An arched deck truss bridge carries its deck above a curved, triangulated supporting structure. Deck loads pass through posts and web members into the arch and its supports. The animation illustrates that arrangement, while the calculator shows how a single point load’s position changes the reactions of an ideal three-hinged arch.
Arched Deck Truss Bridge Interactive Calculator
Vary span, span-to-rise ratio and a point load to compare arch geometry, horizontal thrust and ideal support reactions.
Equation Used
The calculator uses the article rise-to-span relationship r/L, expressed as L:r = n, then estimates horizontal abutment thrust for a point truck load on a simplified three-hinged arch. Lower n means a deeper arch and usually lower thrust demand; higher n means a shallower arch with higher foundation thrust sensitivity.
- Simplified teaching estimate for a three-hinged arched deck truss.
- Truck load is treated as a single vertical point load.
- Horizontal thrust is estimated from crown bending relief, not a final bridge design check.
- The global arch reactions are calculated; individual web, post and chord forces are not solved.
The sqrt(H²+(P/2)²) result is a symmetric reference, not the actual support resultant for an off-center truck. The animation additionally gives unequal vertical reactions P(1-x/L) and P*x/L. The model is an ideal three-hinged arch, not a detailed truss-member or bridge-capacity design.
A deck above an arch
The roadway or railway sits above the main arch. Its supporting posts and web members deliver loads to the curved structure. Arch action produces outward horizontal thrust as well as vertical reactions at the springings. The arrangement leaves the space above the deck largely clear of the main arch.
A triangulated web transfers forces through connected members, but a side elevation alone does not show the entire three-dimensional bracing system. It does not prove that lateral buckling, snap-through or connection failure is prevented. Real arches can carry bending as well as compression, especially under uneven loading.
Parts in the illustration
- Deck: carries the selected load above the arch.
- Posts and diagonals: illustrate load transfer between deck and arch.
- Arch: spans between the springings.
- Three hinges: define the ideal static model, with one at each springing and one at the crown.
- Support reactions: equal horizontal magnitudes and position-dependent vertical forces.
The truck stays at the selected position. Moving dots depict a load route; they do not show calculated structural motion. Post dimensions, joint rigidity, section stresses and deflection are outside this global reaction model.
Deck-arch crossings
The New River Gorge Bridge is a steel open-spandrel arch-truss bridge carrying the deck above the arch. The National Park Service distinguishes its approximately 3030 ft overall length, 1700 ft arch span and 876 ft height above the river. These are different dimensions.
The calculator’s initial span value of 876 ft is an illustrative input, not the arch span of that bridge. Entering a real span still does not reproduce a real bridge’s structure or loading: the model has one point load and omits structural dead load and other load cases.
Deck arches can suit sites with space below the deck, but terrain alone does not choose the structural form. Foundation conditions, clearance, access for construction, loading and maintenance all matter. A through arch describes where the deck lies relative to the arch; it is not synonymous with a tied arch.
Point-load reactions for the ideal arch
Let L be span in feet, n = L/r the span-to-rise ratio and u = x/L the load position measured from the left support. Arch Rise r = L/n and Rise Ratio = 100/n percent. For point load P, H = Pn min(u, 1 − u)/2.
The vertical reactions are V_left = P(1 − u) and V_right = Pu. They sum to P. Taking moments about the crown hinge gives the horizontal reaction H; at midspan H = Pn/4. The actual support resultants in this ideal model are √(H² + V_left²) and √(H² + V_right²), shown in the live readout.
The Symmetric reference force tile uses √(H² + (P/2)²). It equals both support resultants only when the load is centered. Away from midspan it is a comparison value, not either support force and not an arch-member stress.
The Truck Load control is labeled ton and results tonf. The arithmetic treats P as a force number and performs no mass-to-force or short-ton/long-ton/metric-ton conversion. Use one consistent ton-force convention throughout; the result must not be treated as an SI conversion.
At fixed n, P and u, changing L also changes r in the same proportion, so H remains unchanged. This is geometric similarity under a fixed point load, not evidence that a longer bridge has unchanged dead load, stiffness or capacity.
Worked example: an off-center load
Use L = 876 ft, n = 5, P = 40 in one consistent ton-force convention and u = 0.25. Arch Rise is 175.2 ft and Rise Ratio is 20.0%. H = 40 × 5 × 0.25/2 = 25.0 tonf.
The Symmetric reference force is √(25² + 20²) = 32.0156 tonf, displayed as 32.0. However, V_left = 30 and V_right = 10 tonf. The corresponding actual resultants are 39.0512 and 26.9258 tonf, displayed in the live readout as 39.05 and 26.93.
Move the load to midspan. H becomes 50.0 tonf and each vertical reaction is 20.0 tonf. Both resultants now equal the reference value √(50² + 20²) = 53.8516 tonf.
At the original quarter-span position, increase n to 10. Rise becomes 87.6 ft, Rise Ratio becomes 10.0% and H doubles to 50.0 tonf. The model gives forces, not an allowable truck load or a recommendation for a shallower arch.
Deck position and thrust restraint
| Arrangement | Distinction |
|---|---|
| Deck arch | The deck is supported above the arch. |
| Through arch | The deck passes between the arch ribs and may be suspended by hangers. |
| Tied arch | A designed tie balances horizontal arch thrust between the ends. |
| Girder or truss bridge | Main span action and reactions depend on its member arrangement and support restraints. |
Deck location and the use of a tie are separate characteristics. They do not establish a universal cost ranking, service life, reserve capacity or preferred span range.
Point-load arch questions
A point load closer to one support produces a larger vertical reaction there. V_left = P(1 − u) and V_right = Pu satisfy global equilibrium.
The reference uses P/2 at both sides. The live resultants use the position-dependent vertical reactions. They agree at midspan.
Rise increases with span when the ratio is fixed. In the point-load thrust equation L/r becomes n, so the absolute length cancels.
No. The National Park Service lists its arch span as 1700 ft; 876 ft is its height above the river. The initial calculator geometry is illustrative.
No. It includes the entered single point load. Dead load, multiple axles, lane loading and other load cases need separate analysis.
No. Through describes deck position. A tie is a specific structural member and load path, and must be explicitly included in the structural model.
No. It has no material stiffness, section sizes, connection details, temperature or support-movement model. It cannot diagnose an existing bridge or establish remaining capacity.
No. Lateral stability is a three-dimensional structural problem involving members, bracing, connections and imperfections. The side-view equilibrium illustration does not calculate it.
Bridge reference
National Park Service: New River Gorge Bridge. The record identifies the structural form and distinguishes arch span, overall length and height above the river. The point-load equilibrium model on this page is a separate ideal example.
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