CELE Steel & Timber Design — Steel ConnectionsCheat Sheet
One-page cheat sheet for CELE Steel & Timber Design — Steel Connections. Every formula, definition, and key fact you need for this chapter, condensed to a single printable page. Designed for the final review session before the CELE 2026.
Exam context
On the CELE 2026, the Steel & Timber Design subtest carries a "Core" weight in Professional Regulation Commission (PRC) — Board of Civil Engineering's pattern. Steel Connections lands at position 4th out of 5 in the standard review order. Target score is 70% weighted average, no sub-test below 50%, and roughly a meaningful share of items come from Steel & Timber Design on a typical CELE paper.
Steel Connections - Cheat Sheet
Rapid-fire reference for bolted and welded steel connections under AISC 360-16 and LRFD. Covers bolt shear, bearing, block shear, fillet welds, and design limit states. Steel connections fail where force transfers — the board tests this heavily.
Sections
Formulas
Formula
R_n = F_nv × A_b; φR_n = 0.75 × F_nv × A_b
Meaning
R_n = nominal shear strength; F_nv = nominal shear stress (ASTM A325); A_b = nominal bolt area (π/4 × d_b²); φ = 0.75 (LRFD)
Watch Out
A325-N (threads in plane) = 372 MPa; A325-X (threads excluded) = 469 MPa. Threads-in-plane dramatically reduces capacity — verify drawing spec.
When To Use
Single-shear bolt; multiply by 2 for double shear (two planes)
Formula
A_b = (π/4) × d_b²
Meaning
d_b = nominal bolt diameter (mm); use nominal ASTM diameter, not hole size
Watch Out
Do NOT use clearance hole diameter (typically d_b + 2 mm). Use the bolt size (M20 = 20 mm, not 22 mm hole).
When To Use
Every bolt shear problem — calculate area first
Common Values
Value
372 MPa
Symbol
F_nv
Quantity
ASTM A325-N shear stress (threads in plane)
Value
469 MPa
Symbol
F_nv
Quantity
ASTM A325-X shear stress (threads excluded)
Value
314 mm²
Symbol
A_b
Quantity
M20 bolt nominal area
Value
452 mm²
Symbol
A_b
Quantity
M24 bolt nominal area
Value
0.75
Symbol
φ
Quantity
LRFD resistance factor for connections
Section Title
Bolted Connections — Bolt Shear Strength
Important Facts
- φ = 0.75 for all connection limit states (LRFD).
- Bolt shear capacity per bolt = 0.75 × F_nv × A_b. Multiply by number of bolts AND shear planes.
- Double shear = 2 × single-shear strength (two load paths).
- ASTM A325 nominal diameters: M16 = 253 mm², M20 = 314 mm², M24 = 452 mm², M27 = 573 mm².
- Design strength always = 0.75 × nominal strength for connections (no exceptions in LRFD).
- Bolt group in shear: capacity = φ × R_n per bolt × number of bolts × number of shear planes.
Key Definitions
Term
Single Shear
Example
Two plates lapped, bolt connecting them side-by-side.
Definition
Bolt cut by one shear plane; one force direction through the bolt.
Term
Double Shear
Example
Gusset plate sandwiched between two angle members.
Definition
Bolt cut by two shear planes; typically a center plate with bolts through two outer plates.
Term
A325-N vs A325-X
Example
Snug-tight high-strength bolts used for most connections; slip-critical or X-type used for fatigue or high-slip applications.
Definition
N = threads included in shear plane (372 MPa); X = threads excluded (469 MPa). Always verify on structural drawing which is specified.
Diagrams To Know
- Single-shear lap joint (force through one plane)
- Double-shear gusset connection (force through center plate)
- Bolt loading diagram (tension, shear, combined)
Formulas
Formula
R_n = min(1.2 × l_c × t × F_u, 2.4 × d_b × t × F_u); φR_n = 0.75 × R_n
Meaning
l_c = clear distance (edge or between holes in direction of force); t = plate thickness; d_b = bolt diameter; F_u = plate ultimate tensile strength
Watch Out
The 2.4 d_b t F_u term caps the strength. 1.2 l_c t F_u is often larger but ignored if 2.4 term is smaller. ALWAYS apply both and take the minimum.
