Deck checking: formulas and assumptions
This sheet documents the method behind the TG20 Platform Checker. Every formula is shown and every assumption stated, in the same order as the calculator: Inputs (sections 1–7), Analysis (sections 8–11), Results (sections 12–16) and Component data (sections 17–20).
Part A — Inputs
1. Notation
Symbol
Meaning
Unit
Default
q₁
Uniform service load on the main boards
kN/m²
2.0 (class 3)
F₁, F₂
Concentrated loads on 500 × 500 mm and 200 × 200 mm
kN
1.5, 1.0
q₂, aₚ
Partial area load and its area factor (classes 4–6)
kN/m², –
not used
qᵢₙ
Imposed load on the inside boards
kN/m²
0.75
g
Deck self-weight (boards + layers + other dead load)
kN/m²
0.245
nb
Number of main boards
–
5
nᵢₙ
Number of inside boards
–
2
b
Board width
mm
225
D
Tube outside diameter
mm
48.3
W
Ledger spacing, outer to inner (centres)
mm
1,173
c
Transom cantilever beyond the inner ledger
mm
524
nL
Ledgers under the main boards
–
2
nᵤₚ
Uprights along each ledger
–
3 (2 bays)
Lb
Bay length (upright spacing)
m
2.0
sₘ
Board span m (distance between adjacent transoms)
m
1.0
nₜ, nₗ
Transoms at one position; tubes in one ledger
–
1, 1
Mₐ, Vₐ
Safe working moment and shear of one member
kNm, kN
1.12, 29.10 (steel tube)
Fₛ
Safe working slip load of one right-angle coupler
kN
9.1 (class B)
M, V, δ, R
Bending moment, shear, deflection, reaction
kNm, kN, mm, kN
–
u
Utilisation = load effect ÷ safe working value
%
–
x runs along the ledgers from upright U1; y runs across the platform from ledger 1 (outer).
Loads are positive downward; reactions positive upward; sagging moment positive.
All loads are working (unfactored) loads compared with safe working values. No partial safety factors are applied.
2. Load class
The class buttons fill in the BS EN 12811-1 service loads used by TG20:21. Any value can be overwritten.
Class
TG20 duty
q₁ kN/m²
F₁ kN
F₂ kN
q₂ kN/m²
aₚ
1
Inspection / very light duty
0.75
1.5
1.0
–
–
2
Light duty
1.50
1.5
1.0
–
–
3
General purpose (default)
2.00
1.5
1.0
–
–
4
Heavy duty
3.00
3.0
1.0
5.0
0.4
5
Masonry
4.50
3.0
1.0
7.5
0.4
6
Special duty
6.00
3.0
1.0
10.0
0.5
q₁, F₁, F₂ and q₂ are separate load cases; they are never added together.
Choosing a class resets q₁ to aₚ. Loads tagged “class” in the load cases follow these values until edited.
3. Section: boards, inside boards and ledgers
Main boards fit between the outer and inner standards, which stand on the ledger lines.
Inside boards start at the face of the inner standard and sit on the transom cantilever, or on an extra ledger at their inside edge.
Each board is a strip b wide. Load is only taken where there are boards; nothing is counted over the standards.
The inside board load qᵢₙ is a user value applied separately from the main platform load. 0.75 kN/m² is a default, not a TG20 value.
Intermediate ledgers are equally spaced and every ledger has an upright at every upright line.
4. Deck layers
Extra board or plywood layers can be laid on the main boards, and optionally on the inside boards. Layers are not fixed together: each bends on its own and they share load in proportion to their stiffness. For each layer i, per metre width: eᵢ = EI, mᵢ = Mₐ, vᵢ = Vₐ.
The layer that reaches its own safe value first governs the deck, so a thin sheet can add little capacity.
The spread acts across the boards only (y direction), only on concentrated and point loads, and only where layers are present.
Layers change the transoms and ledgers only through their self-weight.
5. Bays and transoms
A transom is always present at every upright line and cannot be moved.
Dragging a transom on the plan snaps it to 25 mm.
Transoms at one position share load equally and deflect together.
