Enter bridge and member data
Formula used
Design multiplier: γd = load factor × (1 + impact ÷ 100)
Factored point load: Pd = P × γd
Factored distributed load: wd = w × γd
Support reactions: RA = Pd(L - a) ÷ L + wdL ÷ 2
Bending moment: M(x) = RAx - wdx² ÷ 2 - Pd(x - a)
Chord force: Fchord = Mmax ÷ h
Diagonal force: Fdiag = Vmax ÷ sinθ
Member stress: σ = F ÷ A
Allowable stress: σallow = yield strength ÷ required safety factor
Euler buckling: Pcr = π²EI ÷ (KL)², with I = Ar²
Deflection: δ ≈ Pab²a² ÷ (3EIL) + 5wL⁴ ÷ (384EI)
How to use this calculator
- Enter the bridge span, truss height, and panel count.
- Add a point load, a distributed load, or both.
- Set load factor and impact allowance for design demand.
- Enter chord, diagonal, and vertical member areas.
- Add material strength, modulus, radius values, and length factor.
- Press Calculate Stress to view results above the form.
- Check the governing utilization and revise member sizes if needed.
- Use CSV or PDF buttons to save the result.
Example data table
| Input | Example value | Meaning |
|---|---|---|
| Span | 30 m | Clear support distance |
| Height | 4 m | Top to bottom chord lever arm |
| Point load | 120 kN | Vehicle or concentrated design load |
| Distributed load | 12 kN/m | Deck, railing, and live load allowance |
| Chord area | 3,500 mm² | Area for top and bottom chords |
| Yield strength | 250 MPa | Material yield limit |
| Modulus | 200,000 MPa | Elastic stiffness of steel |
| Deflection ratio | 360 | Span divided by allowed deflection |
Why truss stress matters
A truss bridge carries loads through connected triangular members. Each member mainly resists axial tension or compression. That behavior keeps the structure efficient. It also makes stress checks very important. A small area can create high stress. A long compression member can buckle before yielding. This calculator helps compare both limits during early design.
Load path and reactions
The tool treats the bridge as a simply supported span. It accepts a point load and a distributed load together. The point load can sit anywhere along the span. The distributed load covers the full bridge length. A load factor and impact allowance raise service loads. Those adjusted loads estimate a design demand.
Member force estimate
The maximum bending moment is converted into chord force. The truss height acts like the lever arm between top and bottom chords. A deeper truss usually lowers chord force. Shear is converted into diagonal force using the panel angle. Vertical force is estimated from the maximum support shear. These values give practical starting stresses.
Stress and safety margin
Stress equals axial force divided by member area. The calculator reports stress for chord, diagonal, and vertical members. It then compares each stress with yield strength. The required factor of safety sets an allowable stress. A utilization value above one means the section needs review. Increasing area lowers stress and improves margin.
Buckling review
Compression members need another check. Slender members may buckle at loads below yield. Euler buckling depends on elastic modulus, radius of gyration, effective length factor, and unsupported length. The calculator estimates critical force for chords, diagonals, and verticals. A high slenderness ratio signals sensitivity to alignment and bracing.
Deflection estimate
Bridge stiffness affects comfort and serviceability. The calculator provides an approximate midspan deflection. It combines point load deflection with distributed load deflection. The effective inertia represents the overall truss system. This value is only an estimate. Detailed bridge analysis should use joint coordinates, member stiffness, and support conditions.
Reading the results
Start with the governing stress row. Then review buckling utilization. Next compare deflection with your project limit. The result badge gives a quick status. Green means the entered values satisfy the chosen checks. Amber means the design is close. Red means one or more limits are exceeded. Always verify final bridge designs professionally.
Design notes
Use realistic units and consistent assumptions. Truss members may not share load equally. Connections can add eccentricity. Deck stiffness may distribute wheel loads between panels. Wind, braking, temperature, fatigue, and vibration may govern some bridges. Corrosion loss can reduce effective area over time. For better accuracy, build a joint model and check every load combination. Treat this page as a planning aid, not a final design certificate. Use surveyed dimensions, verified material data, and local bridge rules before construction. Keep load records for review. Revised traffic data can change demands substantially after inspection again.
FAQs
What does this calculator estimate?
It estimates truss bridge reactions, axial member forces, stress, safety factor, buckling capacity, and approximate deflection from entered loads and geometry.
Is this a final bridge design tool?
No. It is an early design and study aid. Final bridge design needs complete analysis, codes, load combinations, connection checks, and professional review.
Why does truss height affect stress?
Truss height creates the lever arm between chords. A larger height usually reduces chord force because the same moment is resisted over a greater depth.
What is the point load position?
It is the distance from the left support to the concentrated load. Changing it changes reactions, moment, shear, and member stress.
What area should I enter for members?
Enter the net axial area for each member group. Use reduced area when holes, corrosion, or section loss affects strength.
Why is buckling included?
Compression members can fail by instability before reaching yield stress. Buckling checks help reveal risks in long and slender truss members.
What is radius of gyration?
Radius of gyration describes how area is distributed around an axis. Larger values improve buckling resistance for the same area.
What does utilization mean?
Utilization is demand divided by capacity. A value below one usually means the check passes under the entered assumptions.
Can I include both point and distributed loads?
Yes. The calculator combines both loads, applies the design multiplier, and computes reactions and maximum moment from the combined case.
How accurate is the deflection result?
It is approximate because the truss is simplified as a beam. Detailed deflection needs member stiffness, joints, bracing, and support modeling.
Why can the result show review required?
The result appears when stress, buckling, or deflection utilization exceeds the selected limit. Increase member size or reduce loads.