When To Use
When bolt-hole deformation at service load IS a design consideration (standard case). Otherwise use 1.5 l_c t F_u ≤ 3.0 d_b t F_u.
Formula
φR_n = 0.75 × min(1.2 l_c t F_u, 2.4 d_b t F_u) per bolt
Meaning
Design bearing strength per single bolt. For bolt group, multiply by number of bolts.
Watch Out
If problem states 'deformation NOT a design consideration,' use higher values: 1.5 l_c t F_u ≤ 3.0 d_b t F_u. Exam will specify.
When To Use
Every bolted connection bearing check; standard AISC J3.10 condition.
Common Values
Value
400 MPa
Symbol
F_u
Quantity
A36 structural steel ultimate strength
Value
450 MPa
Symbol
F_u
Quantity
A572 Gr.50 ultimate strength
Section Title
Bearing Strength at Bolt Holes
Important Facts
- Bearing strength is per bolt; multiply by number of bolts to get total connection bearing capacity.
- The minimum of the two terms (1.2 l_c t F_u and 2.4 d_b t F_u) always governs.
- Clear distance l_c is measured in the direction of force application only.
- Plate ultimate tensile strength F_u typically ranges 400–450 MPa for structural steel (A36 ≈ 400 MPa).
- If edge distance is small, 1.2 l_c term controls and severely limits capacity.
- If bolts are close together, 1.2 l_c between holes controls; spacing must be ≥ 2.67 d_b for other modes to govern.
- Bearing check is independent of bolt shear check — BOTH must be satisfied.
Key Definitions
Term
Clear Distance l_c
Example
Two holes 60 mm apart, each d_b = 20 mm: l_c between holes = 60 − 20 = 40 mm (center to center minus one diameter).
Definition
Shortest distance from bolt hole edge to edge of plate (tension direction) or to next hole. Measured perpendicular to load direction.
Term
Bearing Limit State
Example
Shallow edge distance → 1.2 l_c term governs. Large d_b with thick plate → 2.4 d_b term governs.
Definition
Plate material crushes or tears at the bolt hole. Two competing modes: hole edge yield/rupture (1.2 l_c) vs hole crushing (2.4 d_b).
Diagrams To Know
- Bearing failure modes: plate edge crush (shallow l_c) and hole deformation (large d_b)
- Clear distance geometry: l_c from hole edge to plate edge or center-to-center minus d_b
Formulas
Formula
R_n = 0.6 × F_u × A_nv + U_bs × F_u × A_nt ≤ 0.6 × F_y × A_gv + U_bs × F_u × A_nt; φR_n = 0.75 × R_n
Meaning
A_gv, A_nv = gross and net shear areas (tension + shear rupture path); A_nt = net tension area (transverse rupture); U_bs = 1.0 (uniform tension) or 0.5 (non-uniform); F_u = ultimate, F_y = yield
Watch Out
First term uses F_u × A_nv (rupture strength). Second term (cap) uses F_y × A_gv (yield). Take the SMALLER result. U_bs reduces strength for eccentric loading (usual case = 1.0 only if perfectly centered).
When To Use
Bolt group (typically 3+ bolts) at angle, bracket, or gusset connections. Check when bolts are close to plate edge.
Formula
A_nv = (l_v − 0.5 × n_holes × d_hole) × t; A_nt = (l_t − 0.5 × n_holes × d_hole) × t
Meaning
l_v = length of shear failure path (edge to hole line); l_t = length of tension failure path (perpendicular); subtract net area for holes; t = plate thickness
Watch Out
Hole diameter for area deduction = d_b + 2 mm (clearance hole, not nominal bolt). Failure plane is a staircase path (shear + tension combined).
When To Use
Calculating actual failure path geometry for block shear.
Section Title
Block Shear Rupture
Important Facts
- Block shear is checked after bolt shear and bearing — it is the third limit state.
- The connection capacity is the MINIMUM of bolt shear, bearing, and block shear.
- Block shear typically governs when bolts are clustered near an edge.
- U_bs = 1.0 is rare; assume 0.5 unless problem explicitly states uniform tension.
- First term (rupture-path strength) is the primary calculation; second term (yield cap) limits it if smaller.
- For a single bolt or widely spaced bolts, block shear is not critical.
- Always sketch the failure plane: staircase from bolt row to edge.