6. Members and couplers
Transoms and ledgers can each be any member in the library (section 17). The defaults are 48.3 mm steel tube for both.
Each tube of a doubled ledger is assumed to have its own coupler at every upright.
Galvanised tubes in good condition are taken as new.
7. Load cases
A load case is a list of loads acting together. Each load can be ticked, edited or removed, and new cases added.
Load
How it is applied
Deck self-weight
g on the main boards, gᵢₙ on the inside boards, every bay
Member self-weight
wₜ × nₜ along every transom; wₜ × nₗ along every ledger
Uniform load
q on one zone (main or inside boards); every bay or pattern-loaded
Concentrated load
q = F ÷ (lₓ × ly) over its area; fixed x, y or worst position
Partial area load
q₂ over Aₚ at the worst position; with “replaces uniform load” the added intensity is q₂ − q₁
Point load
q = P ÷ (0.1 × ly) over 100 mm along the span and 100 mm (or sₛₚ) across
Default case
Loads acting together
LC1 Uniform load q₁
Self-weights + q₁ on main boards (pattern) + qᵢₙ on inside boards (pattern)
LC2 Concentrated F₁
Self-weights + F₁ on 500 × 500, worst position + qᵢₙ
LC3 Concentrated F₂
Self-weights + F₂ on 200 × 200, worst position + qᵢₙ
LC4 Partial area q₂
Self-weights + q₁ + q₂ on Aₚ replacing q₁ below it + qᵢₙ (classes 4–6 only)
LC5 Point loads
Self-weights + 1.5 kN at x 1.0, y 0.6 m + 1.0 kN at x 0.5, y 0.3 m + qᵢₙ
Load cases are independent. Each member’s result is its worst over all active cases.
Pattern loading finds the largest sagging, hogging and reactions, including an unloaded inside cantilever, which gives the largest sagging in the main transom span.
Only one load per case can move to its worst position; pattern loading is not combined with a moving load (uniform loads then act on every bay).
Each member keeps its own worst position. The search was checked against a brute-force scan on a 20 × 12.5 mm grid and is within 1%.
Loads that fall outside the boards are ignored and flagged; concentrated loads are clipped to their zone.
All loads are static and vertical. Wind, impact, dynamic and horizontal loads are not included.
Part B — Analysis
8. Load path
Loads go from the boards to the transoms, from the transoms to the ledgers, and from the ledgers into the uprights through the right-angle couplers.
The lever rule is exact for boards simply supported between adjacent transoms.
The transom at an upright passes its load straight into the coupler at that upright.
9. Boards
Each board strip is checked span by span, simply supported between two adjacent transoms.
Boards are not taken as continuous over transoms. This is conservative for sagging and ignores staggered board ends.
Every board and every span is checked; the worst is reported.
10. Transoms and ledgers
Transoms are continuous over the ledgers, with the inside cantilever where there is no extra ledger. Ledgers are continuous over the uprights. Both are solved with the three-moment equation.
M₀, V₀, R₀ are the simply supported values of each span. The support moments are solved directly (tridiagonal system).
Moment and shear are exact. Deflection is integrated numerically at 96 points per span.
Supports are rigid and joints are pins: coupler rotational stiffness, slip and eccentricity are ignored.
Shear deformation is ignored for all members.
11. Superposition
The analysis is linear elastic, so loads acting on every bay are solved once and added to each moving or patterned arrangement.
Supports never lift off. A negative reaction is reported as uplift but the support stays in the model.
Part C — Results
12. Utilisation and result
Utilisation u
Result shown
u ≤ 90%
PASS
90% < u ≤ 100%
PASS · CLOSE
u > 100%
FAIL
span/100 is the BS EN 12811-1 deflection limit for platform units. Each board span uses its own length.
n = nₜ for transoms and nₗ for ledgers; |M| is the larger of sagging and hogging.
Transom and ledger deflections are shown but not checked against a limit.
The 90% band is a visual warning only; it is not a code limit.
13. Plan and upright reactions
The plan shows the load arrangement that governs the selected member, including where a moving load or q₂ area sits.
With pattern or moving loads each upright shows its own largest value, so the values do not add up to one arrangement.
