Iteration 03 · November 14, 2026 · 38 × 8 ft roof with two shores
Compare three tube walls for the same shored roof. Our declared stress screen gives conceptual ceilings of 7, 10 and 13 people.
As modeled conceptually, subject to change once we survey our specific bus, Earl Thomas. These are roof-frame stress-screen ceilings. The actual admission limit still requires verified supports, connections, floor motion and vehicle checks.
Thicker walls improve the stress margin and add weight overhead. Change your target and see which concepts clear the same calculation criterion.
Colors describe the calculated roof-frame stress margin at your selected crowd. Green still requires the bus survey and engineering checks.
Conceptual stress-screen ceiling
7 people
■ Above the stress ceiling at 20 people
Conceptual stress-screen ceiling
10 people
■ Above the stress ceiling at 20 people
Conceptual stress-screen ceiling
13 people
■ Above the stress ceiling at 20 people
None of these three walls clears the declared stress criterion at 20 people. More structural development is needed for that target.
Default score: 70% stress reserve, 30% lower frame-and-plywood weight. Scores compare these three concepts; they are not probabilities of safety.
The yield-only factor compares assumed steel yield with calculated stress. This screen requires at least 1.67; it does not measure the safety of the bus or its connections.
The interactive data could not load. The fixed headcount findings and calculations below remain available.
For the largest conceptual crowd in this comparison, ¼-inch walls lead: 13 people. The 3/16-inch option reaches 10, and ⅛-inch reaches 7, under the declared stress criterion. A target of 20 exceeds that criterion for all three. Thicker walls alone have not resolved the 20-dancer target under these assumptions.
Even with ideal rigid shores, the ¼-inch concept reaches 14 people under this stress criterion. At the boundary counts, the transverse bearers govern. Further design work should examine those members and their connections. The ¼-inch frame and plywood add about 1,917 lb compared with ⅛ inch. At smaller crowds, a lighter option can rank better. The recommendation considers only options that clear the stress screen; when none does, it asks for a design revision.
Movement remains a separate concern. At their respective ceilings, all three calculate roughly 1.1 inches of peak deck movement under the amplified load. This study has no agreed deflection or vibration acceptance criterion, so the displayed counts do not establish comfort or dancing suitability.
The counts are lower than the earlier 20-person comparisons because iteration 03 adds an explicit criterion: twice the people load and a 207 MPa stress ceiling. Earlier iterations reported ordinary static gravity loads against assumed first yield of 345 MPa. The roof geometry and shore stiffness are unchanged.
The orange vertical shores sit beneath the two edge girders, halfway between the interior bearers. Upper pads meet the girder undersides. Lower pads mark proposed structural landing zones on the Thomas; reinforcing those zones and tracing their loads to the chassis remains survey work.
The reference bus shell is shown with the framing; sheep panels, floor and equipment are hidden here for inspection. The 70 mm display struts and pad dimensions illustrate positions. They are not selected fabrication sections, and their mass remains excluded from the calculation.
Inspect all layers in the panel workshop · Download the shored concept model
Calculation record
Inputs, equations, governing cases and verification for engineering review. All stresses are elastic normal-stress demands from the beam model.
| Input | Value / assumption |
|---|---|
| Deck | 38 × 8 ft. Front x = −6.357811 m, aft x = 5.224589 m, floor top z = 4.0204 m. |
| Roof members | Two 100 × 60 mm edge girders (60 mm vertical), 13 joists, eight roof diagonals, two transverse bearers, four interior uprights and front/rear portals. Exact members and axes are in the downloadable geometry. |
| Trial tube walls | 3.175, 4.7625, 6.35 mm across the modeled tubes, including original posts and portal sills. The new shores remain effective springs. |
| Steel | E = 200 GPa, ν = 0.30, ρ = 7,850 kg/m³; assumed Fᵧ = 345 MPa. Grade, wall tolerances and actual HSS properties await confirmation. |
| Plywood | 19.05 mm at 600 kg/m³. Gravity only; no composite stiffness. |
| People | 225 lbf each. Baseline amplification α = 2 on live load only. Dead load remains at 1×. |
| Selected stress ceiling | 0.60 Fᵧ = 207 MPa, equivalent to a yield-only factor of 1.667. This is a project screening choice, not a completed code strength check. |
| Shore positions | x = −0.2618115 m, y = ±1.1692 m, girder centerline z = 3.8604 m. |
| Shore restraint | Compression only, zero initial gap; k = 5,000 lbf/in per complete prop/body/chassis path. No lateral or moment restraint is credited. |
| Rear load path | Both rear corners transfer through the rear drop-frame to the chassis rails. Same idealized sections and fixed rail-seat restraint as the front portal; actual interfaces remain unmeasured. |
| Other original supports | Eight idealized rail seats have six restrained degrees of freedom. They may resist tension. Internal member joints are rigid; seating offsets are collapsed as in iteration 02. |
| Excluded from dead load | New shores, pads, reinforcement, rails, art, stairs and unweighed equipment. Their final loads must be included before release. |
The 2× multiplier is a deliberately stated equivalent-static sensitivity. It is not a demonstrated upper bound on rhythmic force, resonance or bus-motion effects. AISC’s vibration guidance treats frequency, forcing harmonics and damping explicitly and distinguishes vibration serviceability from strength and fatigue.
