CELE Steel & Timber Design — Steel ConnectionsRevision Notes

Exam Tips

• Memorize φ = 0.75 for ALL connection limit states: shear, bearing, block shear, weld rupture.
• The design strength of a connection = minimum of all limit state capacities — always state which limit state governs.
• Read the problem carefully for whether bolts are in single or double shear — this doubles the capacity.
• When asked for 'number of bolts required,' divide the factored load Pu by the governing per-bolt φRn, then round UP.

Key Points

• Connections must transfer all applied forces and moments between structural members without premature failure.
• LRFD design philosophy: φRn ≥ Pu, where φ = 0.75 for connection limit states (bolt shear, bearing, block shear, weld rupture).
• The two primary fastener types are high-strength bolts (ASTM A325, A490) and welds (fillet, groove).
• The governing (controlling) design strength of a connection is always the MINIMUM value across all applicable limit states.
• Limit states for bolted connections: bolt shear, bearing, block shear, net-section tension, gross-section yielding.
• Limit states for welded connections: weld throat shear rupture, base metal shear yielding, base metal shear rupture.
• NSCP 2015 Section 502.3 and AISC 360-16 Chapter J govern connection design in Philippine practice.
• RA 544 (Philippine Civil Engineering Law) requires the Registered Civil Engineer to ensure all connections comply with applicable codes.

Definitions

Section Title

1. Fundamentals of Steel Connection Design

Common Mistakes

• Using φ = 0.90 (tension member factor) instead of φ = 0.75 for connection elements — always φ = 0.75 for connections.
• Forgetting to check all limit states and reporting only the bolt shear capacity as the connection capacity.
• Confusing nominal bolt area (based on nominal diameter) with the stress area (used only for tension rupture of bolts, not shear).
• Applying the wrong resistance factor for slip-critical connections (φ = 1.00 for serviceability-based slip check, φ = 0.85 for strength-level slip).

Formulas

Exam Tips

• Memorize key Fnv values: A325-N = 372 MPa, A325-X = 469 MPa, A490-N = 457 MPa, A490-X = 579 MPa.
• Memorize common bolt areas: 16 mm → 201 mm², 20 mm → 314 mm², 22 mm → 380 mm², 24 mm → 452 mm², 25 mm → 491 mm².
• Always write out Ab = π/4 × db² in your solution — board examiners award partial credit for correct formulas.
• For a bolt group, the answer = n × φRn (shear) vs n × φRn (bearing) — pick the smaller as governing.

Key Points

• Bolt shear is the most commonly tested connection limit state in the PRC board exam.
• A bolt in shear fails by sliding of the connected plates across each other, shearing the bolt shaft.
• Single shear: one shear plane through the bolt; double shear: two shear planes — double the strength.
• Nominal bolt shear strength: Rn = Fnv × Ab per bolt per shear plane.
• Design bolt shear strength: φRn = 0.75 × Fnv × Ab (single shear); φRn = 0.75 × Fnv × Ab × 2 (double shear).
• Fnv depends on bolt grade AND thread condition: A325-N (threads IN shear plane) = 372 MPa; A325-X (threads EXCLUDED from shear plane) = 469 MPa per AISC 360-16 Table J3.2.
• A490-N: 457 MPa; A490-X: 579 MPa.
• For a group of n identical bolts, total capacity = n × φRn per bolt.

Definitions

Section Title

2. Bolt Shear Strength

Common Mistakes

• Using Fnv = 469 MPa (A325-X) when the problem specifies or implies threads are in the shear plane — default to N (372 MPa).
• Computing bolt shear strength for double shear without multiplying by 2.
• Using bolt tensile stress area (≈ 245 mm² for 20 mm bolt) instead of the full shank area (314.2 mm²) for shear calculations.
• Forgetting to multiply per-bolt capacity by the number of bolts n when finding total connection shear capacity.

Formulas

Exam Tips

• The 2.4 db t Fu term is the UPPER LIMIT (crushing cap). If 1.2 lc t Fu > 2.4 db t Fu, use 2.4 db t Fu.
• If the problem gives only one bolt row, the edge bolt controls bearing — compute lc for the edge bolt first.
• In multi-bolt problems, the total bearing capacity = sum of individual bolt capacities (each computed with its own lc).
• Quick check: if lc > 2db, then 1.2 lc t Fu > 2.4 db t Fu and crushing governs → φRn = 0.75 × 2.4 db t Fu.