Key Definitions
Term
Block Shear Failure
Example
Angle member bolted to gusset: bolts pull out a rectangular block of angle material from the gusset connection.
Definition
Combined shear and tension rupture along a bolt-hole boundary. Plate tears out as a rectangular block when bolts are close to an edge.
Term
U_bs Coefficient
Example
Two bolts at same row: U_bs = 1.0. Three bolts in triangle: U_bs = 0.5 (eccentric load).
Definition
Eccentricity reduction factor. U_bs = 1.0 for uniform tension across the rupture section; U_bs = 0.5 for non-uniform (typical in practice).
Diagrams To Know
- Block shear failure plane (staircase shear + tension path)
- Angle bracket block shear (bolts on one edge, failure across perpendicular edge)
Formulas
Formula
φR_design = min(φR_bolt-shear, φR_bearing, φR_block-shear, φR_member-rupture)
Meaning
Connection capacity is the SMALLEST of all limit states. Each limit state is checked independently; the weakest controls.
Watch Out
Do NOT ignore any limit state. Even if bolt shear seems adequate, bearing or block shear may govern. Sketch and check all four.
When To Use
Final connection capacity calculation. Board exam always asks: what is the maximum load this connection can transfer?
Section Title
Bolted Connection Limit States — Controlling Design
Important Facts
- φ = 0.75 for all connection limit states (bolt shear, bearing, block shear).
- Connection is only as strong as its weakest link — ignore this and you will fail the exam.
- Always calculate nominal R_n first, then multiply by φ = 0.75 to get design strength.
- Member net-section rupture at the bolt line is also a limit state; usually checked separately in tension members.
- Board exam: 'Design a bolted connection to transfer 200 kN' → calculate all four, find minimum, report governing mode.
Key Definitions
Term
Governing Limit State
Example
Bolt shear = 200 kN, bearing = 150 kN, block shear = 180 kN → bearing (150 kN) governs; connection fails in bearing first.
Definition
The failure mode with the smallest design capacity. Determines the actual connection strength.
Diagrams To Know
- Four-part check flowchart (shear → bearing → block shear → net section)
Formulas
Formula
R_n = 0.60 × F_EXX × (0.707 × a) × L; φR_n = 0.75 × R_n
Meaning
F_EXX = electrode strength (E70 ≈ 482 MPa); a = fillet weld leg size; 0.707a = throat thickness (critical shear plane); L = effective weld length; φ = 0.75
Watch Out
Throat = 0.707 × leg size (NOT the leg size itself). A 6 mm fillet weld has 0.707 × 6 = 4.24 mm throat. This is the failure plane. Forgetting 0.707 is the #1 weld mistake.
When To Use
Every fillet weld strength problem. Design strength per unit length: φR_n/L.
Formula
Strength per unit length = (0.75 × 0.60 × F_EXX × 0.707 × a) / 1 mm = 0.318 × F_EXX × a (N/mm)
Meaning
Quick way to get weld strength/mm without multiplying by length separately.
Watch Out
This simplifies calculations; verify units (N/mm vs kN/m).
When To Use
Sizing welds: required strength (kN) / (0.318 × F_EXX × a) = required length (mm).
Common Values
Value
482 MPa
Symbol
F_EXX
Quantity
E70 electrode ultimate strength
Value
552 MPa
Symbol
F_EXX
Quantity
E80 electrode ultimate strength
Value
0.707
Symbol
k
Quantity
Fillet weld throat factor (equal leg)
Value
0.60
Symbol
C
Quantity
LRFD shear strength coefficient for weld
Section Title
Fillet Welds — Strength
Important Facts
- Fillet weld capacity is proportional to leg size (a) and length (L). Double the leg size or length → double the capacity.
- φ = 0.75 for welds (same as bolts).
- E70 (482 MPa) is standard; E80 = 552 MPa, E90 = 620 MPa, etc. Board will specify.
- Effective weld length ≤ overall length (end returns, edge distances matter).
- Minimum fillet weld size = 3 mm (or per AISC J2.2b based on plate thickness).
- Maximum fillet weld size on edge ≤ plate thickness (or t + 3 mm for internal angle).
- Groove (full-penetration) welds develop 100% of base-metal strength (no 0.60 or throat factor).
