Engineering Reference Tables

Recovery Library — Doc #017

Scope: Structural, hydraulic, electrical, and mechanical reference tables for field engineering without specialist software. Values are computed from the formulae stated or taken from the cited standards. Any calculation can be re-derived from the governing equations given in each section preamble.

Material basis: Timber data uses Radiata Pine (SG8/MSG8 grade) per NZS 3603. Hydraulic data uses Hazen-Williams (H-W). Electrical data follows AS/NZS 3008.1.1 principles. Thread data follows ISO 68-1 and ISO 261/262.

Conservative use: These tables give working-load deflections and capacities. Apply appropriate safety factors per the relevant design standard. In the absence of a licensed engineer, use a minimum factor of 2.0 on calculated loads for life-safety applications.


1. Beam Deflection Tables

Radiata Pine, E = 8.0 GPa (NZS 3603 SG8/MSG8). Sections listed as depth × breadth (standard NZ notation).

Reading the tables: For a point-load table, multiply the tabulated value by your actual load in kN to obtain mid-span deflection in mm. For a UDL table, multiply by load in kN/m.

Span/deflection ratio check: L/360 is a common serviceability limit for floors (e.g. 5 m span → 13.9 mm limit). L/240 is typical for roofs.

1.1 Simply Supported — Central Point Load

Formula: δ = PL³ / (48EI)
Tabulated: Deflection per kN of point load (mm/kN)

Span (m) 90×45 140×45 190×45 240×45 290×45
I (m⁴) I=2.7×10⁻⁶ m⁴ I=10.3×10⁻⁶ m⁴ I=25.7×10⁻⁶ m⁴ I=51.8×10⁻⁶ m⁴ I=91.5×10⁻⁶ m⁴
2 m 7.62 2.02 0.81 0.40 0.23
3 m 25.72 6.83 2.73 1.36 0.77
4 m 60.97 16.20 6.48 3.22 1.82
5 m 119.07 31.63 12.66 6.28 3.56
6 m 205.76 54.66 21.87 10.85 6.15
7 m 326.74 86.81 34.73 17.23 9.77
8 m 487.73 129.58 51.84 25.72 14.58

1.2 Simply Supported — Uniformly Distributed Load (UDL)

Formula: δ = 5wL⁴ / (384EI)
Tabulated: Deflection per kN/m of UDL (mm per kN/m)

Span (m) 90×45 140×45 190×45 240×45 290×45
I (m⁴) I=2.7×10⁻⁶ m⁴ I=10.3×10⁻⁶ m⁴ I=25.7×10⁻⁶ m⁴ I=51.8×10⁻⁶ m⁴ I=91.5×10⁻⁶ m⁴
2 m 9.53 2.53 1.01 0.50 0.28
3 m 48.23 12.81 5.13 2.54 1.44
4 m 152.42 40.49 16.20 8.04 4.56
5 m 372.11 98.86 39.55 19.62 11.12
6 m 771.60 204.99 82.01 40.69 23.06
7 m 1429.49 379.77 151.93 75.38 42.73
8 m 2438.65 647.88 259.19 128.60 72.89

1.3 Cantilever — End Point Load

Formula: δ = PL³ / (3EI)
Tabulated: Deflection per kN of point load (mm/kN)

Span (m) 90×45 140×45 190×45 240×45 290×45
I (m⁴) I=2.7×10⁻⁶ m⁴ I=10.3×10⁻⁶ m⁴ I=25.7×10⁻⁶ m⁴ I=51.8×10⁻⁶ m⁴ I=91.5×10⁻⁶ m⁴
2 m 121.93 32.39 12.96 6.43 3.64
3 m 411.52 109.33 43.74 21.70 12.30
4 m 975.46 259.15 103.68 51.44 29.16
5 m 1905.20 506.15 202.49 100.47 56.95
6 m 3292.18 874.64 349.91 173.61 98.41
7 m 5227.86 1388.89 555.64 275.69 156.26
8 m 7803.69 2073.21 829.40 411.52 233.26

1.4 Cantilever — Uniformly Distributed Load (UDL)

Formula: δ = wL⁴ / (8EI)
Tabulated: Deflection per kN/m of UDL (mm per kN/m)

