Evaluation of Critical Live Load Effects in the Bridge Superstructure Using Girder-line Analysis

Evaluation of Critical Live Load Effects in the Bridge Superstructure Using Girder-line Analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Evaluation of Critical Live Load Effects in the Bridge Superstructure Using Girder-line Analysis Fahim Nasir, Muhammad umer This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9444264/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Highway bridges form the skeletal backbone of any national transportation network, yet in Pakistan they remain among the most critically under evaluated infrastructure assets. The country's formal bridge design standard, the Pakistan Code of Practice for Highway Bridges (PCPHB 1967), has not been revised since its original publication and continues to rely on British loading provisions introduced to the Indian subcontinent in 1935. Meanwhile, commercial truck traffic on Pakistani highways has grown substantially heavier and more complex in axle configuration, creating a widening gap between the loads bridges were designed to carry and the loads they are actually asked to sustain. This study was undertaken to address that gap directly. The primary aim of this research is to evaluate and compare the critical live load effects specifically absolute maximum shear force and bending moment induced in the superstructures of simply supported highway bridges spanning between 10 and 40 metres, a range that encompasses the overwhelming majority of bridges currently in service on Pakistan's National Highway N-5 corridor and, by extension, the broader national network. To achieve this, three parallel objectives were pursued. First, a systematic field survey was conducted along National Highway N-5 from Rawalpindi to Hassan Abdal, documenting the geometric, structural, and condition-related characteristics of fourteen bridges representative of the existing stock. Second, a MATLAB-based Girder-Line Analysis program was developed to compute shear force and bending moment envelopes for simply supported beams subjected to moving vehicular loads across span lengths of 10 to 40 metres in increments of 2.5 metres. Third, 3 distinct live load models were applied within this analytical framework and their critical load effects compared: the NHA legal load limits governing actual truck traffic on Pakistani roads, the AASHTO HL-93 notional load model increasingly adopted by Pakistani engineers, and the PCPHB 1967 standard including its Class AA military vehicle loading. All results were independently verified through hand calculations and SAP 2000 modelling. The analysis reveals that the PCPHB 1967 Class AA loading a 70-ton military tracked vehicle governs both shear and moment demands across the entire span range studied, exceeding all other load models by a margin that widens significantly with increasing span length. Among legally permitted civilian vehicles, the NHA 6-axle configuration produces the highest shear demands. The AASHTO HL-93 model, when assessed on a service-load basis without load factors, falls close to but generally below the NHA 6-axle envelope, a result explained by the conservative load and resistance factors that the LRFD design framework subsequently applies. Critically, the study demonstrates that gross vehicle weight is not the primary determinant of bridge load effects. It is the axle load magnitude, axle spacing geometry, and position of the heaviest axle relative to the span that drive critical shear and moment demands a finding with direct and immediate implications for load enforcement policy on Pakistan's highway network. Civil Engineering Mechanical Engineering bridge superstructure girder-line analysis AASHTO HL-93 PCPHB 1967 NHA legal loads live load effects bending moment shear force Pakistan highway bridges Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction One of the most essential components of a modern transportation system is bridges. More than their practical purpose of crossing rivers, valleys, and intersections, they are lifelines: a bridge failure can cut off a whole transportation route. The 2005 Kashmir earthquake is just one example of how history has demonstrated this fact: the earthquake badly damaged a major bridge near Balakot and made rescue and relief efforts into the Pakistani northern valleys severely hampered rescue and relief access. The national highway system in Pakistan has a high number of short and medium span bridges with majority of them ranging between 10 and 40 meters. These are almost all of the slab-girder type, either reinforced concrete T-beam (RCC-T) or restressed concrete I-girder (PS-I), and are simply supported, statically determinate structures. These properties allow them to be analyzed rationally but computationally efficiently by a one-dimensional simplification of the three-dimensional bridge system called Girder-Line Analysis, which is explicitly supported by the AASHTO LRFD Bridge Design Specifications. Although this infrastructure is under pressure due to the increasing commercial traffic, the formal bridge design standard in Pakistan, the Pakistan Code of Practice on Highway Bridges (PCPHB 1967) has not been updated since its publication. It is based on British loading provisions that were introduced to the Indian subcontinent in 1935. In the meantime, the American AASHTO LRFD framework has become more popular in the engineering practice in Pakistan. This variation brings about a practical necessity to comprehend the comparisons of these various load models, and how they correlate with the real truckloads that are allowed on Pakistani roads by the National Highway Authority (NHA). This paper will directly respond to that need. It combines field measurements, published load specifications, and computational analysis using MATLAB to assess and compare critical live load effects among three different load models and a span length range that is representative of the stock of highway bridges in Pakistan. 1.1 Objectives To conduct a field survey of highway bridges along N-5 and document their structural and geometric characteristics. To develop a MATLAB-based Girder-Line Analysis program capable of computing shear force and bending moment envelopes for moving vehicular loads. To compare critical live load effects (absolute maximum shear and moment) produced by the NHA legal loads, AASHTO HL-93, and PCPHB 1967 models across span lengths of 10 to 40 meters. To draw practical conclusions useful to bridge designers working on Pakistan’s highway network. 2. Bridge Taxonomy and Primary Components It is convenient to define some standard terms to describe the types of bridges and their parts before considering loading, as the vocabulary determines the way loads are imposed and the way the effects of loads are followed through a structure. 2.1 Structural Configuration The most widespread type of bridges found on the national highways in Pakistan is the beam-girder type. In Girder Bridge, the superstructure is made of longitudinal beams that the girders are spanning between the supports and the concrete deck slab is spanning transversely between them. Traffic load is transferred through the deck slab to the girders, through bearings to the piers or abutments and finally to the foundation soil. This is a straightforward and clear load path and girder bridges are the simplest to analyze and the least expensive to build in the 10-to-40-meter span range. Other structural configurations arch bridges (which carry load through compression along a curved profile), suspension bridges (which suspend the deck from cables hanging between towers), cable-stayed bridges (where cables run directly from towers to deck), and cantilever bridges (which balance loads about intermediate supports) are encountered in Pakistan but typically only for special crossings or large river spans. This is not the focus of this study. 2.2 Bridge Components A highway bridge is best understood as an assembly of distinct subsystems, each carrying a defined structural role The surface that carries the traffic is the bridge deck. It shares the wheel loads with the girders beneath and, when compositely acting with the girders, adds greatly to the flexural resistance of the cross-section. The most common type of deck is cast-in-place reinforced concrete. The major longitudinal load-carrying members of the superstructure are girders. The most common ones in Pakistan are RCC-T beams and prestressed concrete I-girders (PS-I). A normal span has four to ten girders, with a spacing of approximately equal distances across the deck width. Bearings are located at the junction of the superstructure and the substructure, which carry the vertical loads and allow the movements caused by thermal expansion, creep, and deflection of the live loads. The most common in modern Pakistani practice are elastomeric bearings rubber pads reinforced with steel plates. The intermediate vertical supports of multi-span bridges are known as piers. In Pakistan, circular and solid square piers are mostly solid. Abutments are used at the ends of the bridge, which also hold the earthwork of the approach embankments. All the loads are transferred to the underlying stratum by the foundation system; both pile foundations and strip footings are common. 3. Live Load Models There are three different live load structures applicable to the design and evaluation of Pakistani highway bridges. The rationale and structure of each is vital to the interpretation of the comparative results of this study. 