- Fillet weld strength is independent of weld direction (horizontal, vertical, overhead all have same capacity in LRFD).
Key Definitions
Term
Fillet Weld
Example
A 6 mm fillet weld is 6 mm on each leg (cathetus), but strength is through the 4.24 mm throat.
Definition
Triangular weld applied to the corner of two plates. Strength develops through the throat (0.707 × leg size), not the leg itself.
Term
Throat Thickness
Example
10 mm leg → 7.07 mm throat.
Definition
The effective load-carrying dimension of a fillet weld, perpendicular to the failure plane. Throat = 0.707 × leg size for equal-leg welds.
Term
E70 Electrode
Example
E70 welds are assumed unless noted (e.g., E80 for higher strength).
Definition
Mild steel filler metal with 70 ksi (482 MPa) minimum ultimate strength. Most common in structural work.
Diagrams To Know
- Fillet weld cross-section (leg vs throat vs failure plane)
- Effective weld length (full length minus end returns)
Formulas
Formula
φR_n = φ × F_u × A_weld (matches base metal); effectively φ × F_y × A_weld (yield governs)
Meaning
Full-penetration groove weld develops full base-metal strength. No reduction factors (no 0.60 or throat area). Design strength = base-metal strength × weld area.
Watch Out
Groove welds are STRONGER than fillet welds. Do NOT apply the 0.60 factor or 0.707 throat reduction. Area = weld width × thickness.
When To Use
Complete joint-penetration groove welds (CJP). Used at primary tension members, splices, and where full continuity is critical.
Section Title
Groove (Full-Penetration) Welds
Important Facts
- CJP groove welds are assumed to develop base-metal strength (F_y or F_u depending on failure mode).
- No strength reduction like fillet welds. Use weld area as-is (not throat).
- Groove welds are used at primary load paths (member splices, flange connections) where reliability is critical.
- Fillet welds are cheaper and easier to inspect; groove welds are stronger but more expensive and require full penetration verification.
- Board exam rarely goes deep into groove weld design; fillet welds dominate the connections section.
Key Definitions
Term
Complete Joint Penetration (CJP) Weld
Example
Flange-to-web splice plate: groove weld ensures no stress concentration at the toe.
Definition
Groove weld that fuses throughout the full thickness of the joined members. Develops full base-metal strength.
Term
Partial Joint Penetration (PJP) Weld
Example
Older buildings or cost-constrained work; less common in code-driven projects.
Definition
Groove weld that does NOT penetrate full thickness. Strength limited by penetration depth; rare in modern design.
Diagrams To Know
- Groove weld cross-section (full thickness penetration)
Formulas
Formula
R_n = μ × D_u × h_f × T_b × n_s; φR_n = 1.0 × R_n
Meaning
Slip-critical (friction) capacity; μ = slip coefficient (0.3–0.5 depending on surface); D_u = pretension factor; h_f = number of interfaces; T_b = bolt pretension; n_s = number of bolts. φ = 1.0 (no reduction for slip-critical).
Watch Out
Pretensioning required: snug-tight assembly is NOT sufficient. Controlled-torque or turn-of-nut method. φ = 1.0 (not 0.75) because bolts are pre-stressed.
When To Use
Connections where slip is unacceptable: fatigue loads, oversized holes, or service-load slip criteria. Less common than bearing bolts.
Formula
R_n = F_nt × A_b; φR_n = 0.75 × F_nt × A_b
Meaning
Bolt in pure tension; F_nt = nominal bolt tensile stress (A325: 620 MPa); A_b = bolt area.
Watch Out
Tension capacity is DIFFERENT from shear capacity. A325 shear ≠ tension stress. Check ASTM or AISC table J3.2.
When To Use
Bolts loaded in tension (eyebar splices, hanger connections). Rarely stand-alone; combined shear + tension is typical.
Formula
F_v (at T) = 0.6 F_nv [1 − (1.3 T / (D_u × T_b))]
Meaning
Shear capacity is reduced if bolt also carries tension T. As tension increases, shear capacity drops linearly.
Watch Out
If T is significant, shear capacity drops severely. Always check combined limit state when tension is present.
When To Use
Combined shear + tension loading (e.g., bolts in a bracket under eccentric pull).