Reactions are from this lift’s platform only. Other lifts, ties, bracing and wind are not included.
14. Section and member diagrams
Diagrams show the governing arrangement for the chosen member: loads and reactions, moment, shear and deflection.
A region left unloaded by pattern loading is drawn dashed and labelled “not loaded in this arrangement”.
Concentrated loads show the part that reaches the member, e.g. 1.5 kN → 1.31 kN on this transom.
15. Load case and combination tables
Utilisation by load case lists each member’s worst result in each case, and the largest upright reaction.
Ledgers and couplers lists each ledger’s worst moment and coupler load.
The combinations table repeats the full check for 2, 3 and 4 ledgers with 2, 3 and 4 uprights, using the same deck, members and loads.
16. Worked example (default inputs)
Class 3, 5 main boards + 2 inside boards on a cantilever (qᵢₙ = 0.75 kN/m²), 2 ledgers, 3 uprights, Lb = 2.0 m, one intermediate transom per bay (s = 1.0 m), steel tubes (Mₐ = 1.12 kNm), class B couplers (Fₛ = 9.1 kN), one board layer.
Board — LC5, 1.0 kN point load at x 0.5 m (mid-span of span 1, board 2):
Self-weight on one board w = 0.245 × 0.225
0.0552 kN/m
M = 0.0552 × 1.0² ÷ 8 + 1.0 × 1.0 ÷ 4 − 1.0 × 0.1 ÷ 8
0.244 kNm
u = 0.244 ÷ 0.475
51%
Transom T2 — LC1, bay 1 loaded on the main boards, inside boards unloaded:
wₘₐᵢₙ = 2.245 kN/m over 1.125 m; wᵢₙ = 0.245 kN/m over 0.450 m; tube 0.0429 kN/m
total 2.709 kN
Cantilever moment at L2 = −0.245 × 0.45 × 0.2492 − 0.0429 × 0.524² ÷ 2
−0.033 kNm
RL1 = (2.526 × 0.5867 + 0.0429 × 1.1733² ÷ 2 − 0.033) ÷ 1.1733
1.260 kN
M at zero shear (x = 0.574 m) = 1.260 × 0.574 − 0.0429 × 0.574² ÷ 2 − 2.245 × 0.550² ÷ 2
0.377 kNm
u = 0.377 ÷ 1.12
34%
Ledger 2 (inner) — LC1, bay 2 loaded: transom loads T2 = 0.33 kN, T4 = 1.86 kN.
Support moment at U2: 8 MB = −(0.33 × 1.5 + 1.86 × 1.5 + 2 × 0.0429 × 2)
−0.432 kNm
M under T4 = 1.86 ÷ 2 × 1.0 + 0.0429 × 1.0 − 0.0429 ÷ 2 − 0.432 ÷ 2
0.735 kNm
u = 0.735 ÷ 1.12
66%
Coupler L2 at U2 (all bays loaded): 4.52 ÷ 9.1
50%
Load case
Arrangements
Boards
Transoms
Ledgers
Couplers
LC1 Uniform load q₁
9
13%
34%
66%
50%
LC2 Concentrated F₁
319
28%
26%
58%
32%
LC3 Concentrated F₂
402
49%
22%
52%
30%
LC5 Point loads
3
51%
46%
57%
27%
Worst
–
51%
46%
66% — governs
50%
Ledgers
Uprights
Boards
Transoms
Ledgers
Couplers
Max R kN
2
2
51%
42%
85%
21%
1.93
2
3
51%
46%
66%
50%
4.52
2
4
51%
46%
70%
47%
4.32
3
2
51%
10%
79%
18%
1.64
3
3
51%
10%
72%
43%
3.88
3
4
51%
10%
71%
41%
3.73
4
2
51%
10%
69%
1.54
4
3
51%
10%
54%
32%
2.95
4
4
51%
10%
54%
31%
2.80
All values agree with the calculator’s output for the default inputs. Upright reactions, LC1: L1 1.17 / 3.10 / 1.17 kN and L2 1.71 / 4.52 / 1.71 kN at U1 / U2 / U3. With 18 mm plywood added, the boards drop from 51% to 26%.