3.1 NHA Legal Load Limits The National Highway Authority (NHA) stipulates the maximum gross vehicle weight and the maximum individual axle weight that can be legally used on the national highways in Pakistan. They define the upper bound of load the network is legally required to sustain. Table 1 is a summary of the allowable gross loads of truck configurations between two-axle (the popular Bedford and Hino/Nissan models) and six-axle articulated combinations. The axle load limits are established at 5.5 tons on front (steer) axles, 12 tons on single rear axles, 22 tons on tandem axle groups, and 32 tons on tridem axle groups. Table 1 NHA Legal Load Limits for Truck Configurations Operating on Pakistani Highways Axles Truck Configuration Description Max Gross Load(tons) 2 1 + 1 Bedford / Hino / Nissan (2-axle) 17.5 3 1 + Tandem 3-axle truck 27.5–29.5 4 1 + 1 + Tandem / 1 + Tandem 4-axle truck or tractor-trailer 39.5–41.5 5 1 + 1 + Tridem / 1 + Tandem + Tandem 5-axle articulated combination 48.5–51.5 6 1 + Tandem + Tridem 6-axle articulated combination 58.5–61.5 Source: National Highway Authority, Pakistan. Axle load sub-limits: front axle ≤ 5.5 t; single rear ≤ 12 t; tandem ≤ 22 t; tridem ≤ 32 t. The field survey conducted for this study measured the axle widths and axle spacing’s of approximately 60 trucks. Table 2 presents representative values by truck type information that directly informed the axle geometry used in the MATLAB analysis. Table 2 Typical Axle Width and Axle Spacing (metres) for Pakistani Truck Configurations Truck Type Axle Config. Axle Width (m) S 12 (m) S 23 (m) S 34 (m) S 45 (m) S 56 (m) 2-Axle 1 + 1 2.18 4.60 — — — — 3-Axle 1 + Tandem 2.32 6.10 1.37 — — — 4-Axle 1 + 1+Tandem 2.55 3.38 6.84 1.34 — — 5-Axle (a) 1 + 1+Tridem 2.50 3.28 5.13 1.36 1.36 — 5-Axle (b) 1 + Tandem+Tandem 2.45 4.39 1.37 4.57 1.34 — 6-Axle 1 + Tandem+Tridem 2.49 3.52 1.23 5.83 1.37 1.28 Based on field measurements of approximately 60 trucks along N-5. S i ⱼ denotes spacing between consecutive axles i and j. 3.2 PCPHB 1967 Live Loading The Code of Practice of Highway Bridges in Pakistan (PCPHB 1967) defines three classes of live loads: Class A (standard loading train), Class B (a lighter version of Class A to be used on temporary or lightly used bridges), and Class AA (a 70-ton military tracked vehicle). Class A loading is a convoy of eight axles a driving unit and two trailers with defined axle loads and spacing. Class B loading is 60 percent of Class A, and the same axle geometry. Class AA loading, based on military classification criteria, is a 70-ton tracked vehicle 3.6 metres wide and approximately 7 metres long between centers of the tracks. The shortest distance between two successive Class AA vehicles is 91.4 metres nose to tail. This loading is required on bridges on national and state highways and in industrial areas, and bridges intended to be loaded in this manner must also be inspected under Class A loading, as the latter may sometimes be controlling to some structural designs. Table 3 provides the axle load data and ground contact dimensions specified under PCPHB 1967. Table 3 PCPHB 1967 Axle Loads and Ground Contact Dimensions Loading Class Axle Load(tons) Contact Width C(mm) Contact Width W(mm) Class A 11.34 250 500 Class A 6.80 200 375 Class A 2.72 150 200 Class B 5.67 200 375 Class B 3.40 150 300 Class B 1.36 125 175 Source: PCPHB 1967. C = contact dimension in direction of traffic; W = contact dimension transverse to traffic. 3.3 AASHTO HL-93 Live Loading In 1993, the AASHTO LRFD HL-93 loading model was introduced to generate extreme force effects that were roughly equal to those produced by the population of heavy trucks actually using the American highway network during a 75-year design life. It is composed of three interacting components: The Design Truck (HS20-44) has three axles: a 35-kN (4-ton) front steer axle, a 145-kN (16-ton) drive axle, and a 145-kN (16-ton) trailer axle. The distance between the two axes at the back is adjustable between 4.3 m and 9 m, and the analysis chooses the distance that gives the maximum effect of the force in question. The Design Tandem is made up of two 110-kN (12-ton) axles with a distance of 1.2 m. In short span bridges, this arrangement normally dominates the three-axle design truck. Design Lane Load is a load of 9.3 kN/m that is uniformly distributed over a 3.0-metre width. In longer spans, the lane load is the most significant contributor. HL-93 design load is the greater of: (a) design truck plus lane load; or (b) design tandem plus lane load. In continuous structures, a special two-truck combination controls negative moment at interior piers, but this is not applicable to the simply supported spans considered here. Table 4 AASHTO HL-93 Load Model Summary Component Configuration Load Intensity Governs(Typical) Design Truck (HS20-44) 3-axle: 4 t / 16 t / 16 t; rear axle spacing 4.3–9.0 m 325 kN total (3 axles) Medium spans Design Tandem 2-axle: 12 t each, spaced 1.2 m 220 kN total (2 axles) Short spans (≤ 12 m) Design Lane UDL over 3.0 m width 9.3 kN/m Long spans HL-93 (combined) Truck + Lane OR Tandem + Lane (whichever governs) Per above All spans Source: AASHTO LRFD Bridge Design Specifications (4th ed. and later). Note: axle width 1.8 m for all vehicular components. 4. Field Survey: Bridges along N-5 A systematic field survey was conducted along a stretch of National Highway N-5, following the Grand Trunk Road, to establish the physical reality of the bridge infrastructure in Pakistan, between Rawalpindi and Hassan Abdal. A total of fourteen bridges were surveyed. The GPS coordinates of each structure were noted and then overlaid in Google Earth to give a spatial map of the survey corridor. 4.1 General Observations All bridges that were met in the survey were of the slab-girder type. The typology used in the analytical stage of the study was verified by the girder cross-sections being either RCC-T beam or PS-I (prestressed concrete I-beam). The bridges had four to ten girders per span, and the span lengths were mostly within the 10–30 metre range. Substructures were solid circular or solid square reinforced concrete piers. The state of the bridges was quite different. Some of them had concrete spalling and shear cracking in the girder webs, which were in line with poor maintenance. Others had been retrofitted by injecting grout to close cracks. Expansion joints in several bridges had become so worn that they were open and unguarded with a gap of up to 180 mm (7 inches) wide. One bridge had been widened by adding new girders alongside the original ones to accommodate an additional traffic lane an improvised intervention that raises legitimate concerns about load redistribution and long-term structural compatibility. 4.2 Representative Bridge Data Here two bridges are pointed out to show the variety of structures that are encountered. Their main features are given in Table 5 and Table 6 . Table 5 Features of Taxila Bridge (N-5, near Taxila) Parameter Value Location Taxila, Khyber Pakhtunkhwa Number of Spans 3 Span Length 23.47 m (each span) Girder Type PS-I (Prestressed Concrete I-beam) Number of Girders per Span 7 (5 original + 2 new widening) Number of Piers 8 (4 original + 4 new) Pier Type Solid square reinforced concrete Table 6 Features of Kashmir Highway Bridge (Rawalpindi) Parameter Value Location Rawalpindi, Punjab Number of Spans 4 Span Length 16.408 m (exterior) / 22.2 m (interior) Girder Type PS-I (Prestressed Concrete I-beam) Number of Girders per Span 7 Number of Piers 7 Pier Type Solid circular reinforced concrete 5. Analytical Methodology: Girder-Line Analysis 5.1 Theoretical Basis The AASHTO LRFD standard allows a three-dimensional bridge superstructure to be reduced to a single beam the “girder line” to compute the effects of live loads forces. This simplification is physically reasonable when dealing with simply supported, right-angled bridges where the distribution of loads to individual girders can be addressed independently by calculating distribution factors. In the current analysis, the girder-line it is the subject of interest: i.e. finding out the maximum shear and moment that the bridge system has to support, and then allocating it to individual girders. The concept of influence line is the focus of this analysis. An influence line for a chosen response quantity say, midspan bending moment or end shear plots the value of that quantity as a unit load traverses the span from one support to the other. That is plotted by the value of that response quantity as a unit load moves across the span between the two ends. When the influence line has been determined, the maximum response of any arbitrary vehicle loading is determined by locating the vehicle in such a way that the axle forces of the vehicle multiply the largest positive ordinates of the influence line. In the case of a simply supported beam, this location is easy to determine: the vehicle moves systematic across the span, and the shear and moment at each point are calculated. 5.2 MATLAB Program This process was automated in a special MATLAB program to run over the entire span length (10 to 40 metres, in 2.5-metre steps) and all three-load models. The main computational procedures were: Model the girder line as a simply supported beam with the given span. Introduce each vehicle load as a collection of moving point loads (up to eight axles) with given axle weights and spacing’s, and a uniformly distributed lane load where necessary. Move the vehicle over the span in 100 mm steps, calculating shear force and bending moment at each beam section at each truck position. Build the shear and moment envelopes i.e., the maximum and minimum values at each section over all vehicle positions. Take the absolute maximum shear and the absolute maximum positive bending moment of the envelope of that span. Repeat with all span lengths to produce span-effect curves. In the case of the AASHTO design truck, the variable rear axle spacing (4.3 to 9.0 m) was processed by scanning through all the possible spacing’s and keeping the controlling value. Hand calculations and SAP 2000 models were used to independently verify the results; there was a high level of agreement. 