Common Values
Value
620 MPa
Symbol
F_nt
Quantity
A325 bolt tensile stress
Value
372 MPa
Symbol
F_nv
Quantity
A325 shear stress (N, threads in plane)
Value
0.3
Symbol
μ
Quantity
Slip coefficient (clean mill scale)
Value
0.5
Symbol
μ
Quantity
Slip coefficient (blast-cleaned)
Section Title
Slip-Critical and Tension Bolts
Important Facts
- Slip-critical bolts are preloaded (typically 70% of minimum tensile strength); bearing bolts are snug-tight.
- φ = 1.0 for slip-critical (bolts already stressed); φ = 0.75 for bearing-type bolts.
- A325 tensile stress (620 MPa) is higher than shear stress (372 N or 469 X).
- Combined shear + tension reduces shear capacity; interaction formula reduces shear as tension rises.
- Slip-critical connections are more expensive (controlled torque, pretensioning verification) and used only when slip is critical (fatigue, deflection-sensitive).
Key Definitions
Term
Slip-Critical Connection
Example
Welded plate girder splice; fatigue-critical bolted hanger.
Definition
High-strength bolts preloaded to prevent sliding at service loads. Friction (not bolt shear) transfers force.
Term
Bearing Connection
Example
Routine frame connections, column-to-base plate, most structural joints.
Definition
Bolts allowed to slip under service load; design based on bolt shear and bearing strength (not friction).
Diagrams To Know
- Shear vs tension interaction plot (shear capacity vs applied tension)
Formulas
Formula
a_required = (Required Strength) / (0.75 × 0.60 × F_EXX × 0.707 × L) = (R_required) / (0.318 × F_EXX × L)
Meaning
Solve for fillet weld leg size (a) given required load and weld length.
Watch Out
Round UP to next practical size (3, 4, 5, 6, 8, 10, 12 mm). Do NOT interpolate fractional sizes. Verify a ≤ min(plate thickness, 3 mm + t for internal corner).
When To Use
Design problem: 'Weld a 200 kN load with two 150 mm welds (both sides); size the fillet.' Calculate a, then round to nearest practical size.
Formula
a_min = (t / 8) (in inches, per AISC J2.2); ≈ 3 mm (metric, practical minimum)
Meaning
Minimum fillet weld size based on connected plate thickness.
Watch Out
Metric conversion: AISC table gives inch values. For SI: a_min ≈ 3 mm for t < 6 mm; for t > 6 mm, a_min ≈ t/8 (approximately).
When To Use
Check if proposed weld size meets code minimums. Smaller welds risk lack of penetration and defects.
Formula
a_max = t (on one side of an internal corner); a_max = t + 3 mm (external angle)
Meaning
Maximum fillet weld leg size to avoid excessive heat input and distortion.
Watch Out
Thicker plates allow larger welds. A 25 mm plate can support a 25 mm fillet; a 10 mm plate is limited to 10 mm.
When To Use
Practical limit to avoid weld defects and fabrication issues. Larger welds require special procedures (preheat, cooling).
Common Values
Value
3 mm
Symbol
a_min
Quantity
Minimum fillet weld leg size
Value
= plate thickness t
Symbol
a_max
Quantity
Maximum fillet weld leg size (internal angle)
Section Title
Weld Sizing and Practical Limits
Important Facts
- Minimum fillet weld size = 3 mm (metric). Smaller welds lack penetration.
- Maximum fillet weld size = plate thickness (or t + 3 for internal angle). Larger welds cause distortion.
- Practical leg sizes: 3, 4, 5, 6, 8, 10, 12, 16 mm. Do not specify 7 mm or other non-standard sizes.
- Effective length is slightly less than overall length due to end tapering (design assuming 85–90% of length develops full strength, or use AISC reduction).
- Longer welds on thin plates can cause lamellar tearing (through-thickness stress). Avoid very long welds on t < 12 mm.
- Weld length and size are the two levers to achieve required strength; optimize both for cost.
Key Definitions
Term
Effective Weld Length
Example
A 200 mm long fillet weld (5 mm leg): effective length ≈ 200 − 2(0.5 × 5) ≈ 195 mm (assumes 5 mm end return each side).
Definition
Length over which the weld develops full shear strength. Typically full length minus small end returns (≈ 0.5 × a at each end, per AISC J2.2c).