Span (m) 90×45 140×45 190×45 240×45 290×45
I (m⁴) I=2.7×10⁻⁶ m⁴ I=10.3×10⁻⁶ m⁴ I=25.7×10⁻⁶ m⁴ I=51.8×10⁻⁶ m⁴ I=91.5×10⁻⁶ m⁴
2 m 91.45 24.30 9.72 4.82 2.73
3 m 462.96 123.00 49.21 24.41 13.84
4 m 1463.19 388.73 155.51 77.16 43.74
5 m 3572.25 949.04 379.67 188.38 106.78
6 m 7407.41 1967.93 787.29 390.62 221.41
7 m 13723.14 3645.83 1458.55 723.68 410.19
8 m 23411.07 6219.63 2488.21 1234.57 699.77

Source: Beam deflection formulae from Roark’s Formulas for Stress and Strain (Young & Budynas, 8th ed., Table 3). Section properties from NZS 3603:1993 and standard metric timber sizes.


2. Pipe Flow Tables (Hazen-Williams)

Formula: Q = 0.849 × C × A × R^0.63 × S^0.54
where Q = flow (m³/s), C = roughness coefficient, A = pipe cross-section area (m²), R = hydraulic radius = D/4 (m), S = hydraulic gradient (m/m, i.e. head loss per unit length).
Flow values below are in litres per second (L/s) for full-bore flow.

Velocity can be estimated as V = Q / A. Recommended maximum design velocity: 1.5–3.0 m/s for water supply; 0.6–1.0 m/s minimum for self-cleansing in sewers.

2.1 C = 150 — New smooth plastic (PVC/PE)

Diameter (mm) 1:100 1:200 1:500 1:1000
Internal dia S=0.01000 S=0.00500 S=0.00200 S=0.00100
25 0.21 0.15 0.089 0.061
32 0.41 0.28 0.17 0.12
40 0.73 0.50 0.31 0.21
50 1.32 0.90 0.55 0.38
65 2.62 1.80 1.10 0.76
80 4.53 3.11 1.90 1.31
100 8.14 5.60 3.41 2.35
150 23.7 16.3 9.92 6.82
200 50.4 34.7 21.1 14.5

2.2 C = 130 — New steel / galvanised

Diameter (mm) 1:100 1:200 1:500 1:1000
Internal dia S=0.01000 S=0.00500 S=0.00200 S=0.00100
25 0.18 0.13 0.077 0.053
32 0.35 0.24 0.15 0.10
40 0.63 0.44 0.27 0.18
50 1.14 0.78 0.48 0.33
65 2.27 1.56 0.95 0.66
80 3.92 2.70 1.65 1.13
100 7.06 4.85 2.96 2.04
150 20.5 14.1 8.60 5.91
200 43.7 30.0 18.3 12.6

2.3 C = 100 — Old steel / concrete

Diameter (mm) 1:100 1:200 1:500 1:1000
Internal dia S=0.01000 S=0.00500 S=0.00200 S=0.00100
25 0.14 0.097 0.059 0.041
32 0.27 0.19 0.11 0.078
40 0.49 0.34 0.20 0.14
50 0.88 0.60 0.37 0.25
65 1.75 1.20 0.73 0.50
80 3.02 2.08 1.27 0.87
100 5.43 3.73 2.28 1.57
150 15.8 10.8 6.61 4.55
200 33.6 23.1 14.1 9.69

2.4 C = 80 — Old cast iron / corroded steel

Diameter (mm) 1:100 1:200 1:500 1:1000
Internal dia S=0.01000 S=0.00500 S=0.00200 S=0.00100
25 0.11 0.078 0.048 0.033
32 0.22 0.15 0.091 0.063
40 0.39 0.27 0.16 0.11
50 0.70 0.48 0.29 0.20
65 1.40 0.96 0.59 0.40
80 2.41 1.66 1.01 0.70
100 4.34 2.99 1.82 1.25
150 12.6 8.68 5.29 3.64
200 26.9 18.5 11.3 7.75

Pipe Velocity Reference

Full-bore velocity V = Q/A. At 1 L/s through each pipe size:

Diameter (mm) Area (cm²) V at 1 L/s (m/s)
25 4.91 2.037
32 8.04 1.243
40 12.57 0.796
50 19.63 0.509
65 33.18 0.301
80 50.27 0.199
100 78.54 0.127
150 176.71 0.057
200 314.16 0.032

Source: Hazen-Williams equation per Mays, L.W. (ed.), Water Distribution Systems Handbook (McGraw-Hill, 2000), §2.4. C-values per Chadwick, A. et al., Hydraulics in Civil and Environmental Engineering (5th ed., 2013), Table 8.1.