5.3 Key Programme Features and Limitations The Programme can produce envelopes of both shear and bending moment of any combination of up to eight moving point loads, and uniformly distributed loads. It is able to find the critical truck position of each span. Output graphs are automatically stored in PDF format to report. The program has a number of intentional constraints. It only works on simply supported beams and does not consider continuous spans, skew, or curvature. It performs a service-load analysis only load factors and resistance factors of the LRFD framework are not applied. It does not consider transverse load distribution (girder distribution factors) or the width of the design lane. These restrictions were deemed suitable to the comparative nature of the study; the aim is to compare relative critical load effects between models, not to conduct a complete design. 6. Results and Discussion 6.1 AASHTO HL-93: Design Truck vs. Design Tandem In the AASHTO HL-93 model, there are two sub-models of vehicles: the three-axle design truck and the two-axle design tandem. They are both added to the lane load, and the extreme combination Prevails. Figures 2 through 5 present the complete set of shear and moment envelopes for all load models. Figure 2 shows the AASHTO shear comparison between design truck and design tandem combinations. In the case of shear force, the design truck and the lane load give rise to critical values in the entire range of spans examined (10 to 40 metres). The design tandem combined with the lane load consistently produces lower shear demands than the design truck combination. The difference between the two curves increases with the span. In the case of bending moment, the image is more subtle. The design tandem plus lane load is the controlling combination in spans up to about 12 metres. Beyond 12 metres, the design truck plus lane load takes over as the critical case. This shift is indicative of the fact that the closely spaced tandem axles are extremely efficient at loading the short-span influence line, whereas the greater individual axle weights of the truck dominate on longer spans where the influence line ordinates are greater and more dispersed. In the design truck analysis itself, the critical moment of spans longer than the total truck length is determined by the rear axle spacing of 4.3 metres, and the longer spacing of 9.0 metres is more critical in short spans where it is beneficial to have multiple heavy axles on the span at the same time. 6.2 PCPHB 1967: Class A, Class B, and Class AA The Class AA loading (70-ton military tank) controls both the shear force and bending moment throughout the entire span range of 10 to 40 metres under the PCPHB 1967 framework. The Class A standard truck train always produces greater values than Class B (as would be the case, because Class B is 60% of Class A), but neither of them comes anywhere near the values generated by the concentrated, heavy tracked vehicle of Class AA. The Class AA shear envelope is very flat compared to Class A, indicating that a tracked vehicle loads its weight on a finite contact area, not at discrete axle points. The moment envelope of Class AA increases rapidly with the span length and by 30 metres; it exceeds all other models by a substantial and widening margin 6.3 Comparative Analysis: All Load Models First, the PCPHB Class AA loading has the greatest shear and moment demands of any model at all span lengths. This is in line with the fact that Class AA is a specialized and very heavy military vehicle that has nothing to do with the civilian truck traffic that the NHA legal limits govern. Second, the 6-axle (1 + Tandem+Tridem, gross weight up to 58.561.5 tons) is the NHA legal vehicle with the highest shear requirements. It has a widely spaced axle arrangement, which implies that it carries heavy loads at numerous points across the span at the same time. Third, the AASHTO HL-93 curve, evaluated on a service-load basis (no load factors applied), is lower or close to the NHA 6-axle curve of shear, and near the cluster of heavier NHA configurations of moment. This is an important result: it implies that the AASHTO load model, which was adjusted to American truck traffic, does not significantly overestimate the demand of the heaviest legal Pakistani trucks. The margins which the design framework of AASHTO at the time imposes the impact factor (dynamic load allowance) of 33% and the load factor of 1.75 on live load in the Strength I limit state, and the implicit amplification of dead-load, cause the factored design demands to be far above the service-load NHA limits, making the design safe even when the limits are exceeded in practice. Fourth, and, probably, most practical, the gross vehicle weight of the truck is not the decisive factor. The experiment shows that the critical shear and moment requirements depend on the magnitude of the axle loads and the geometry of the axle spacing. A lighter truck with a concentrated axle configuration than a heavier truck with well-distributed weight can cause the local load effects. This has direct consequences on enforcement: it is not enough to control gross weight, but axle load limits should be enforced. 6.4 Summary of Key Numerical Benchmarks Table 7 provides indicative values of absolute maximum shear and moment at three representative span lengths under each governing load model. These values are drawn directly from the MATLAB analysis envelopes and reflect service-load conditions without load factors. Table 7 Indicative Critical Live Load Effects at Selected Span Lengths (Service Load, No Load Factors) Load Model Span 10 m Shear(kN) Span 10m Moment (kNm) Span 25m Shear(kN) Span 25m Moment (kNm) Span 40m Shear(kN) AASHTO HL-93 ~ 290 ~ 590 ~ 390 ~ 2 400 ~ 490 Load Model Span 10 m Shear(kN) Span 10m Moment (kNm) Span 25m Shear(kN) Span 25m Moment (kNm) Span 40m Shear(kN) NHA 6-Axle (governing) ~ 560 ~ 870 ~ 430 ~ 2 700 ~ 520 PCPHB Class AA (governing) ~ 560 ~ 1 350 ~ 620 ~ 3 750 ~ 660 NHA 2-Axle (min.) ~ 145 ~ 300 ~ 175 ~ 800 ~ 165 Values are approximate, extracted from the MATLAB envelope plots. Moment figures for 40 m spans omitted to maintain table width; Moment values for 40 m spans are not listed here but are visible in Fig. 7. 7. Conclusions This paper has consolidated field survey data, three different live load models and a custom-written MATLAB Girder-Line Analysis software to assess the important live load effects in Pakistani highway bridge superstructures between 10 and 40 metres. The main findings are as follows. 7.1 Load Model Comparison The PCPHB 1967 Class AA loading (70-ton military tracked vehicle) has the greatest shear and moment demands of any model in the group, at all span lengths. Check designers using the PCPHB code must not limit their attention to Class A alone— Class AA governs throughout the span range studied and must always. Class A itself rules over Class B all the way, as it should. When evaluated at service level (no load factors), the AASHTO HL-93 model yields demands that are broadly similar to, but tend to be somewhat lower than, the NHA 6-axle legal load configuration in shear, and similar to the heavier NHA configurations in moment. The seeming sufficiency of the current bridges to legal truckloads, even with the closeness of the HL-93 curve, is attributed to the large safety factors that the LRFD method introduces in terms of load and resistance, dynamic load allowance, and dead load amplification. 7.2 Design-Relevant Findings The AASHTO design tandem to a span of about 12 metres governs the HL-93 moment; the design truck governs beyond that. In the case of shear, the design truck combination prevails. The implicit design of bridges on Pakistani national highways is not despite the AASHTO framework but because of it: the load factors and the conservative nature of the HL-93 notional amplify service-load demands to super-legal levels for the purpose of design. 7.3 Critical Insight: Axle Load Governs, Not Gross Weight The most practical conclusion of this research, perhaps, is that the gross vehicle weight of a truck is not the most important factor in determining the critical shear or moment demand of a simply supported bridge girder. The important factors are the magnitude of the axle load, the geometry of the axle spacing, and the location of the heaviest axle in relation to the span. A truck with many, closely spaced axles can be less harmful, per ton of gross weight, than a truck with fewer, more heavily loaded axles. Enforcement regimes that emphasize gross vehicle weight but do not strictly regulate the axle loads offer partial protection to bridge infrastructure. 7.4 Practical Utility The span-effect curves produced in this research offer an easy-to-use reference to bridge engineers in the highway network of Pakistan. With a span length, a designer can simply read the critical service-load shear and moment of each loading model, without re-running the analysis. This is especially useful during the pre-design or feasibility stage, and in quick evaluation of existing bridges. 7.5 Recommendations The PCPHB 1967 code is overdue for revision. The loading models it prescribes no longer reflect either the current vehicle fleet or contemporary bridge engineering practice. Pakistan’s highway bridge stock shows signs of inadequate maintenance. A systematic bridge inspection Programme with standardized condition rating should be established nationally. Axle load enforcement, rather than gross weight enforcement alone, should be prioritized by NHA to protect bridge infrastructure. The girder-line analytical approach developed in this study should be extended to account for skew, continuity, and transverse load distribution factors, to enable full girder-level design checks. Future work should incorporate weigh-in-motion (WIM) data from Pakistani highways to develop a site-specific live load model calibrated to actual traffic. References AASHTO (2004) AASHTO LRFD Bridge Design Specifications, 3rd Edition. American Association of State Highway and Transportation Officials, Washington, D.C Barker RM, Puckett JA (2007) Design of Highway Bridges: An LRFD Approach, 2nd Edition. John Wiley & Sons, Hoboken, NJ Pakistan Code of Practice for Highway Bridges (PCPHB) (1967) National Transport Research Centre / Ministry of Communications, Government of Pakistan National Highway Authority (NHA), Pakistan (2007) Axle Load Survey Report and Legal Load Limits Specification. NHA Technical Publication Zokaie T (2000) AASHTO-LRFD Live Load Distribution Specifications. J Bridge Eng ASCE 5(2):131–138 Nowak AS (1993) Live Load Model for Highway Bridges. Struct Saf 13(1–2):53–66 (Basis for AASHTO HL-93 calibration.) Ali SM (2009) Study of Dissipation Capacity of R.C. Bridge Columns under Seismic Demand. M.Sc. Thesis, University of Engineering & Technology Peshawar McGraw-Hill Access Science (2010) Highway Bridge Engineering. McGraw-Hill, New York Additional Declarations The authors declare no competing interests. 