AASHTO LRFD
Intermediate
Bridge & Framed Structures
Warren & Pratt Truss Bridge Analysis
Solve Method of Joints 2D nodal equilibrium under moving deck truck live loads and check Euler buckling.
Calculates all internal axial forces (tension vs compression) across a 6-bay steel truss bridge as live vehicular traffic traverses the lower deck chord. Verifies compression members against Euler critical column buckling.
Governing Physical Law & Equations
\sum \vec{F}_{node} = 0, \quad P_{cr} = \frac{\pi^2 E I}{(K L)^2}
Nodal static equilibrium and Euler column buckling threshold.
Law: Newton’s Static Equilibrium & Euler Column Buckling | Standard Reference: AASHTO LRFD Bridge Design Specifications / AISC 360-16 / Eurocode 1 (EN 1991-2)
Adjustable System Parameters
| Parameter |
Nominal Value |
Dynamic Range |
Physical Role |
| Bridge Span L (L) |
24 m |
12 to 36 m |
Total span length of the truss bridge structure |
| Truss Depth H (H) |
4.5 m |
3 to 8 m |
Vertical distance between top and bottom chords |
| Moving Truck Load (P_truck) |
80 kN |
20 to 200 kN |
Wheel load of passing heavy vehicle |
| Dead Load / Joint (w_d) |
15 kN |
5 to 40 kN |
Permanent deck self-weight per lower node |
Analytical Proof & Derivation
Planar pin-jointed truss equilibrium relies on static determinacy: b + r = 2j. At each node, the vector force balance ∑ F_x = 0 and ∑ F_y = 0 is formulated into a global equilibrium matrix [A] {F} = {P}. For compressive members of length L and radius of gyration r_g, Euler column theory establishes the elastic critical buckling capacity: P_cr = (π² E I) / (K L)², where effective length factor K = 1.0 for pinned chord/web joints.
Verification Benchmark
AASHTO LRFD benchmark: 6-bay Warren truss (span L = 24 m, height H = 4.5 m) with dead load w_d = 15 kN/joint and truck axle P = 80 kN. Nodal reactions and internal forces achieve perfect static balance (∑ F_y = 0.000 kN). Critical compression member verifies Euler buckling factor.
Field Engineering Insights
AASHTO LRFD specifies member slenderness limit K L / r ≤ 120 for main compression members and ≤ 140 for secondary bracing. Impact dynamic allowance (IM = 33%) is applied to vehicular axle live loads.