Diagrams To Know
- Fillet weld size limits (min vs max vs plate thickness)
Formulas
Formula
φR_n = 0.75 × F_u × A_n
Meaning
Tension member rupture at bolt holes: A_n = gross area − holes. F_u = ultimate tensile strength.
Watch Out
A_n must account for ALL holes (not just the controlling hole). Subtract d_hole = d_b + 2 mm per hole. If staggered holes exist, check the critical section (minimum A_n path).
When To Use
Check if member net section fails before bolts shear. Member rupture is a limit state separate from the bolt group check.
Section Title
Net-Section Rupture and Member Fracture
Important Facts
- Member rupture is checked in addition to bolt-group capacity. Connection strength is still the minimum of all limit states.
- Shear lag (U_n factor) may apply for unequal member geometries (e.g., angle bolted through one leg only).
- For tension members: φ = 0.75; R_n = F_u × A_n.
- For compression members at bolt holes: local buckling or crushing usually governs before rupture.
- Board exam: 'Design a bolted tension splice' → verify bolt shear AND bearing AND block shear AND member net section rupture. All four.
Key Definitions
Term
Net Area A_n
Example
Plate: 200 mm wide × 10 mm thick; two M20 holes (22 mm effective): A_n = (200 − 2 × 22) × 10 = 1560 mm².
Definition
Gross cross-sectional area minus the projected area of bolt holes along the failure plane.
Section Title
NSCP 2015 and AISC 360-16 Key References
Important Facts
- NSCP 2015 = AISC 360-16 in Filipino context. Board exam may cite NSCP Section 5, but content is identical to AISC.
- RA 544 (Structural Engineers Registration Act) requires licensed engineers to design connections per applicable code (NSCP).
- Exam will NOT ask you to recite codes; it will ask you to APPLY them (calculate φR_n, identify limit states, size welds).
- All formulas in this cheat sheet come directly from NSCP 2015 Section 5.11–5.12 (bolts and welds).
Key Definitions
Term
NSCP 2015 Section 5 (Steel Design)
Example
Exam will reference NSCP Section 5.11 or 5.12 for bolts/welds, not directly AISC.
Definition
Philippines building code adoption of AISC 360-16 LRFD and ASD methods. Governs all steel connection design in PH.
Term
AISC 360-16 Chapter J (Connections)
Example
φ = 0.75 for connection limit states comes from AISC 360-16 Table J1.1.
Definition
Primary US standard for bolt and weld design. NSCP 2015 adopts AISC 360-16 wholesale for Filipino practice.
Must Remember
- φ = 0.75 for ALL connection limit states (bolt shear, bearing, block shear, fillet weld, tension bolts). This is the single #1 constant in connections.
- Connection strength = MINIMUM of bolt shear, bearing, block shear, and member net section. Always check all four; one governs.
- Bolt shear: A325-N = 372 MPa (threads in plane), A325-X = 469 MPa (threads out). Threads-in-plane dramatically weaker. Drawing must specify.
- Bearing cap: 2.4 d_b t F_u term almost always governs because 1.2 l_c term is usually larger. Apply BOTH, take minimum.
- Fillet weld throat = 0.707 × leg size. A 6 mm weld has 4.24 mm throat. Forgetting 0.707 is the #1 student error.
- Block shear: multiply by 0.75 and remember U_bs = 1.0 (rare, uniform load) vs 0.5 (typical, eccentric). Check the first term (F_u A_nv) and cap it with yield (F_y A_gv).
- Fillet weld strength: φR_n = 0.75 × 0.60 × F_EXX × 0.707a × L. Quick formula per unit length: 0.318 × F_EXX × a (N/mm). E70 = 482 MPa standard.
- Clear distance l_c: measure perpendicular to load, from hole edge to plate edge (or to next hole). Small l_c → bearing governs severely.
- A_b for bolts: use nominal ASTM diameter (M20 = 314 mm²). Do NOT use hole diameter. Clearance hole ≈ d_b + 2 mm but A_b stays nominal.
- Slip-critical bolts: φ = 1.0 (preloaded, no reduction). Bearing bolts: φ = 0.75. Always verify which type is specified on drawings.
Last Minute Tips
- EVERY bolted connection problem: set up a 2×2 table — list all bolts, shear planes, then calculate φR_n for shear, bearing, and block shear per bolt. Find the minimum; that's your answer. Speed + accuracy.