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Nasir","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+UlEQVRIiWNgGAWjYBAC9gYehgMgBhsD8wEDiQogi5m5Aa8WngNwLWwJBRZnQFoYCWuBMRU+VLaBGIS0sJ89eOjmDjt7PukzjBtuzquN5m8HavlRsQ23Fp68hMO5Z5IT2/hyDxvO3HY8d8ZhxgbGnjO3cWqxZ8gxOJzbxpzAxsOXZiy57VhuA1ALM2Mbbi08/G9AWurt2Xh4zH//nXMsdz5BLRJgWw4ztvHwGBhINtTkbiCsBWzL8cQ2HrYEA4ljB3I3ArUcxOcXHv4c48+5bdX28j2gqKypy513/vDBBz8qcGtBB4fB5AGi1QNBHSmKR8EoGAWjYIQAAJC8Wmz4kp5AAAAAAElFTkSuQmCC","orcid":"","institution":"University of Engineering \u0026 Technology, Peshawar","correspondingAuthor":true,"prefix":"","firstName":"Fahim","middleName":"","lastName":"Nasir","suffix":""},{"id":624837817,"identity":"8533d3e5-e17e-4b04-8b96-5dd2ba61fa0a","order_by":1,"name":"Muhammad umer","email":"","orcid":"","institution":"University of Engineering \u0026 Technology, Peshawar","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"umer","suffix":""}],"badges":[],"createdAt":"2026-04-17 05:20:48","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9444264/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9444264/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107298180,"identity":"bc2cbf38-54d2-4131-a645-4d238bbf0e0a","added_by":"auto","created_at":"2026-04-20 07:06:59","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":47702,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eillustrates the three components of the HL-93 loading scheme and the manner in which the design truck or tandem is combined with the lane load\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-9444264/v1/a5c3e7bef3c71b104a24af3a.png"},{"id":107298182,"identity":"ab93125e-f322-4d95-94ae-dce710537d65","added_by":"auto","created_at":"2026-04-20 07:06:59","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":95313,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eshows the AASHTO shear comparison between design truck and design tandem combinations.\"\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-9444264/v1/a6cb65853fc8352b4972f0a3.png"},{"id":107485917,"identity":"22f642f5-e098-41a0-b1e0-9e1b7f3f5d3b","added_by":"auto","created_at":"2026-04-22 02:36:47","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":83247,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003econfirms the crossover at approximately 12 metres, beyond which the design truck plus lane load governs bending moment\u003c/strong\u003e.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-9444264/v1/4843e9d35b94f37df64faea2.png"},{"id":107298184,"identity":"604cbc38-ae33-40e5-b790-28fe4d0d93b5","added_by":"auto","created_at":"2026-04-20 07:06:59","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":73921,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003edisplays the shear envelopes for all three PCPHB classes, illustrating how Class AA dominates across all span lengths.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-9444264/v1/6aa0f0783aa58adaad7f5b61.png"},{"id":107485927,"identity":"757f38d2-15a6-4614-bff0-f3b7c0840ae5","added_by":"auto","created_at":"2026-04-22 02:36:50","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":81075,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eshows the moment counterpart: Class AA diverges sharply from Classes A and B beyond 20 metres, reaching nearly 6,000 kN·m at 40 metres.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-9444264/v1/93a73f6de2f93786cb90087c.png"},{"id":107486393,"identity":"93702cc7-8653-40c9-a58f-cc6d3dbc7bf9","added_by":"auto","created_at":"2026-04-22 02:38:15","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":124546,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eplots the absolute maximum shear envelopes for all NHA legal vehicle configurations alongside the PCPHB and AASHTO HL-93 curves. Several important conclusions emerge from this comparison.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-9444264/v1/0a911c05b4e5271dc59588fc.png"},{"id":107298187,"identity":"e38144e3-73e5-4523-90f4-f591b9d138f1","added_by":"auto","created_at":"2026-04-20 07:06:59","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":162285,"visible":true,"origin":"","legend":"\u003cp\u003epresents the corresponding moment envelopes, reinforcing the same hierarchy of load severity and confirming that PCPHB Class AA loading exceeds all other models by a widening margin as span length increases.\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-9444264/v1/d2d288a49a9174a5a614c5f5.png"},{"id":107868656,"identity":"7a05c240-63d6-4961-8fe1-da2cd2ab1d50","added_by":"auto","created_at":"2026-04-27 07:30:47","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":841471,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9444264/v1/57162ea3-9e82-438d-9d2a-4a63d794da1f.pdf"},{"id":107484319,"identity":"576223aa-84a1-4c86-afbd-5082f3def53d","added_by":"auto","created_at":"2026-04-22 02:31:35","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":15535,"visible":true,"origin":"","legend":"","description":"","filename":"AppendixA.docx","url":"https://assets-eu.researchsquare.com/files/rs-9444264/v1/d63e62a38c2dc91e4af78b7e.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eEvaluation of Critical Live Load Effects in the Bridge Superstructure Using Girder-line Analysis\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eOne of the most essential components of a modern transportation system is bridges. More than their practical purpose of crossing rivers, valleys, and intersections, they are lifelines: a bridge failure can cut off a whole transportation route. The 2005 Kashmir earthquake is just one example of how history has demonstrated this fact: the earthquake badly damaged a major bridge near Balakot and made rescue and relief efforts into the Pakistani northern valleys severely hampered rescue and relief access. The national highway system in Pakistan has a high number of short and medium span bridges with majority of them ranging between 10 and 40 meters. These are almost all of the slab-girder type, either reinforced concrete T-beam (RCC-T) or restressed concrete I-girder (PS-I), and are simply supported, statically determinate structures. These properties allow them to be analyzed rationally but computationally efficiently by a one-dimensional simplification of the three-dimensional bridge system called Girder-Line Analysis, which is explicitly supported by the AASHTO LRFD Bridge Design Specifications. Although this infrastructure is under pressure due to the increasing commercial traffic, the formal bridge design standard in Pakistan, the Pakistan Code of Practice on Highway Bridges (PCPHB 1967) has not been updated since its publication. It is based on British loading provisions that were introduced to the Indian subcontinent in 1935. In the meantime, the American AASHTO LRFD framework has become more popular in the engineering practice in Pakistan. This variation brings about a practical necessity to comprehend the comparisons of these various load models, and how they correlate with the real truckloads that are allowed on Pakistani roads by the National Highway Authority (NHA). This paper will directly respond to that need. It combines field measurements, published load specifications, and computational analysis using MATLAB to assess and compare critical live load effects among three different load models and a span length range that is representative of the stock of highway bridges in Pakistan.\u003c/p\u003e \u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.1 Objectives\u003c/h2\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eTo conduct a field survey of highway bridges along N-5 and document their structural and geometric characteristics.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTo develop a MATLAB-based Girder-Line Analysis program capable of computing shear force and bending moment envelopes for moving vehicular loads.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTo compare critical live load effects (absolute maximum shear and moment) produced by the NHA legal loads, AASHTO HL-93, and PCPHB 1967 models across span lengths of 10 to 40 meters.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTo draw practical conclusions useful to bridge designers working on Pakistan\u0026rsquo;s highway network.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"2. Bridge Taxonomy and Primary Components","content":"\u003cp\u003eIt is convenient to define some standard terms to describe the types of bridges and their parts before considering loading, as the vocabulary determines the way loads are imposed and the way the effects of loads are followed through a structure.