3. Timber Span Tables

Material: Radiata Pine, MSG8/SG8 grade, NZS 3603:1993.
Design bending strength f’b = 14.0 MPa (characteristic 18.0 MPa × modification factors k₁=0.8 for long-term load duration, k₄=1.0 for dry service, k₈=1.0 for single member — conservative).
E = 8.0 GPa.
Spans governed by lesser of bending (M ≤ f’b·Z, wL²/8) or deflection (L/360 floor, L/240 roof). Values rounded DOWN to nearest 50 mm.

Load basis: Floor = 1.5 kPa (dead + live). Roof/rafter = 0.5 kPa (dead + live, light roofing).
Tributary load per joist or rafter (kN/m) = pressure × spacing.

3.1 Floor Joists — Design Load 1.5 kPa

Joist spacing: 400 mm centres (w = 0.600 kN/m)

Section (d×b mm) Max Span (m) Governed by
140×45 3.05 deflection
190×45 4.15 deflection
240×45 5.25 deflection
290×45 6.35 deflection

Joist spacing: 600 mm centres (w = 0.900 kN/m)

Section (d×b mm) Max Span (m) Governed by
140×45 2.65 deflection
190×45 3.65 deflection
240×45 4.60 deflection
290×45 5.55 deflection

3.2 Rafters — Design Load 0.5 kPa

Rafter spacing: 600 mm centres (w = 0.300 kN/m)

Section (d×b mm) Max Span (m) Governed by
90×45 2.85 deflection
140×45 4.40 deflection
190×45 6.00 deflection
240×45 7.60 deflection
290×45 9.20 deflection

Rafter spacing: 900 mm centres (w = 0.450 kN/m)

Section (d×b mm) Max Span (m) Governed by
90×45 2.45 deflection
140×45 3.85 deflection
190×45 5.25 deflection
240×45 6.65 deflection
290×45 8.00 deflection

Note: These spans are indicative for initial sizing. Final design must account for lateral restraint, notching, end fixity, load sharing (k₈ > 1.0 for multiple members), and connection capacity per NZS 3603:1993. Spans may be extended by 5–15% when load sharing applies.

Source: NZS 3603:1993 Timber Structures Standard, Tables 2.1, 2.4, B1–B6. Deflection limits per NZS 3604:2011 §6.


4. Wire and Cable Ampacity — Copper Conductors

Current-carrying capacity (amperes) for copper conductors with thermoplastic (PVC/XLPE) insulation, 75°C conductor temperature rating.
Reference standard: AS/NZS 3008.1.1:2017, Table 7.

Installation methods:
- In conduit: conductors in enclosed conduit, 40°C ambient
- Clipped direct: surface-mounted, 30°C ambient
- Free air: spaced away from surface, 30°C ambient

Voltage drop (approx, 230V single-phase): V_drop = I × R × L / 1000 where R (mΩ/m) from table below.

Size (mm²) In Conduit (A) Clipped Direct (A) Free Air (A) R at 75°C (mΩ/m)
1.0 10 13 15 20.92
1.5 13 17 20 13.95
2.5 18 24 27 8.37
4.0 24 32 36 5.23
6.0 31 41 46 3.49
10.0 42 57 63 2.09
16.0 57 76 85 1.31
25.0 75 101 112 0.84

4.1 Derating Factors

Apply derating factors by multiplying tabulated current by all applicable factors.