Key Points

• Bearing is the localized compression (crushing) of the plate material around the bolt hole.
• Two sub-limit states exist: tearout (low clear distance) governed by 1.2 lc t Fu, and crushing governed by 2.4 db t Fu.
• Bearing capacity per bolt = smaller of the two sub-limits, then multiplied by φ = 0.75.
• lc is the CLEAR distance in the direction of force: from the edge of the hole to the edge of the plate (edge bolt) or to the edge of the adjacent hole (interior bolt).
• lc = L - dh/2 for edge bolts (where dh = hole diameter = db + 2 mm for standard holes).
• lc = s - dh for interior bolts (where s = center-to-center bolt spacing).
• Bearing applies to EVERY plate the bolt passes through — check the thinner/weaker plate.
• When hole deformation IS a design consideration (standard condition): use 1.2 lc t Fu ≤ 2.4 db t Fu.
• When hole deformation is NOT a design consideration: use 1.5 lc t Fu ≤ 3.0 db t Fu (higher, less common in board problems).

Definitions

Section Title

3. Bearing Strength at Bolt Holes

Common Mistakes

• Computing lc from the BOLT CENTER instead of from the HOLE EDGE — subtract dh/2 for edge bolts, subtract dh for interior bolt-to-bolt.
• Using hole deformation NOT a design consideration (1.5/3.0 coefficients) when the standard (1.2/2.4) applies — read the problem carefully.
• Forgetting that bearing must be checked for EVERY plate (connected plate AND connecting plate) — the thinner/weaker plate governs.
• Summing bearing capacities incorrectly when bolts have different lc values (edge vs interior) — compute each bolt separately then sum.

Formulas

Exam Tips

• Always check BOTH expressions: rupture-rupture path and the shear-yield cap. Report whichever is smaller.
• In a simple gusset plate with a single row of bolts: Ubs = 1.0 (standard board-exam assumption).
• Block shear often appears in combination with bolt shear and bearing — always compare all three and report the governing limit state.
• Draw the failure block outline: shade it, then compute shear plane area (parallel to force) and tension plane area (perpendicular to force).

Key Points

• Block shear is a tearing-out failure of a block of plate material, combining shear yielding or rupture on one plane with tension rupture on a perpendicular plane.
• It is critical at gusset plates, clip angles, beam webs, and any element with a bolt-group layout.
• AISC 360-16 Section J4.3 (adopted in NSCP 2015): Rn = 0.60 Fu Anv + Ubs Fu Ant ≤ 0.60 Fy Agv + Ubs Fu Ant.
• The first expression (with Fu Anv) is the rupture-rupture path; the cap (with Fy Agv) prevents it from exceeding the shear-yield path.
• φ = 0.75 applies to block shear.
• Ubs = 1.0 when tension stress is uniform (single line of bolts, symmetric connection).
• Ubs = 0.5 when tension stress is non-uniform (two or more lines of bolts, eccentric connections).
• Block shear frequently governs when edge distances are small or when few bolts are used.

Definitions

Section Title

4. Block Shear

Common Mistakes

• Deducting hole areas from BOTH the shear and tension areas without checking whether the cap (shear yield + tension rupture) governs.
• Using Ubs = 1.0 for a two-row bolt pattern — check symmetry and load path first.
• Forgetting to add the tension rupture term (Ubs Fu Ant) to the shear term — some students compute only the shear component.
• Using db instead of (db + 2) mm for the hole width deduction in net area calculations.

Formulas

Exam Tips

• If the problem says 'slip-critical,' use the μ Du hf Tb ns formula. If it says 'bearing-type,' use Fnv Ab.
• Class A (μ = 0.35) is the default assumption for unpainted steel — most board problems specify Class A.
• Bolt pretension Tb values are given in AISC Table J3.1 — the most common are for 20 mm and 22 mm A325 bolts (142 kN and 176 kN).

Key Points

• Bearing-type connections allow slip; slip-critical connections develop friction to prevent slip entirely.
• Slip-critical connections are required for: connections subject to fatigue, oversized holes, connections where slip is unacceptable (precision machinery, bridges).
• Design slip resistance (serviceability): φRn = φ μ Du hf Tb ns, with φ = 1.00 (serviceability) or 0.85 (strength).
• μ = mean slip coefficient: 0.35 (Class A, unpainted clean mill scale), 0.50 (Class B, blast-cleaned).
• Tb = minimum bolt pretension (from AISC Table J3.1): 142 kN for 20 mm A325; 176 kN for 22 mm A325.
• Du = 1.13 (ratio of mean installed pretension to specified minimum).
• hf = 1.0 for standard-hole connections (no filler plates).
• ns = number of slip planes.
• Bolts in tension: φRn = 0.75 × Fnt × Ab, where Fnt = 620 MPa (A325), 780 MPa (A490).
• Combined shear + tension (bearing type): use reduced Fnt' = 1.3 Fnt - (Fnt/φFnv) × frv ≤ Fnt.