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Structural Configuration\u003c/h2\u003e \u003cp\u003eThe most widespread type of bridges found on the national highways in Pakistan is the beam-girder type. In Girder Bridge, the superstructure is made of longitudinal beams that the girders are spanning between the supports and the concrete deck slab is spanning transversely between them. Traffic load is transferred through the deck slab to the girders, through bearings to the piers or abutments and finally to the foundation soil. This is a straightforward and clear load path and girder bridges are the simplest to analyze and the least expensive to build in the 10-to-40-meter span range. Other structural configurations arch bridges (which carry load through compression along a curved profile), suspension bridges (which suspend the deck from cables hanging between towers), cable-stayed bridges (where cables run directly from towers to deck), and cantilever bridges (which balance loads about intermediate supports) are encountered in Pakistan but typically only for special crossings or large river spans. This is not the focus of this study.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Bridge Components\u003c/h2\u003e \u003cp\u003eA highway bridge is best understood as an assembly of distinct subsystems, each carrying a defined structural role\u003c/p\u003e \u003cp\u003eThe surface that carries the traffic is the bridge deck. It shares the wheel loads with the girders beneath and, when compositely acting with the girders, adds greatly to the flexural resistance of the cross-section. The most common type of deck is cast-in-place reinforced concrete. The major longitudinal load-carrying members of the superstructure are girders. The most common ones in Pakistan are RCC-T beams and prestressed concrete I-girders (PS-I). A normal span has four to ten girders, with a spacing of approximately equal distances across the deck width. Bearings are located at the junction of the superstructure and the substructure, which carry the vertical loads and allow the movements caused by thermal expansion, creep, and deflection of the live loads. The most common in modern Pakistani practice are elastomeric bearings rubber pads reinforced with steel plates. The intermediate vertical supports of multi-span bridges are known as piers. In Pakistan, circular and solid square piers are mostly solid. Abutments are used at the ends of the bridge, which also hold the earthwork of the approach embankments. All the loads are transferred to the underlying stratum by the foundation system; both pile foundations and strip footings are common.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Live Load Models","content":"\u003cp\u003eThere are three different live load structures applicable to the design and evaluation of Pakistani highway bridges. The rationale and structure of each is vital to the interpretation of the comparative results of this study.\u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 NHA Legal Load Limits\u003c/h2\u003e \u003cp\u003eThe National Highway Authority (NHA) stipulates the maximum gross vehicle weight and the maximum individual axle weight that can be legally used on the national highways in Pakistan. They define the upper bound of load the network is legally required to sustain.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e is a summary of the allowable gross loads of truck configurations between two-axle (the popular Bedford and Hino/Nissan models) and six-axle articulated combinations. The axle load limits are established at 5.5 tons on front (steer) axles, 12 tons on single rear axles, 22 tons on tandem axle groups, and 32 tons on tridem axle groups.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eNHA Legal Load Limits for Truck Configurations Operating on Pakistani Highways\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAxles\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTruck Configuration\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMax Gross Load(tons)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026thinsp;+\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBedford / Hino / Nissan (2-axle)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e17.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026thinsp;+\u0026thinsp;Tandem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3-axle truck\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e27.5\u0026ndash;29.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026thinsp;+\u0026thinsp;1 + Tandem / 1\u0026thinsp;+\u0026thinsp;Tandem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4-axle truck or tractor-trailer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e39.5\u0026ndash;41.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026thinsp;+\u0026thinsp;1 + Tridem / 1\u0026thinsp;+\u0026thinsp;Tandem\u0026thinsp;+\u0026thinsp;Tandem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5-axle articulated combination\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48.5\u0026ndash;51.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026thinsp;+\u0026thinsp;Tandem\u0026thinsp;+\u0026thinsp;Tridem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6-axle articulated combination\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e58.5\u0026ndash;61.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eSource: National Highway Authority, Pakistan. Axle load sub-limits: front axle\u0026thinsp;\u0026le;\u0026thinsp;5.5 t; single rear\u0026thinsp;\u0026le;\u0026thinsp;12 t; tandem\u0026thinsp;\u0026le;\u0026thinsp;22 t; tridem\u0026thinsp;\u0026le;\u0026thinsp;32 t.\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe field survey conducted for this study measured the axle widths and axle spacing\u0026rsquo;s of approximately 60 trucks. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents representative values by truck type information that directly informed the axle geometry used in the MATLAB analysis.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTypical Axle Width and Axle Spacing (metres) for Pakistani Truck Configurations\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e Truck Type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAxle Config.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAxle Width (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eS\u003csub\u003e12\u003c/sub\u003e (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eS\u003csub\u003e23\u003c/sub\u003e(m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eS\u003csub\u003e34\u003c/sub\u003e(m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eS\u003csub\u003e45\u003c/sub\u003e(m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eS\u003csub\u003e56\u003c/sub\u003e(m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2-Axle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026thinsp;+\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3-Axle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026thinsp;+\u0026thinsp;Tandem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4-Axle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026thinsp;+\u0026thinsp;1+Tandem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5-Axle (a)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026thinsp;+\u0026thinsp;1+Tridem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5-Axle (b)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026thinsp;+\u0026thinsp;Tandem+Tandem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6-Axle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026thinsp;+\u0026thinsp;Tandem+Tridem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eBased on field measurements of approximately 60 trucks along N-5. S\u003csub\u003ei\u003c/sub\u003eⱼ denotes spacing between consecutive axles i and j.\u003c/b\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2 PCPHB 1967 Live Loading\u003c/h2\u003e \u003cp\u003eThe Code of Practice of Highway Bridges in Pakistan (PCPHB 1967) defines three classes of live loads: Class A (standard loading train), Class B (a lighter version of Class A to be used on temporary or lightly used bridges), and Class AA (a 70-ton military tracked vehicle). Class A loading is a convoy of eight axles a driving unit and two trailers with defined axle loads and spacing. Class B loading is 60 percent of Class A, and the same axle geometry.\u003c/p\u003e \u003cp\u003eClass AA loading, based on military classification criteria, is a 70-ton tracked vehicle 3.6 metres wide and approximately 7 metres long between centers of the tracks. The shortest distance between two successive Class AA vehicles is 91.4 metres nose to tail. This loading is required on bridges on national and state highways and in industrial areas, and bridges intended to be loaded in this manner must also be inspected under Class A loading, as the latter may sometimes be controlling to some structural designs.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e provides the axle load data and ground contact dimensions specified under PCPHB 1967.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePCPHB 1967 Axle Loads and Ground Contact Dimensions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLoading Class\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAxle Load(tons)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eContact Width C(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eContact Width W(mm)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClass A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e11.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClass A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e375\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClass A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClass B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e375\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClass B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClass B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e175\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eSource: PCPHB 1967. C\u0026thinsp;=\u0026thinsp;contact dimension in direction of traffic; W\u0026thinsp;=\u0026thinsp;contact dimension transverse to traffic.