Condition Derating Factor
2 circuits grouped (touching) 0.80
3 circuits grouped 0.70
4–6 circuits grouped 0.60
7–9 circuits grouped 0.50
Ambient 45°C (vs 30°C base) 0.91
Ambient 50°C 0.82
Ambient 55°C 0.71
Ambient 60°C 0.58
Fully enclosed in thermal insulation 0.50
Partially covered by thermal insulation 0.75

4.2 Common Voltage Drop Budget (230 V, ≤5% limit = 11.5 V)

Maximum single-phase circuit length (m) for 5% voltage drop at full load:
L_max = 11.5 × 1000 / (I × R_mΩm × 2) (factor 2 for return conductor)

Size (mm²) 10 A load 16 A load 20 A load 32 A load
1.0 27 m 17 m 14 m 9 m
1.5 41 m 26 m 21 m 13 m
2.5 69 m 43 m 34 m 21 m
4.0 110 m 69 m 55 m 34 m
6.0 165 m 103 m 82 m 52 m
10.0 275 m 172 m 137 m 86 m
16.0 440 m 275 m 220 m 137 m
25.0 687 m 430 m 344 m 215 m

Source: AS/NZS 3008.1.1:2017 Electrical Installations — Selection of Cables, Table 7 (current capacity) and Table 30 (resistance). Derating factors from Tables 22–25 of the same standard.


5. ISO Metric Thread Dimensions

Based on ISO 68-1 (thread profile), ISO 261 (coarse series), ISO 262 (fine series).

Formulae (all dimensions in mm):
- Pitch diameter d₂ = D − 0.6495 × P
- Minor dia (bolt) d₁ = D − 1.2269 × P
- Minor dia (nut) D₁ = D − 1.0825 × P
- Tap drill (75% thread) ≈ D − P

For class 6g/6H (standard commercial tolerance), add tolerance from ISO 965-1.

5.1 Coarse Pitch Series

Size Pitch (mm) Pitch Dia d₂ (mm) Minor (bolt) d₁ (mm) Minor (nut) D₁ (mm) Tap Drill (mm)
M3 0.50 2.675 2.387 2.459 2.50
M4 0.70 3.545 3.141 3.242 3.30
M5 0.80 4.480 4.018 4.134 4.20
M6 1.00 5.351 4.773 4.918 5.00
M8 1.25 7.188 6.466 6.647 6.75
M10 1.50 9.026 8.160 8.376 8.50
M12 1.75 10.863 9.853 10.106 10.25
M14 2.00 12.701 11.546 11.835 12.00
M16 2.00 14.701 13.546 13.835 14.00
M18 2.50 16.376 14.933 15.294 15.50
M20 2.50 18.376 16.933 17.294 17.50
M22 2.50 20.376 18.933 19.294 19.50
M24 3.00 22.052 20.319 20.753 21.00

5.2 Fine Pitch Series

Size Pitch (mm) Pitch Dia d₂ (mm) Minor (bolt) d₁ (mm) Minor (nut) D₁ (mm) Tap Drill (mm)
M6 0.75 5.513 5.080 5.188 5.25
M8 1.00 7.351 6.773 6.918 7.00
M10 1.25 9.188 8.466 8.647 8.75
M12 1.25 11.188 10.466 10.647 10.75
M14 1.50 13.026 12.160 12.376 12.50
M16 1.50 15.026 14.160 14.376 14.50
M18 1.50 17.026 16.160 16.376 16.50
M20 1.50 19.026 18.160 18.376 18.50
M22 1.50 21.026 20.160 20.376 20.50
M24 2.00 22.701 21.546 21.835 22.00

5.3 Thread Engagement and Strength Notes

  • Minimum thread engagement in steel: 1.0 × D
  • Minimum thread engagement in aluminium: 1.5 × D
  • Minimum thread engagement in cast iron / grey iron: 1.25 × D
  • Minimum thread engagement in plastics: 2.0 × D
  • Standard nut height (coarse) ≈ 0.8 × D (grade 8 nuts ≈ 1.0 × D)
  • Self-locking torque (nyloc inserts): add ~20–30% to standard torque

Source: ISO 68-1:2013 General purpose screw threads — Basic profile. ISO 261:1998 ISO general-purpose metric screw threads — General plan. Tap drill guidance per Machinery’s Handbook (31st ed., p. 1924).


6. Metric Bolt Proof Loads and Tightening Torques

Per ISO 898-1:2013 Mechanical properties of fasteners — Bolts, screws and studs.

Proof load = proof stress × tensile stress area.
Tensile stress area: A_s = π/4 × (D − 0.9382P)² (ISO 898-1 Annex A).

