Howe vs Pratt Truss Design: Structural Engineering Lecture

This section explores advanced truss designs for improved efficiency. The Baltimore truss strengthens the Pratt design by adding more support to long members. The Parker truss replaces the straight top with a polygon forming a round arch, concentrating material where bending moments are highest (center of bridge). The bowstring truss uses a curved arch design, the most efficient use of materials, but is harder to build. The lenticular truss has a lens shape with the arch on top (for vehicles underneath). The K truss avoids long diagonals by extending the V-shape to the top. The Whipple truss uses cables for additional strengthening.

This lecture introduces five famous truss types used in structural analysis: (1) Warren Truss - formed by connecting equilateral triangles without vertical members; (2) Warren Truss with Vertical Members - adds vertical supports to the basic Warren design; (3) Quadrangular Warren Truss - incorporates vertical members and zigzag connections; (4) Pratt Truss - features a rectangular configuration with lateral numbering; (5) Baltimore Truss - a Pratt Truss variant with additional diagonal members connecting ends to midpoints of adjacent sides.

Truss bridges use triangular geometry because triangles are the strongest shape—they evenly distribute weight and maintain their proportions under force, unlike squares which collapse into parallelograms. A truss bridge consists of abutments, bearings, chords (top and bottom), verticals, diagonals, and a deck slab. Single-span truss bridges function like simply supported beams, creating compression in top chords and tension in bottom chords. Common truss types include Pratt (downward-sloping diagonals), Howe (upward-sloping diagonals), Warren (only diagonals with equilateral triangles), Brown (combination of Pratt and Howe), K-Truss (K-shaped panels), and Bowstring (arch top chord). Truss bridges are classified by roadbed position: deck truss (roadbed on top), through truss (roadbed in middle/bottom with connected sides), and pony truss (roadbed in middle/bottom with unconnected sides). For analysis, truss members are assumed to have frictionless pinned connections, carry only axial forces (tension or compression), and are analyzed using the method of joints or method of sections.

This section explains truss design principles and common applications. Truss members must be connected by pins with no member passing through joints. Load distribution requires all members to be part of the load path. Bridge trusses include strangers (longitudinal members) and flanges/wings (transverse members). Common truss types include roof trusses, bridge trusses (Warren, Pratt, Howe, Baltimore, K-truss), and stadium trusses. Only structural members carrying loads are considered in analysis.

Trusses are structural frameworks composed of triangles that distribute loads efficiently; different truss types (Howe, Pratt, Warren, Town lattice, K-truss, Fink, King post, Queen post, Scissor, Hammer beam, Vierendeel) are distinguished by their member arrangements, force distributions (tension/compression), and structural efficiency, with some named trusses actually being frame systems that carry bending rather than pure axial forces.

Finite Element Analysis (FEA) is a computational method that idealizes real-world structures into discrete nodes and elements (line elements for frames, plate/shell elements for slabs/walls, and solid elements for 3D volumes) to predict structural behavior under various loads. The FEA workflow involves geometry creation, material and section property assignment, boundary condition definition, load application, analysis execution, and result interpretation including reactions, displacements, forces, and stresses. This webinar demonstrates practical applications using midas Gen software, covering 2D truss analysis (using truss elements with axial force output), 2D/3D frame analysis (using beam elements with six degrees of freedom), buckling analysis (for stability verification), and steel section optimization (automated design checks and economical section selection).

This tutorial demonstrates how to analyze and design a truss using StaadPro software, covering key steps including creating a truss model with appropriate geometry (length, height, bay divisions), assigning steel angle sections to members, applying pin supports at both ends, and critically, applying loads only at joints (not between members) as trusses are designed for joint loading. The design process involves iterative optimization where members that fail design requirements are replaced with alternative sections (such as channel sections or larger angle sections) until all members pass the design criteria, with the yield stress of steel (e.g., 415 N/mm²) serving as a key design parameter.

This video demonstrates the complete process of developing and analyzing a truss structure, including geometry creation with specific dimensions (7m span, 2.25m height), member grouping (top chord, bottom chord, vertical webs, diagonal webs), section property assignment (2x2x3/16 inch angle sections), support configuration (pin and roller supports), load case creation (dead, live, and wind loads), and structural analysis to verify member capacity and displacement limits (maximum displacement of 1.203mm compared to allowable 29mm).