\u003c/b\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.3 AASHTO HL-93 Live Loading\u003c/h2\u003e \u003cp\u003eIn 1993, the AASHTO LRFD HL-93 loading model was introduced to generate extreme force effects that were roughly equal to those produced by the population of heavy trucks actually using the American highway network during a 75-year design life. It is composed of three interacting components:\u003c/p\u003e \u003cp\u003eThe Design Truck (HS20-44) has three axles: a 35-kN (4-ton) front steer axle, a 145-kN (16-ton) drive axle, and a 145-kN (16-ton) trailer axle. The distance between the two axes at the back is adjustable between 4.3 m and 9 m, and the analysis chooses the distance that gives the maximum effect of the force in question.\u003c/p\u003e \u003cp\u003eThe Design Tandem is made up of two 110-kN (12-ton) axles with a distance of 1.2 m. In short span bridges, this arrangement normally dominates the three-axle design truck.\u003c/p\u003e \u003cp\u003eDesign Lane Load is a load of 9.3 kN/m that is uniformly distributed over a 3.0-metre width. In longer spans, the lane load is the most significant contributor.\u003c/p\u003e \u003cp\u003eHL-93 design load is the greater of: (a) design truck plus lane load; or (b) design tandem plus lane load. In continuous structures, a special two-truck combination controls negative moment at interior piers, but this is not applicable to the simply supported spans considered here.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAASHTO HL-93 Load Model Summary\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComponent\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eConfiguration\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLoad Intensity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGoverns(Typical)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDesign Truck (HS20-44)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3-axle: 4 t / 16 t / 16 t; rear axle spacing 4.3\u0026ndash;9.0 m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e325 kN total (3 axles)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMedium spans\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDesign Tandem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2-axle: 12 t each, spaced 1.2 m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e220 kN total (2 axles)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eShort spans (\u0026le;\u0026thinsp;12 m)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDesign Lane\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUDL over 3.0 m width\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.3 kN/m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLong spans\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHL-93 (combined)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTruck\u0026thinsp;+\u0026thinsp;Lane OR Tandem\u0026thinsp;+\u0026thinsp;Lane (whichever governs)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePer above\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAll spans\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eSource: AASHTO LRFD Bridge Design Specifications (4th ed. and later). Note: axle width 1.8 m for all vehicular components.\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Field Survey: Bridges along N-5","content":"\u003cp\u003eA systematic field survey was conducted along a stretch of National Highway N-5, following the Grand Trunk Road, to establish the physical reality of the bridge infrastructure in Pakistan, between Rawalpindi and Hassan Abdal. A total of fourteen bridges were surveyed. The GPS coordinates of each structure were noted and then overlaid in Google Earth to give a spatial map of the survey corridor.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.1 General Observations\u003c/h2\u003e \u003cp\u003eAll bridges that were met in the survey were of the slab-girder type. The typology used in the analytical stage of the study was verified by the girder cross-sections being either RCC-T beam or PS-I (prestressed concrete I-beam). The bridges had four to ten girders per span, and the span lengths were mostly within the 10\u0026ndash;30 metre range. Substructures were solid circular or solid square reinforced concrete piers.\u003c/p\u003e \u003cp\u003eThe state of the bridges was quite different. Some of them had concrete spalling and shear cracking in the girder webs, which were in line with poor maintenance. Others had been retrofitted by injecting grout to close cracks. Expansion joints in several bridges had become so worn that they were open and unguarded with a gap of up to 180 mm (7 inches) wide. One bridge had been widened by adding new girders alongside the original ones to accommodate an additional traffic lane an improvised intervention that raises legitimate concerns about load redistribution and long-term structural compatibility.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Representative Bridge Data\u003c/h2\u003e \u003cp\u003eHere two bridges are pointed out to show the variety of structures that are encountered. Their main features are given in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFeatures of Taxila Bridge (N-5, near Taxila)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLocation\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTaxila, Khyber Pakhtunkhwa\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNumber of Spans\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSpan Length\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e23.47 m (each span)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eGirder Type\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePS-I (Prestressed Concrete I-beam)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNumber of Girders per Span\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7 (5 original\u0026thinsp;+\u0026thinsp;2 new widening)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNumber of Piers\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8 (4 original\u0026thinsp;+\u0026thinsp;4 new)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePier Type\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSolid square reinforced concrete\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFeatures of Kashmir Highway Bridge (Rawalpindi)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLocation\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRawalpindi, Punjab\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNumber of Spans\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSpan Length\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16.408 m (exterior) / 22.2 m (interior)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eGirder Type\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePS-I (Prestressed Concrete I-beam)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNumber of Girders per Span\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNumber of Piers\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePier Type\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSolid circular reinforced concrete\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Analytical Methodology: Girder-Line Analysis","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n\u003ch2\u003e5.1 Theoretical Basis\u003c/h2\u003e\n\u003cp\u003eThe AASHTO LRFD standard allows a three-dimensional bridge superstructure to be reduced to a single beam the \u0026ldquo;girder line\u0026rdquo; to compute the effects of live loads forces. This simplification is physically reasonable when dealing with simply supported, right-angled bridges where the distribution of loads to individual girders can be addressed independently by calculating distribution factors. In the current analysis, the girder-line it is the subject of interest: i.e. finding out the maximum shear and moment that the bridge system has to support, and then allocating it to individual girders.\u003c/p\u003e\n\u003cp\u003eThe concept of influence line is the focus of this analysis. An influence line for a chosen response quantity say, midspan bending moment or end shear plots the value of that quantity as a unit load traverses the span from one support to the other. That is plotted by the value of that response quantity as a unit load moves across the span between the two ends. When the influence line has been determined, the maximum response of any arbitrary vehicle loading is determined by locating the vehicle in such a way that the axle forces of the vehicle multiply the largest positive ordinates of the influence line. In the case of a simply supported beam, this location is easy to determine: the vehicle moves systematic across the span, and the shear and moment at each point are calculated.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n\u003ch2\u003e5.2 MATLAB Program\u003c/h2\u003e\n\u003cp\u003eThis process was automated in a special MATLAB program to run over the entire span length (10 to 40 metres, in 2.5-metre steps) and all three-load models. The main computational procedures were:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eModel the girder line as a simply supported beam with the given span.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eIntroduce each vehicle load as a collection of moving point loads (up to eight axles) with given axle weights and spacing\u0026rsquo;s, and a uniformly distributed lane load where necessary.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eMove the vehicle over the span in 100 mm steps, calculating shear force and bending moment at each beam section at each truck position.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eBuild the shear and moment envelopes i.e., the maximum and minimum values at each section over all vehicle positions.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eTake the absolute maximum shear and the absolute maximum positive bending moment of the envelope of that span.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eRepeat with all span lengths to produce span-effect curves.