Part D — Component data
17. Scaffold beams, tubes and boards
Member
Mₐ kNm
Vₐ kN
kg/m
I cm⁴
A cm²
EI kNm²
Ladder Beam
13.50
12.00
11.9
2,600
11.10
5,271
Unit Beam
27.70
18.50
14.5
10,572
–
21,320
Haki 750
41.30
30.60
7.5
17,182
16.90
11,856
Haki 450
15.70
12.70
4.2
4,481
11.10
3,087
Apollo X 750
42.90
45.40
8.0
17,097
12.14
11,796
ASP 750
36.50
30.70
6.5
16,563
12.32
11,594
Layher 450
13.94
12.32
5.0
4,481
–
3,137
Layher 750
33.50
25.60
6.0
15,195
–
10,637
Dessa D78
38.87
31.66
5.5
16,520
12.30
11,399*
Triangle Rail
11.20
21.60
10.68*
281
13.60
576*
Steel tube 48.3 Ø (default)
1.12
29.10
4.37
13.77
5.57
28.22*
Aluminium tube 48.3 Ø
1.33
25.52
1.65
–
6.15
10.45
Scaffold board 38 × 225
0.475 per board
4.60 per board
25 kg/m²
–
–
29.0 per m width
Values marked * are derived, not taken from a datasheet:
Steel tube 48.3 × 4.0
EI = 205 GPa × 13.77 cm⁴ = 28.2 kNm²
Dessa D78 (aluminium)
EI = 69 GPa × 16,520 cm⁴ = 11,399 kNm²
Triangle Rail (steel assumed)
EI = 205 GPa × 281 cm⁴ = 576 kNm²; 13.6 cm² × 7,850 kg/m³ = 10.68 kg/m
Board EI read per metre width
Board values per metre width
m = 0.475 ÷ 0.225 = 2.111 kNm/m; v = 4.60 ÷ 0.225 = 20.44 kN/m
Safe working values are from manufacturers’ datasheets and must be checked against current manufacturer information. All values are editable on the Component data tab.
The board EI is taken per metre width because per board it would need E ≈ 28,000 N/mm², which is not possible for timber.
18. Plywood
Per metre width, face grain along the span, from typical values over the full thickness t:
Thickness
Mₐ kNm/m
Vₐ kN/m
EI kNm²/m
kg/m²
6 mm
0.048
2.00
0.108
3.6
9 mm
0.108
3.00
0.364
5.4
12 mm
0.192
4.00
0.864
7.2
15 mm
0.300
5.00
1.688
9.0
18 mm (default layer)
0.432
6.00
2.916
10.8
22 mm
0.645
7.33
5.324
13.2
25 mm
0.833
8.33
7.813
15.0
These are typical figures, not a supplier’s data. Replace them with the supplier’s declared values.
19. Right-angle couplers
Coupler
Slipping force kN
Cruciform stiffness kNm/rad
Cruciform bending kNm
Class A
6.1
10.0
0.32
Class B (default)
9.1
15.0
0.48
Only the slipping force is used in the checks. Cruciform values are for reference; joints are analysed as pins.
20. Not checked
Uprights (standards), base plates, sole boards and ground bearing.
Ties, bracing, wind, lateral and dynamic loads.
Transom-to-ledger fixings, check couplers and hop-up brackets.
System scaffold components; use the manufacturer’s data.
Loads from other lifts. The checker covers one boarded lift.
Guidance only. Imposed loads are the BS EN 12811-1 service classes used by TG20:21; the 0.75 kN/m² inside board load is a default, not a TG20 value. Safe working values are from manufacturers’ datasheets; board EI is taken per metre width and plywood properties are typical values, so replace them with your supplier’s data. Boards are simply supported between transoms and checked to span/100; transoms and ledgers are continuous beams with pinned joints and rigid supports; layers share load by stiffness; g = 9.81 m/s². Uprights, ties, bracing, wind and fittings other than ledger couplers are not checked. Designs should be checked by a competent temporary works engineer. Results are for preliminary estimation and educational purposes only. They do not replace professional engineering judgement, applicable codes and standards, or design verification by a qualified engineer. Use at your own risk.