Applied gravity:
Equilibrium on free degrees of freedom:
Compression-only bearings (vertical displacement positive upward):
For finite k, the equivalent complementarity conditions are rᵢ ≥ 0, uᵢ + rᵢ/kᵢ ≥ 0, and rᵢ(uᵢ + rᵢ/kᵢ) = 0. The solver enumerates the four active sets of two bearings. In the rigid limit, closed bearings have uᵢ = 0 and open bearings have rᵢ = 0.
Ideal sharp-corner rectangular hollow section:
Iᵧ = [bh³ − (b − 2t)(h − 2t)³]/12; I𝓏 = [hb³ − (h − 2t)(b − 2t)³]/12. Member axes, section orientation and the thin-wall torsion approximation are recorded in the solver.
Section corner envelope:
Nₐ is member axial force, distinct from the dancer count N. This envelope covers axial and biaxial bending normal stress. Values above 345 MPa flag departure from the assumed elastic range; their computed displacement does not predict post-yield movement. It does not evaluate combined shear/torsion failure, local buckling, connection capacity or a complete HSS interaction equation.
Conceptual headcount ceiling:
Each integer count is solved directly with its own crowd footprints. We report the last count before the first criterion exceedance. No ratio of 20-person peak stresses is used to extrapolate a headcount.
Each solve includes dead load, uniform full-deck loading, either full half-deck, a centered driver-side 12 × 4 ft group and an aft driver-side 12 × 4 ft group. The driver-side sweep uses 12 × 4 ft and (0.6N) × 4 ft footprints, moving in 1 ft steps plus exact centered and aftmost positions. The shorter footprint retains the prior study’s chosen crowd density. For counts above 20 the second footprint is longer. Other shapes, individual footfalls and continuous placements remain untested.
Case names of the form patch_Lft_at_Xft specify a group of length L feet starting X feet aft of the new front deck edge. The envelope includes all these cases. Stress is sampled at element ends and midpoints; deck displacement at roof nodes. Peaks of stress, drop and reaction are independent and can occur at different crowd positions. The original three-subdivision mesh is used for publication; five-subdivision replays check the boundary counts.
| Wall | People | Stress MPa | Drop in | One shore lbf | Seat uplift lbf | Stress member | Stress placement |
|---|---|---|---|---|---|---|---|
| ⅛″ | 7 | 201.22 | 1.133 | 2,268 | 23 | Transverse deck bearer 2 | patch_4.2ft_at_26ft |
| ⅛″ | 8 | 223.07 | 1.242 | 2,545 | 60 | Transverse deck bearer 1 | patch_4.8ft_at_9ft |
| 3/16″ | 10 | 201.50 | 1.120 | 3,029 | 46 | Transverse deck bearer 1 | patch_6ft_at_8ft |
| 3/16″ | 11 | 216.57 | 1.178 | 3,295 | 70 | Transverse deck bearer 1 | patch_6.6ft_at_8ft |
| ¼″ | 13 | 200.19 | 1.113 | 3,671 | 44 | Transverse deck bearer 2 | patch_7.8ft_at_24ft |
| ¼″ | 14 | 212.31 | 1.170 | 3,850 | 63 | Transverse deck bearer 2 | patch_8.4ft_at_24ft |
These are amplified-load displacements and reactions. The original chassis-seat model can develop uplift, which requires a verified hold-down detail. The two new shores release in tension.
Changing the chosen force multiplier changes the ceiling even with identical steel and geometry. Changing the effective body-path stiffness also changes it. Every table entry uses the same 207 MPa stress criterion.
People-load multiplier · k = 5,000 lbf/in per shore
| Multiplier | ⅛″ | 3/16″ | ¼″ |
|---|---|---|---|
| 1× | 16 | 24 | 30 |
| 1.5× | 9 | 14 | 20 |
| 2× | 7 | 10 | 13 |
| 3× | 4 | 6 | 8 |
Shore stiffness · α = 2
| Each shore | ⅛″ | 3/16″ | ¼″ |
|---|---|---|---|
| 1,000 lbf/in | 6 | 9 | 10 |
| 5,000 lbf/in | 7 | 10 | 13 |
| 20,000 lbf/in | 7 | 10 | 14 |
| Rigid | 7 | 10 | 14 |
Let R = 207/σₘₐₓ at the selected headcount, and γᵧ = 345/σₘₐₓ. The displayed “yield-only factor” is γᵧ; it is not a factor of safety for the whole vehicle.