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eIn the case of the AASHTO design truck, the variable rear axle spacing (4.3 to 9.0 m) was processed by scanning through all the possible spacing\u0026rsquo;s and keeping the controlling value. Hand calculations and SAP 2000 models were used to independently verify the results; there was a high level of agreement.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\n\u003ch2\u003e5.3 Key Programme Features and Limitations\u003c/h2\u003e\n\u003cp\u003eThe Programme can produce envelopes of both shear and bending moment of any combination of up to eight moving point loads, and uniformly distributed loads. It is able to find the critical truck position of each span. Output graphs are automatically stored in PDF format to report.\u003c/p\u003e\n\u003cp\u003eThe program has a number of intentional constraints. It only works on simply supported beams and does not consider continuous spans, skew, or curvature. It performs a service-load analysis only load factors and resistance factors of the LRFD framework are not applied. It does not consider transverse load distribution (girder distribution factors) or the width of the design lane. These restrictions were deemed suitable to the comparative nature of the study; the aim is to compare relative critical load effects between models, not to conduct a complete design.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"6. Results and Discussion","content":"\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\n\u003ch2\u003e6.1 AASHTO HL-93: Design Truck vs. Design Tandem\u003c/h2\u003e\n\u003cp\u003eIn the AASHTO HL-93 model, there are two sub-models of vehicles: the three-axle design truck and the two-axle design tandem. They are both added to the lane load, and the extreme combination\u003c/p\u003e\n\u003cp\u003ePrevails. Figures\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e through 5 present the complete set of shear and moment envelopes for all load models. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e shows the AASHTO shear comparison between design truck and design tandem combinations.\u003c/p\u003e\n\u003cp\u003eIn the case of shear force, the design truck and the lane load give rise to critical values in the entire range of spans examined (10 to 40 metres). The design tandem combined with the lane load consistently produces lower shear demands than the design truck combination. The difference between the two curves increases with the span.\u003c/p\u003e\n\u003cp\u003eIn the case of bending moment, the image is more subtle. The design tandem plus lane load is the controlling combination in spans up to about 12 metres. Beyond 12 metres, the design truck plus lane load takes over as the critical case. This shift is indicative of the fact that the closely spaced tandem axles are extremely efficient at loading the short-span influence line, whereas the greater individual axle weights of the truck dominate on longer spans where the influence line ordinates are greater and more dispersed.\u003c/p\u003e\n\u003cp\u003eIn the design truck analysis itself, the critical moment of spans longer than the total truck length is determined by the rear axle spacing of 4.3 metres, and the longer spacing of 9.0 metres is more critical in short spans where it is beneficial to have multiple heavy axles on the span at the same time.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\n\u003ch2\u003e6.2 PCPHB 1967: Class A, Class B, and Class AA\u003c/h2\u003e\n\u003cp\u003eThe Class AA loading (70-ton military tank) controls both the shear force and bending moment throughout the entire span range of 10 to 40 metres under the PCPHB 1967 framework. The Class A standard truck train always produces greater values than Class B (as would be the case, because Class B is 60% of Class A), but neither of them comes anywhere near the values generated by the concentrated, heavy tracked vehicle of Class AA.\u003c/p\u003e\n\u003cp\u003eThe Class AA shear envelope is very flat compared to Class A, indicating that a tracked vehicle loads its weight on a finite contact area, not at discrete axle points. The moment envelope of Class AA increases rapidly with the span length and by 30 metres; it exceeds all other models by a substantial and widening margin\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\n\u003ch2\u003e6.3 Comparative Analysis: All Load Models\u003c/h2\u003e\n\u003cp\u003eFirst, the PCPHB Class AA loading has the greatest shear and moment demands of any model at all span lengths. This is in line with the fact that Class AA is a specialized and very heavy military vehicle that has nothing to do with the civilian truck traffic that the NHA legal limits govern.\u003c/p\u003e\n\u003cp\u003eSecond, the 6-axle (1\u0026thinsp;+\u0026thinsp;Tandem+Tridem, gross weight up to 58.561.5 tons) is the NHA legal vehicle with the highest shear requirements. It has a widely spaced axle arrangement, which implies that it carries heavy loads at numerous points across the span at the same time.\u003c/p\u003e\n\u003cp\u003eThird, the AASHTO HL-93 curve, evaluated on a service-load basis (no load factors applied), is lower or close to the NHA 6-axle curve of shear, and near the cluster of heavier NHA configurations of moment. This is an important result: it implies that the AASHTO load model, which was adjusted to American truck traffic, does not significantly overestimate the demand of the heaviest legal Pakistani trucks. The margins which the design framework of AASHTO at the time imposes the impact factor (dynamic load allowance) of 33% and the load factor of 1.75 on live load in the Strength I limit state, and the implicit amplification of dead-load, cause the factored design demands to be far above the service-load NHA limits, making the design safe even when the limits are exceeded in practice.\u003c/p\u003e\n\u003cp\u003eFourth, and, probably, most practical, the gross vehicle weight of the truck is not the decisive factor. The experiment shows that the critical shear and moment requirements depend on the magnitude of the axle loads and the geometry of the axle spacing. A lighter truck with a concentrated axle configuration than a heavier truck with well-distributed weight can cause the local load effects. This has direct consequences on enforcement: it is not enough to control gross weight, but axle load limits should be enforced.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\n\u003ch2\u003e6.4 Summary of Key Numerical Benchmarks\u003c/h2\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e provides indicative values of absolute maximum shear and moment at three representative span lengths under each governing load model. These values are drawn directly from the MATLAB analysis envelopes and reflect service-load conditions without load factors.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab7\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eIndicative Critical Live Load Effects at Selected Span Lengths (Service Load, No Load Factors)\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eLoad Model\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSpan 10 m Shear(kN)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSpan 10m Moment (kNm)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSpan 25m Shear(kN)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSpan 25m Moment (kNm)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSpan 40m Shear(kN)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAASHTO HL-93\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;290\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;590\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;390\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;2 400\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;490\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eLoad Model\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSpan 10 m Shear(kN)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSpan 10m Moment (kNm)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSpan 25m Shear(kN)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSpan 25m Moment (kNm)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSpan 40m Shear(kN)\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNHA 6-Axle (governing)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;560\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;870\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;430\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;2 700\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;520\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePCPHB Class AA (governing)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;560\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;1 350\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;620\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;3 750\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;660\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNHA 2-Axle (min.)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;145\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;175\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;800\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e~\u0026thinsp;165\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cstrong\u003eValues are approximate, extracted from the MATLAB envelope plots. Moment figures for 40 m spans omitted to maintain table width; Moment values for 40 m spans are not listed here but are visible in Fig.\u0026nbsp;7.\u003c/strong\u003e\u003c/p\u003e\n\u003c/div\u003e"},{"header":"7. Conclusions","content":"\u003cp\u003eThis paper has consolidated field survey data, three different live load models and a custom-written MATLAB Girder-Line Analysis software to assess the important live load effects in Pakistani highway bridge superstructures between 10 and 40 metres. The main findings are as follows.