- Weld sizing: Required load / (0.318 × F_EXX × L) = a_required. Always round UP to next standard size (3, 4, 5, 6, 8, 10, 12 mm). Never fractional sizes.
- Bearing strength bottleneck: If a problem says 'bolts are 20 mm, plate is 10 mm thick, edge distance is 35 mm' — your bearing φR_n will be roughly 0.75 × 1.2 × 35 × 10 × F_u ≈ 0.75 × 1.2 × 35 × 10 × 400 ≈ 126 kN (per bolt). Compare to bolt shear (likely 87 kN); bearing likely governs.
- Block shear is a sneaky limit state: only check it if bolts are 3+ and clustered near an edge. Single or widely-spaced bolts rarely fail block shear. Don't overthink it if geometry looks okay.
- Weld throat: every single time you see a fillet weld leg size, multiply by 0.707 in your head. 5 mm → 3.54 mm, 6 mm → 4.24 mm, 8 mm → 5.66 mm. Practice this reflex until exam day.
Comparison Tables
Rows
Values
- R_n = F_nv × A_b
- Bolts are too small or bolt material weak
- 0.75
- φR_n = 0.75 × 372 (N) or 469 (X) × A_b
Property
Bolt Shear
Values
- R_n = min(1.2 l_c t F_u, 2.4 d_b t F_u)
- Edge distance too small OR bolts too large for plate thickness
- 0.75
- φR_n = 0.75 × [smaller of two terms]
Property
Bearing (Hole Crush)
Values
- R_n = 0.6 F_u A_nv + U_bs F_u A_nt (capped by yield)
- Bolts cluster near edge; staircase tear-out occurs
- 0.75
- φR_n = 0.75 × [rupture path, limited by yield]
Property
Block Shear
Values
- R_n = F_u × A_n
- Plate net area is small relative to bolts
- 0.75
- φR_n = 0.75 × F_u × A_n
Property
Net-Section Rupture
Columns
- Limit State
- Formula
- Governs When
- Design Factor φ
Table Title
Bolted Connection Limit States — Side-by-Side Comparison
Rows
Values
- φR_n = 0.75 × 0.60 × F_EXX × 0.707a × L
- φR_n = φ × F_u × A_weld (full base-metal strength)
Property
Strength Formula
Values
- Throat = 0.707 × leg size (failure plane)
- Full thickness (no reduction)
Property
Critical Area
Values
- 0.75
- 0.75 (or 0.90 for tension, depending on base metal)
Property
Strength Factor φ
Values
- 0.60 × F_EXX (60% of electrode strength)
- 1.0 × F_y or F_u (100% of base metal)
Property
Material Factor
Values
- Lap splices, corner joints, lateral bracing (most connections)
- Flange splices, primary load paths, tension members
Property
Common Application
Values
- Lower (easier to inspect, no full penetration required)
- Higher (requires full penetration and stricter QC)
Property
Cost
Values
- Very high (~80% of weld problems)
- Lower (~20% of weld problems)
Property
Exam Frequency
Columns
- Aspect
- Fillet Weld
- Groove Weld (CJP)
Table Title
Fillet Weld vs Groove Weld — Design Comparison
Rows
Values
- 372 MPa
- In the shear plane (reduced capacity)
- Most connections (snug-tight, bearing)
Property
A325-N (Standard)
Values
- 469 MPa
- Excluded from shear plane (full capacity)
- Fatigue, slip-critical, when extra strength needed
Property
A325-X (High Strength)
Columns
- Bolt Type
- Nominal Shear Stress F_nv
- When Threads Are...
- Typical Use
Table Title
A325 Bolt Shear Stress — Threads In vs Out
Rows
Values
- 482 MPa
- General structural (A36, A572 Grade 50 members)
- Standard (baseline)
Property
E70
Values
- 552 MPa
- Higher strength steel (A572 Grade 60+) or high-load connections
- Higher
Property
E80
Values
- 620 MPa
- Heavy industrial, quake-prone regions, specialty applications
- Highest
Property
E90
Columns
- Electrode
- Ultimate Strength F_EXX
- Common Use
- Cost
Table Title
Weld Electrode Types — Strength and Applications
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