Commercial CAD software includes AutoCAD, Inventor, Creo, SolidWorks, SpaceClaim, MicroStation, Bentley, and TurboCAD. FEA solvers include Abaqus, ANSYS, NASTRAN, RADIOSS, LS-DYNA, Moldflow, and COMSOL Multiphysics. Free options include CalculiX, ANSYS Student version (32,000 node limit), VisualFEA Educational version, and FreeCAD. Practical applications demonstrate FEA's value: thermomechanical coupled analysis of shell-and-tube heat exchangers predicts thermal stresses at tube sheet junctions; axisymmetric pressure vessel analysis reduces computational effort while capturing critical stress concentrations; vibration analysis identifies natural frequencies to avoid resonance; topology optimization achieves significant weight reduction (57%) while improving stiffness and reducing costs.

This video demonstrates how to analyze a truss structure using Ftool software, including modeling the truss geometry with 7 nodes and 8 loads, defining support conditions (fixed articulated support at point A with reactions in both x and y directions, and roller support at point L with reaction only in y direction), applying material properties (steel with 5cm diameter circular section), and calculating forces in specific elements (FH, GH, and GL) where negative values indicate compression and positive values indicate tension.

Beyond standard HL-93 loading, bridges require special considerations: oversized vehicles need permits generating state revenue; military routes require runway-capable design; coal transportation routes (CRTS) need heavier ratings. Average bridge age of 40-45 years leads to load postings on aging infrastructure. Fatigue from ~136 million cycles over 75 years causes failure at stresses far below yield (threshold ~12 ksi vs. steel yield ~50 ksi). Two approaches: finite life (specific cycles) and infinite life (below threshold). Infinite life is more conservative and common for high-traffic bridges. Deflection limit states ensure serviceability. Design balances conservatism against economy, particularly for low-volume roads.

Bridges must be designed to handle dynamic loads, which are loads that change over time or with movement. Dynamic loads can create additional stresses on bridge structures compared to static loads. Proper bridge design must account for these dynamic effects to ensure safety under all operating conditions.

Bridges transfer forces through tension (pulling), compression (pushing), shear (ripping apart), torsion (twisting), and bending. Buckling combines bending and compression, dependent on unbraced length—longer unbraced sections dramatically reduce capacity. Concrete excels in compression but has negligible tensile strength; steel performs well in both tension and compression; cables only resist tension. Bridge loads include dead load (structure weight) and live load (vehicles, pedestrians). Impact load requires a 33% increase due to bouncing. Safety factors use 1.25×dead + 1.75×live load, reflecting greater uncertainty in predicting future live loads. During construction, beams must support wet concrete before curing, often controlling design. Deflection criteria vary: vehicular bridges use L/800 (150 ft span allows 2.25"), pedestrian bridges use L/1000 (150 ft allows 0.75").

Bridge design involves two primary states: resistance (calculating reinforcement for interior and edge strips) and serviceability (controlling bond through steel distribution and calculating camber). Fatigue design focuses on controlling crack width from repeated loading, with critical attention to tensioned steel stress rather than compression fiber. Fatigue load consists only of the design truck with 1452 kg axle separation and 9-meter spacing, with a dynamic load increment applied. Only one lane is considered loaded regardless of total lanes. Fatigue investigation is exempt for deck slabs in bridges with 6 spans or less. Section properties must be based on cracked sections when combined permanent loads plus 1.75 times fatigue load generate tensile stress exceeding 80% of √f'c. Fatigue analysis requires simultaneous consideration of permanent loads and fatigue loads. Reinforced concrete members must satisfy that applied stress range ≤ resistance stress range (1687 - 0.33 × f'm). The stress range is determined by calculating maximum and minimum tensile stresses in the tensioned steel. Verification must be performed for all sections, not just the critical section.

Bridge design uses dynamic live loads rather than static loads. The live load consists of three components: the design truck, design tandem, and line of loads defined by the Colombian Bridge Code 2014. These loads simulate vehicular traffic behavior. Unlike static loads, dynamic loads account for vehicle movement and impact. The design truck and tandem were developed through extensive analysis by engineer Correal from the University of the Andes, considering actual trucks and environmental factors like wind. The design truck has three axles (40 kN, 160 kN, 160 kN) with 4.3m spacing between front and middle axles, and variable 4.3-9m spacing between middle and rear axles. The design tandem has two axles of 125 kN each, separated by 1.2m.