\u003c/p\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e7.1 Load Model Comparison\u003c/h2\u003e \u003cp\u003eThe PCPHB 1967 Class AA loading (70-ton military tracked vehicle) has the greatest shear and moment demands of any model in the group, at all span lengths. Check designers using the PCPHB code must not limit their attention to Class A alone\u0026mdash; Class AA governs throughout the span range studied and must always. Class A itself rules over Class B all the way, as it should.\u003c/p\u003e \u003cp\u003eWhen evaluated at service level (no load factors), the AASHTO HL-93 model yields demands that are broadly similar to, but tend to be somewhat lower than, the NHA 6-axle legal load configuration in shear, and similar to the heavier NHA configurations in moment. The seeming sufficiency of the current bridges to legal truckloads, even with the closeness of the HL-93 curve, is attributed to the large safety factors that the LRFD method introduces in terms of load and resistance, dynamic load allowance, and dead load amplification.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e7.2 Design-Relevant Findings\u003c/h2\u003e \u003cp\u003eThe AASHTO design tandem to a span of about 12 metres governs the HL-93 moment; the design truck governs beyond that. In the case of shear, the design truck combination prevails.\u003c/p\u003e \u003cp\u003eThe implicit design of bridges on Pakistani national highways is not despite the AASHTO framework but because of it: the load factors and the conservative nature of the HL-93 notional amplify service-load demands to super-legal levels for the purpose of design.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec25\" class=\"Section2\"\u003e \u003ch2\u003e7.3 Critical Insight: Axle Load Governs, Not Gross Weight\u003c/h2\u003e \u003cp\u003eThe most practical conclusion of this research, perhaps, is that the gross vehicle weight of a truck is not the most important factor in determining the critical shear or moment demand of a simply supported bridge girder. The important factors are the magnitude of the axle load, the geometry of the axle spacing, and the location of the heaviest axle in relation to the span. A truck with many, closely spaced axles can be less harmful, per ton of gross weight, than a truck with fewer, more heavily loaded axles. Enforcement regimes that emphasize gross vehicle weight but do not strictly regulate the axle loads offer partial protection to bridge infrastructure.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003e7.4 Practical Utility\u003c/h2\u003e \u003cp\u003eThe span-effect curves produced in this research offer an easy-to-use reference to bridge engineers in the highway network of Pakistan. With a span length, a designer can simply read the critical service-load shear and moment of each loading model, without re-running the analysis. This is especially useful during the pre-design or feasibility stage, and in quick evaluation of existing bridges.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec27\" class=\"Section2\"\u003e \u003ch2\u003e7.5 Recommendations\u003c/h2\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe PCPHB 1967 code is overdue for revision. The loading models it prescribes no longer reflect either the current vehicle fleet or contemporary bridge engineering practice.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePakistan\u0026rsquo;s highway bridge stock shows signs of inadequate maintenance. A systematic bridge inspection Programme with standardized condition rating should be established nationally.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAxle load enforcement, rather than gross weight enforcement alone, should be prioritized by NHA to protect bridge infrastructure.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe girder-line analytical approach developed in this study should be extended to account for skew, continuity, and transverse load distribution factors, to enable full girder-level design checks.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eFuture work should incorporate weigh-in-motion (WIM) data from Pakistani highways to develop a site-specific live load model calibrated to actual traffic.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAASHTO (2004) AASHTO LRFD Bridge Design Specifications, 3rd Edition. American Association of State Highway and Transportation Officials, Washington, D.C\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBarker RM, Puckett JA (2007) Design of Highway Bridges: An LRFD Approach, 2nd Edition. John Wiley \u0026amp; Sons, Hoboken, NJ\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePakistan Code of Practice for Highway Bridges (PCPHB) (1967) National Transport Research Centre / Ministry of Communications, Government of Pakistan\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNational Highway Authority (NHA), Pakistan (2007) Axle Load Survey Report and Legal Load Limits Specification. NHA Technical Publication\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZokaie T (2000) AASHTO-LRFD Live Load Distribution Specifications. J Bridge Eng ASCE 5(2):131\u0026ndash;138\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNowak AS (1993) Live Load Model for Highway Bridges. Struct Saf 13(1\u0026ndash;2):53\u0026ndash;66 (Basis for AASHTO HL-93 calibration.)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAli SM (2009) Study of Dissipation Capacity of R.C. Bridge Columns under Seismic Demand. M.Sc. Thesis, University of Engineering \u0026amp; Technology Peshawar\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMcGraw-Hill Access Science (2010) Highway Bridge Engineering. McGraw-Hill, New York\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Engineering and Technology Peshawar","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"bridge superstructure, girder-line analysis, AASHTO HL-93, PCPHB 1967, NHA legal loads, live load effects, bending moment, shear force, Pakistan highway bridges","lastPublishedDoi":"10.21203/rs.3.rs-9444264/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9444264/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHighway bridges form the skeletal backbone of any national transportation network, yet in Pakistan they remain among the most critically under evaluated infrastructure assets. The country's formal bridge design standard, the Pakistan Code of Practice for Highway Bridges (PCPHB 1967), has not been revised since its original publication and continues to rely on British loading provisions introduced to the Indian subcontinent in 1935. Meanwhile, commercial truck traffic on Pakistani highways has grown substantially heavier and more complex in axle configuration, creating a widening gap between the loads bridges were designed to carry and the loads they are actually asked to sustain. This study was undertaken to address that gap directly.\u003c/p\u003e \u003cp\u003eThe primary aim of this research is to evaluate and compare the critical live load effects specifically absolute maximum shear force and bending moment induced in the superstructures of simply supported highway bridges spanning between 10 and 40 metres, a range that encompasses the overwhelming majority of bridges currently in service on Pakistan's National Highway N-5 corridor and, by extension, the broader national network.\u003c/p\u003e \u003cp\u003eTo achieve this, three parallel objectives were pursued. First, a systematic field survey was conducted along National Highway N-5 from Rawalpindi to Hassan Abdal, documenting the geometric, structural, and condition-related characteristics of fourteen bridges representative of the existing stock. Second, a MATLAB-based Girder-Line Analysis program was developed to compute shear force and bending moment envelopes for simply supported beams subjected to moving vehicular loads across span lengths of 10 to 40 metres in increments of 2.5 metres. Third, 3 distinct live load models were applied within this analytical framework and their critical load effects compared: the NHA legal load limits governing actual truck traffic on Pakistani roads, the AASHTO HL-93 notional load model increasingly adopted by Pakistani engineers, and the PCPHB 1967 standard including its Class AA military vehicle loading. All results were independently verified through hand calculations and SAP 2000 modelling.\u003c/p\u003e \u003cp\u003eThe analysis reveals that the PCPHB 1967 Class AA loading a 70-ton military tracked vehicle governs both shear and moment demands across the entire span range studied, exceeding all other load models by a margin that widens significantly with increasing span length. Among legally permitted civilian vehicles, the NHA 6-axle configuration produces the highest shear demands. The AASHTO HL-93 model, when assessed on a service-load basis without load factors, falls close to but generally below the NHA 6-axle envelope, a result explained by the conservative load and resistance factors that the LRFD design framework subsequently applies. Critically, the study demonstrates that gross vehicle weight is not the primary determinant of bridge load effects. It is the axle load magnitude, axle spacing geometry, and position of the heaviest axle relative to the span that drive critical shear and moment demands a finding with direct and immediate implications for load enforcement policy on Pakistan's highway network.\u003c/p\u003e","manuscriptTitle":"Evaluation of Critical Live Load Effects in the Bridge Superstructure Using Girder-line Analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-20 07:06:50","doi":"10.21203/rs.3.rs-9444264/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f408d84c-5c7c-4807-bb47-78ee23375fc2","owner":[],"postedDate":"April 20th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":66625461,"name":"Civil Engineering"},{"id":66625462,"name":"Mechanical Engineering"}],"tags":[],"updatedAt":"2026-04-20T07:06:50+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-20 07:06:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9444264","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9444264","identity":"rs-9444264","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}