Definitions

Section Title

5. Slip-Critical and Bolt Tension

Common Mistakes

• Applying the slip-critical formula to ordinary bearing-type connections — read the problem context carefully.
• Using φ = 0.75 for the serviceability slip check instead of φ = 1.00 (serviceability) or 0.85 (strength-level).
• Forgetting to check bolt shear and bearing EVEN FOR slip-critical connections — slip-critical classification governs service behavior but strength-level checks still apply.

Formulas

Exam Tips

• Memorize φrn per mm for E70, 6 mm fillet weld: φrn = 0.75(0.60)(482)(0.707)(6) = 0.75(0.60)(482)(4.242) ≈ 0.75 × 122,850/200 ≈ 920 N/mm — confirm each time.
• Quick formula memory: φRn = 0.75 × 0.60 × FEXX × 0.707 × a × L = 0.3182 × FEXX × a × L.
• If asked to 'size the weld,' find a_req, round up to the next 1 mm increment, then verify a_req ≥ a_min and a_req ≤ a_max.
• When weld is on both sides of a plate: L_total = 2 × weld length per side — explicitly state this in your solution.

Key Points

• Fillet welds are the most common weld type in structural steel connections (gussets, brackets, beam-to-column).
• Fillet weld strength is based on shear rupture through the weld THROAT, not the leg.
• Effective throat for a 45° equal-leg fillet weld: te = 0.707a, where a = weld leg size (mm).
• Design fillet weld strength: φRn = 0.75 × 0.60 FEXX × 0.707a × L per weld.
• FEXX = electrode classification strength: E70 → 482 MPa (70 ksi), E60 → 414 MPa, E80 → 552 MPa.
• Per unit length: φrn = 0.75 × 0.60 × FEXX × 0.707a (N/mm).
• Minimum weld size: controlled by thicker plate (AISC Table J2.4): plate t ≤ 6 mm → a_min = 3 mm; 6 < t ≤ 13 mm → 5 mm; 13 < t ≤ 19 mm → 6 mm; t > 19 mm → 8 mm.
• Maximum weld size: a_max = t - 2 mm for plate t ≥ 6 mm; a_max = t for plate t < 6 mm.
• Minimum effective weld length: L_eff ≥ 4a (otherwise, use the actual leg as the effective leg).
• Groove (full-penetration) welds: develop full base-metal strength — no separate weld strength check needed.

Definitions

Section Title

6. Welded Connections — Fillet Welds

Common Mistakes

• Using the leg size a as the throat instead of 0.707a — ALWAYS use 0.707a for equal-leg fillet welds.
• Forgetting to multiply by the total weld length L (in mm) when computing total capacity — φrn per mm × L mm = total φRn.
• Not checking minimum and maximum weld size limits after computing the required size.
• Counting weld length as the member length when only portions are welded — use effective weld length only.

Formulas

Exam Tips

• In a 5-item connection problem, the last sub-question often asks 'which limit state governs?' — this tests whether you checked all states.
• State your governing limit state explicitly: 'Bolt shear governs: φRn = 87.7 kN per bolt.' This earns full solution credit.
• If block shear and bolt shear give similar values, double-check your net area calculations — they're likely the discriminating factor.

Key Points

• Step 1 — Identify connection type: bolted (bearing-type or slip-critical) or welded (fillet or groove).
• Step 2 — Identify ALL applicable limit states based on connection geometry and loading.
• Step 3 — Compute φRn for each applicable limit state.
• Step 4 — The governing design strength = MINIMUM of all φRn values.
• Step 5 — For design (finding number of bolts or weld size): n = Pu / (governing φRn per bolt), round UP.
• For bolted connections, always check: (a) bolt shear, (b) bearing on connected plate, (c) bearing on connecting plate, (d) block shear, (e) net-section tension of member.
• For welded connections, always check: (a) weld throat shear rupture, (b) base metal shear yielding, (c) base metal shear rupture.
• The connection capacity is always the MINIMUM — never average or sum the limit states.
• φ = 0.75 for ALL connection limit states listed in AISC 360-16 Chapter J.

Definitions

Section Title

7. Summary of Limit States and Design Procedure

Common Mistakes

• Using the largest φRn (optimistic) instead of the smallest (governing) as the connection capacity.
• Rounding the number of bolts DOWN instead of UP — a fractional bolt is impossible, and rounding down is unconservative.
• Checking only bolt shear and calling it the connection capacity without checking bearing and block shear.