Tightening torque is indicative for lightly oiled or as-received uncoated steel (nut factor K ≈ 0.20). T ≈ K × F_proof × D. Actual torque varies with friction; always use measured or published torque for critical joints.

Proof stresses used (MPa):
- Grade 4.8: 310 MPa
- Grade 8.8: 580 MPa (conservative; spec is 600 for M≤16, 580 for M>16)
- Grade 10.9: 830 MPa
- Grade 12.9: 970 MPa

6.1 Tensile Stress Areas

Size Pitch (mm) Stress Area A_s (mm²)
M6 1.00 20.1
M8 1.25 36.6
M10 1.50 58.0
M12 1.75 84.3
M14 2.00 115.4
M16 2.00 156.7
M18 2.50 192.5
M20 2.50 244.8
M22 2.50 303.4
M24 3.00 352.5

6.2 Proof Loads (kN)

Size Grade 4.8 Grade 8.8 Grade 10.9 Grade 12.9
M6 6.2 11.7 16.7 19.5
M8 11.3 21.2 30.4 35.5
M10 18.0 33.6 48.1 56.2
M12 26.1 48.9 69.9 81.7
M14 35.8 67.0 95.8 112.0
M16 48.6 90.9 130.0 152.0
M18 59.7 111.6 159.8 186.7
M20 75.9 142.0 203.2 237.5
M22 94.1 176.0 251.8 294.3
M24 109.3 204.5 292.6 341.9

6.3 Indicative Tightening Torques (N·m), K = 0.20

Size Grade 4.8 Grade 8.8 Grade 10.9 Grade 12.9
M6 7 14 20 23
M8 18 34 49 57
M10 36 67 96 112
M12 63 117 168 196
M14 100 187 268 314
M16 155 291 416 486
M18 215 402 575 672
M20 304 568 813 950
M22 414 774 1108 1295
M24 525 981 1404 1641

6.4 Bolt Identification — Head Markings

Grade Yield/Tensile (MPa) Typical use
4.8 320 / 420 General light structural, non-critical joints
8.8 640 / 800 Standard structural bolts; most structural connections
10.9 940 / 1040 High-strength; flanged connections, critical machinery
12.9 1100 / 1220 Very high strength; socket-head cap screws, aerospace

6.5 Nut and Washer Selection

Match nut grade to bolt grade:
- Grade 4 nuts → Grade 4.8 bolts
- Grade 8 nuts → Grade 8.8 bolts
- Grade 10 nuts → Grade 10.9 bolts
- Grade 12 nuts → Grade 12.9 bolts

Hardened washers (Grade 300HV) required under head and nut for Grade 8.8 and above in steel structures. Plain washers acceptable for Grade 4.8 in timber and light construction.

Source: ISO 898-1:2013 Mechanical properties of fasteners — Bolts, screws and studs. Torque estimation from Shigley’s Mechanical Engineering Design (10th ed., §8-9, Nut Factor Table 8-15).


Notes on Using These Tables

  1. Check units carefully. Most errors in structural calculations come from unit inconsistency. Verify that load units (kN vs N, kPa vs Pa) are carried correctly through every calculation.

  2. Deflection ≠ strength. A beam may pass a deflection limit at a shorter span than its bending capacity permits, or vice versa. Both criteria must be checked independently.

  3. Hydraulic gradients. The pipe flow tables assume the pipe is flowing full. Partially full flow (gravity drainage) requires Manning’s equation or a hydraulic elements chart. For pressurised systems, add head losses at fittings (typically 10–30% additional equivalent length).

  4. Electrical safety. Ampacity tables assume a single circuit in good condition. Overcurrent protection must be rated ≤ the cable ampacity after all derating factors are applied. When in doubt, use the next larger cable size.

  5. Thread lubrication. Tightening torques change significantly with lubrication: dry threads may require 20–30% more torque than oiled threads for the same clamp force; zinc-plated threads are typically between dry and oiled.

  6. Professional review. These tables are for initial sizing, field estimation, and educational use. Life-safety structures (bridges, occupied buildings, pressure vessels) require review by a licensed Chartered Professional Engineer (CPEng) or equivalent.


Generated by scripts/generate_engineering_tables.py — Recovery Library Doc #017. Date: 2026-02-20.