Bridge Input Form
Formula Used
The calculator uses simplified preliminary tied arch bridge relationships.
- Service line load: q = [(DL + LL × (1 + impact)) × width] + utility load + barrier load
- Factored line load: w = q × load factor
- Load per arch plane: wp = w ÷ number of arch planes
- Horizontal thrust: H = wp × L² ÷ (8f)
- Vertical reaction: V = wp × L ÷ 2
- Arch springing force: N = √(H² + V²)
- Hanger vertical force: Pv = total factored load ÷ total hangers
- Hanger tension: T = Pv ÷ sin(angle)
- Tie stress: σt = H ÷ tie area
- Arch stress: σa = N ÷ arch area
- Deck deflection: δ = 5wL⁴ ÷ 384EI
How To Use This Calculator
- Enter the bridge span, rise, and total deck width.
- Add dead load, live load, impact allowance, and line loads.
- Set the load factor for preliminary design demand.
- Enter the number of arch planes and hanger layout details.
- Add tie, arch, and deck section properties.
- Press Calculate to view results above the form.
- Use CSV or PDF download for saving the output.
- Check all final designs with an approved bridge code.
Example Data Table
| Case | Span m | Rise m | Width m | Dead kN/m² | Live kN/m² | Hangers | Use |
|---|---|---|---|---|---|---|---|
| Urban road bridge | 90 | 18 | 12 | 7.8 | 5.5 | 16 | Early sizing |
| River crossing | 140 | 28 | 15 | 8.9 | 6.5 | 22 | Concept comparison |
| Pedestrian tied arch | 55 | 11 | 5 | 4.2 | 4.0 | 12 | Preliminary check |
Why Tied Arch Bridge Checks Matter
A tied arch bridge carries deck load through a curved rib and a horizontal tie. The arch mainly works in compression. The tie resists the outward thrust that would otherwise push into the foundations. This makes the form useful where weak soil cannot take large horizontal reactions.
How This Tool Helps
This calculator gives a preliminary design picture. It combines span, rise, load, hanger count, material strength, and section data. It then estimates thrust, hanger tension, arch compression, tie stress, deck bending, and vertical deflection. The outputs are not a final bridge design. They are a fast screening guide for early planning.
Key Design Ideas
The parabolic arch estimate assumes a uniform vertical load over the span. Under that condition, the horizontal thrust equals the load times span squared, divided by eight times rise. A higher rise normally lowers thrust. A longer span or heavier deck increases it. Hanger forces depend on the tributary load and hanger angle. Steeper hangers usually reduce axial tension.
Reading The Results
Stress ratios compare calculated stress with entered allowable strength. A ratio below one suggests the selected area may be adequate for the simplified load case. A ratio above one signals that the section, material, rise, or loading should be revised. The deck bending result is based on the entered moment factor. Use a suitable value for the floor system concept.
Practical Limits
Real tied arch bridges need detailed checks. Engineers must review buckling, fatigue, wind, seismic action, connection design, load combinations, erection stages, temperature effects, and code rules. Arch ribs also need out of plane stability checks. Hangers need fatigue details and replacement planning.
Best Use
Use this page during concept design. Try several rise to span ratios. Compare hanger spacing. Adjust section areas and inertia. Save the results as CSV or PDF for review. Always send promising options to a qualified structural engineer before drawings, bidding, fabrication, or construction.
For better decisions, record each assumption beside every output. Small changes in live load, impact allowance, or rise can move the thrust quickly. Comparing several cases helps reveal safe trends before expensive modelling starts, and it makes discussions with reviewers, fabricators, and approval engineers much clearer later.
FAQs
1. What is a tied arch bridge?
It is a bridge where the arch carries compression and the deck tie resists horizontal thrust. This reduces outward force on the foundations.
2. Is this calculator suitable for final design?
No. It is for preliminary sizing and comparison. Final design must follow bridge codes, project specifications, and licensed engineering review.
3. Why does arch rise matter?
A larger rise usually reduces horizontal thrust. A smaller rise often increases tie force and arch demand for the same span and load.
4. What does tie utilization mean?
It compares calculated tie stress with the allowable tie stress. A value above one means the simplified tie check is not adequate.
5. How are hanger forces estimated?
The tool divides total vertical factored load among all hangers. It then adjusts the force using the entered hanger angle.
6. Why enter arch planes?
Many tied arch bridges use two arch ribs. The load is shared between planes, so each rib receives a portion of the total demand.
7. What is deck inertia used for?
Deck inertia is used in the elastic deflection estimate. A larger inertia normally reduces calculated vertical deflection.
8. What checks are missing?
This tool does not check fatigue, buckling, wind, seismic response, connections, construction stages, or code load combinations.