _ 3.0) _ 0.375 = 5.25 in.^2 Net shear area Anv_net = A_nv - 2.5 * (13/16 + 1/16) _ 0.375 = 5.25 - 2.5 _ 0.875 _ 0.375 = 5.25 - 0.820 = 4.43 in.^2 Gross tension area A_nt = 1.5 _ 0.375 = 0.563 in.^2 (approximate, from last bolt to edge) Net tension area A*nt_net = A_nt - 0.5 * 0.875 _ 0.375 = 0.563 - 0.164 = 0.399 in.^2

phi _ R_n = 0.75 _ (0.6 _ 58 _ 4.43 + 1.0 _ 58 _ 0.399) = 0.75 _ (154.2 + 23.1) = 0.75 _ 177.3 = 133.0 kip. DCR = 45 / 133.0 = 0.34. OK.

Step 5 -- Shear tab gross shear yielding: phi _ R_n = 1.00 _ 36 _ 8.0 _ 0.375 = 108.0 kip. DCR = 45 / 108.0 = 0.42. OK.

Step 6 -- Shear tab net shear rupture: Net area = (8.0 - 3 _ 0.875) _ 0.375 = (8.0 - 2.625) _ 0.375 = 2.016 in.^2 phi _ R*n = 0.75 * 58 _ 2.016 = 87.7 kip. DCR = 45 / 87.7 = 0.51. OK.

Step 7 -- Fillet weld capacity: Two 8 in. lines of 5/16 in. fillet weld (E70XX): phi _ R_n = 0.75 _ 0.60 _ 70 _ (0.707 _ 5/16) _ 2 _ 8 = 0.75 _ 0.60 _ 70 _ 0.221 * 16 = 111.5 kip. DCR = 45 / 111.5 = 0.40. OK.

Step 8 -- Block shear on beam web (assuming cope at top flange): This check is required when the beam is coped. For an uncoped beam with the shear tab bolted through the beam web, the beam web block shear is generally adequate for typical configurations but must be verified per project conditions.

Summary DCR table:

Limit State	phi * R_n (kip)	DCR	Status
Bolt shear (3 bolts)	53.7	0.84	Governs
Bearing on tab	97.0	0.46	OK
Block shear (tab)	133.0	0.34	OK
Gross shear yielding	108.0	0.42	OK
Net shear rupture	87.7	0.51	OK
Fillet weld (2 x 8 in.)	111.5	0.40	OK

Governing limit state: bolt shear at DCR = 0.84. The connection has adequate reserve and does not require revision.

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