| Color | Rule | Meaning in this screen |
|---|---|---|
| Green | R ≥ 1.25 (γᵧ ≥ 2.083) | At least 25% capacity-to-demand reserve above the selected criterion. |
| Yellow | 1 ≤ R < 1.25 | Below the stress ceiling, with less than 25% reserve. |
| Red | R < 1 | Exceeds the chosen criterion. |
The comparison score is S = 100[w min(R/1.25, 1) + (1 − w)Mₘᵢₙ/Mₜ], where Mₜ is this frame-and-plywood dead weight and Mₘᵢₙ is the lightest of the three. Default w = 0.70; “favor margin” uses 0.90 and “weight more importance” uses 0.50. These are explicit preference weights. Shore, connection and reinforcement weights are excluded until selected.
The recommendation selects the highest score among options satisfying R ≥ 1. If there are none, it recommends revising the design and identifies the highest-scoring option only as a comparison candidate. Scores are not reliability estimates and do not include unverified landing capacity, cost, fatigue or vehicle stability.
Axial and cantilever element checks and compression-bearing opening/rigid-limit checks passed. Every solve verified applied gravity and force/moment equilibrium. For all three walls, α = 1 replay matched iteration 02 to 10⁻⁵ output units. The six default boundary cases retained their classifications with five subdivisions instead of three. Peak stress and shore reaction were unchanged at practical reported precision; the largest relative change in sampled deck drop was 0.129%. The archive includes the raw verification results.
Download iteration 03 calculation source and verification · Machine-readable inputs, counts and governing results · Original 38 ft static report
The survey must identify and dimension actual roof bows/side posts, body mounts, front portal and rear drop-frame connections, chassis seats and engine/access clearances. A checked design must establish landing stiffness and strength, full dead loads, section properties, buckling and connection capacities, lateral stability, guardrails and stairs. Rhythmic acceleration, resonance, fatigue, braking/turning, axle loads and vehicle stability need their own assessment. No deflection or vibration acceptance criterion has been applied here.
Fabrication and operational occupancy remain unreleased. The conceptual comparison can guide the next design choice. A structural/vehicle engineer must use Earl’s measurements and the complete load cases to establish its operating limits.
AISC: Facts for Steel Buildings 5, Vibrations, section 5, explains rhythmic response and the distinction between vibration serviceability and strength/fatigue. AISC 360 provides the broader strength, stability and serviceability framework; this simplified screen does not claim code compliance.
Use one datum for all proposed support points, including the two speculative rear portal feet. Record fore-aft distance from the front axle centerline, offset from the bus centerline and height from a documented level reference. At each point, locate both the deck-to-post joint and the foot on the bus. Identify the supporting member, measure accessible dimensions and clearances, and photograph both sides with a scale.
| Proposed location | Driver side | Passenger side |
|---|---|---|
| Front portal shoe | Awaiting survey | Awaiting survey |
| Forward interior post | Awaiting survey | Awaiting survey |
| Aft interior post | Awaiting survey | Awaiting survey |
| Rear drop-frame / portal interface | Load transfer assumed; survey pending | Load transfer assumed; survey pending |
| New midspan shore landing | Body member, stiffness and strength await survey | Body member, stiffness and strength await survey |
Trace each front shoe’s load path to the chassis. At the rear, establish the actual main-rail, drop-frame, crossmember and engine-support geometry before locating any new foot. Measure the fully open engine-access envelope against the proposed rear portal, bearer, stairs and landing; record cooling, exhaust, and service clearances. The appearance of a rear foot in the model does not establish its load path or capacity.
| Deliverable | Status | Evidence to record |
|---|---|---|
| As-built survey | Open | Dimensioned sketch, ten labeled photo sets including the provisional rear feet, engine and stair clearances, rear deck overhang. |
| Design loads | Open | Iteration 03 adds explicit stress-screen boundaries, amplified live-load sensitivity and margin/weight scoring. The survey and dynamic checks remain open. Confirm full dead load and parked and moving occupancy. The comparison brief assumes 20 dancers at 225 lb each, moving up to 5 mph. This is a design target. Record deck, rail, stair and equipment weights and locations. |
| Vehicle assessment | Pending inputs | Front and rear axle scale tickets with weighing configuration, axle ratings, and review of stability under uneven loading, braking and turning. |
| Checked framing and connections | Conceptual headcount screen complete; operating limit pending | Engineer-reviewed spans, sections, floor support, brace and splice details, welds, bolts, guardrail and stair connections, chassis interfaces, and operating limits. |
| Fabrication BOM and cut list | On hold | Record the released drawing revision and scope, then list stock grade, tube sizes and walls, lengths, cuts, plates, fasteners and quantities. |
· Iteration 03 presents the conceptual headcount ceilings, color bands, scoring and full calculation record. Added the two shores and provisional landing pads to the displayed/downloadable model. Iterations 01 and 02 remain available.