🌉 Bridge Engineering Quick Formulas
AASHTO LRFD 9th Ed + PTI + Cable-Stayed + Seismic + Substructure
Example: 500 ft segmental box girder
Elastic Shortening ≈ 8.1 ksi
Long-term (Creep+Shrinkage+Relaxation) ≈ 38 ksi
Total Loss ΔfₚT = 46.1 ksi
Force at end = 918 kips → Loss = 23.5%
Example: Prestressed I-girder, bv=12 in, dv=82 in
β ≈ 2.85 | θ ≈ 23.1°
Vc = 285 kips | Vs = 186 kips
ϕVn = 424 kips (ϕ=0.9)
Note: εₓ ≈ (Vu/ϕ - Vp)/(Es As + Ep Aps) for preliminary
Example: 140 ft Bulb-Tee, 54" deep
Camber at erection = 1.7 in
Final camber (after LT) ≈ -0.8 in (negative = sag)
Typical target: +0.5 to +1.0 in remaining
Rotation capacity = hrt / Lpad = 0.0188 rad → OK
Compressive stress ≤ 1.5 ksi → OK
Shear deformation limit: hrt ≥ 2 × Δshear
Example: 24" square PPC pile, 80 ft into medium clay
Qend = 360 kips | Qfriction = 720 kips
Qu = 1080 kips → Allowable (FS=3.0) = 360 kips
Approximate period T ≈ 1.48 sec
Response Modification Factor R = 5
Typical SDC: C or D for most US bridges
Strength I: Mu = 1.25×DC + 1.50×DW + 1.75×(LL+IM)
Mu = 11,650 kip-ft
Example: Spliced bulb-tee girder, 200 ft span
fₚₛ ≈ 258.4 ksi
ϕMn = 32,650 kip-ft (44,280 kN·m)
Example: Prestressed bulb-tee, S = 9.5 ft
DF (multiple lanes) = 0.785
Rule of thumb (S/12) = 0.792
Example: Main span stay, 900 ft horizontal projection
Effective modulus Eₑff = 24,820 ksi
Reduction due to sag = 11.4%
Example: One truck per lane, 120 ft stay spacing
Fatigue stress range Δσ ≈ 54 ksi → NOT OK (limit ≈ 24 ksi)
→ Need larger cable or closer spacing
| Bridge Type | Typical Span Range | Tendon/Cable Stress (Service) | Key Design Control |
|---|---|---|---|
| Pre-tensioned I-girder | 40–160 ft | 0.70–0.75 f_pu | Camber, transfer stress |
| Post-tensioned box | 150–600 ft | 0.70 f_pu jacking | Secondary moments, loss sequence |
| Spliced girder (PT) | 150–300 ft | 0.70 f_pu | Segment joint bursting |
| Extradosed | 300–800 ft | 0.60 f_pu | Fatigue + low tower stress |
| Classic cable-stayed | 600–3000+ ft | 0.45–0.55 f_pu | Fatigue, aero stability, construct. |
Note: These calculations are for preliminary design and estimation only. Always verify with detailed analysis, local codes, and qualified structural engineering judgment for actual construction.