Where does the weight go?: sources & model

Move a load across an inspectable steel truss. Lift its deck, catch a diagonal changing from push to pull, repair a missing restraint and follow forces all the way to the supports.

What supports the explanation?

What this model assumes

1. Quasistatic planar pin-jointed truss, straight massless bars and loads transferred to joints. No inertia, moving-load vibration, self-weight, wind, braking or three-dimensional stability calculation.
2. The front truss is solved. The rear frame, carriage and illustrative steel section shapes supply visual context, not additional solved force or stiffness claims.
3. Changing depth replaces the ideal geometry. Exploding the deck is an inspection operation; neither interaction computes elastic deformation.
4. No material strength, section area, EI, buckling or connection capacity is specified. Force colors do not identify safe loads, damage or failure.
5. Repair diagnostics describe first-order restraint and equilibrium rank, not a simulated finite collapse.
6. The beam and three-hinged arch are separate systems with distinct support constraints and only the primary point load. They are not equal-strength alternatives.
7. Real photographs retain owner provenance. Their exact member geometry, span, hinge behavior and condition are not inferred from appearance.
8. The paper force-polygon exercise is a mathematical activity. No field test, physical paper-bridge trial or learner-outcome study has been performed.
9. Declared geometry and units: The planar teaching truss has A(0,0), B(4,0), C(8,0), D(12,0), E(16,0), F(4,h), G(8,h), H(12,h), in metres. Its bars are AB, BC, CD, DE, AF, FG, GH, HE, BF, CG, DH, FC and CH. The chosen depth h spans 2–6 m. A supplies Ax and Ay; E initially supplies Ey. Neither support supplies a moment.
10. What P represents: P is a force assigned to the front truss, 0–30 kN. The contextual cart is not a measured vehicle mass, and the lesson does not infer how a real deck distributes a whole vehicle load between two side trusses. A separately identified 0–20 kN laboratory load can act downward at G.
11. Panel load transfer preserves force and moment: For a load at x between joints xᵢ and xᵢ+4, η=(x−xᵢ)/4. The downward truss loads are pᵢ=P(1−η) and pᵢ₊₁=Pη. Thus Σp=P and Σxᵢpᵢ=Px. A load directly at A or E can go directly to that support; it need not load the bars.
12. Tension-positive joint equilibrium: Each straight, massless, pin-connected bar is a two-force member. Its positive unknown N acts from a joint toward the bar’s other end. Reversing the isolated object reverses the force arrows: tension pulls apart an isolated member’s ends. The 16 joint equations use unit direction vectors and support columns.
13. An independently checked analytical solution: With downward bottom loads pA…pE and G load W, Ay=Σpᵢ(16−xᵢ)/16+W/2 and Ey=Σpᵢxᵢ/16+W/2. Let Aₙ=Ay−pA, Eₙ=Ey−pE and s=h/√(16+h²). Then FC=(Aₙ−pB)/s, CH=(Eₙ−pD)/s, CG=−W, BF=pB and DH=pD. A separate pivoted matrix solution is checked against the full analytical member solution.
14. Influence lines answer a specific question: A unit downward deck load gives a member-force influence trace. Between panel endpoints it is linear. For FC, N·s/P at x=0,4,8,12,16 m is 0,−¼,½,¼,0. With G unloaded and P positive, its interior crossing is 16/3 m; CH crosses at 32/3 m. Depth changes force magnitudes but not these crossings. Adding W changes the mixed-load crossings.
15. Counting is not a geometry test: For equilibrium matrix A, its rank determines independent constraints. First-order mechanisms = 16−rank; self-equilibrated force modes = number of unknowns−rank. Removing CG and adding Ex leaves 16 unknowns and 16 equations but rank 15: one mechanism and one force mode. A complete two-pin truss instead has rank 16 and one force mode, with no first-order mechanism.
16. A compatible load is not adequate restraint: With CG missing, a bottom-only load can still lie in the matrix column space. A downward G load cannot: it increases the augmented rank. The renderer withholds unsupported unique force colors rather than drawing an approximate solution as balanced. The small G arrow denotes a first-order permitted direction, not finite displacement or collapse.
17. Beam shear and bending: For the separate simply supported beam, V(z)=Ay−P·I(z>x) and M(z)=Ay·z−P·max(0,z−x). At the load show left and right shear limits. M is continuous, with peak Px(16−x)/16. On the isolated left beam segment, positive shear acts downward at its right cut; positive sagging moment acts counterclockwise there.
18. An arch needs its own support model: For the separate three-hinged parabolic arch, y(z)=4hz(16−z)/16², H=Mbeam(8)/h=P·min(x,16−x)/(2h), and March=Mbeam−H·y. Both bases provide horizontal restraint. The shortcut PL/(4h) applies only to a central point load. Base and crown moments vanish; bending between hinges generally does not.
19. Force, stress and strength are different: A bar force has units of force. Stress also needs area, and bending/deflection need section and stiffness information. Buckling, connections, fatigue, dynamics, self-weight, eccentricity and lateral stability need further models. Metallic section shapes in the original assembly do not supply those omitted engineering properties.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

Real aerial bridge image by Nick Giro and Chris Lewis, USGS, Public Domain. The unchanged USGS full-width derivative is bundled with its provenance; the cover is a resized format derivative displayed without a crop. It shows structural context, not the invented eight-joint analytical model or a bridge condition assessment.