CIVL 511
This design summary has been prepared by Andrew. This paper acts is meant to act as a guide and summary and should be read in conjunction with CAN/CSA-S6-00 or the Canadian Highway Bridge Design Code.
Table of Contents
Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 Andrew Chad
1.0
Introduction ..................................................................2
2.0
Limit States Design Method ........................................2
2.1
Load Combination Procedure ........................4
3.0
Design Example ............................................................5
4.0
Simplified Method of Analysis ....................................6
4.1
Dead Load Simplified Method of Analysis ....6
4.2
Live Load Simplified Method of Analysis .....7
4.2.1
Bending Moment Det. SLS & ULS .........8
4.2.2
Bending Moment Det. FLS ......................9
4.2.3
Shear Determination SLS & ULS .........10
4.2.4
Shear Determination FLS ......................11
5.0
Loads ...........................................................................11
5.1
Dead Loads .....................................................12
5.1.1
Formatted Spreadsheet: Dead Loads ....13
5.2
Live Loads.......................................................13
5.2.1
Formatted Spreadsheet: Live Loads .....16
5.3
Wind Loads.....................................................17
5.3.1
Wind on Structure ..................................17
5.3.1.1
Wind Application ..........................17
5.3.2
Wind on Live Load .................................18
5.3.3
Formatted Spreadsheet: Wind………...18
5.4
Earthquake Loads ..........................................18
6.0
Conclusions .................................................................20
References
Appendix A: Formatted Spreadsheet
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CIVL 511
The construction industry in Canada is booming. Large Road and bridge projects are especially prevalent in coastal British Columbia as it prepares for the 2010 winter Olympics. The Sea to Sky highway upgrade as well as the expansion of Highway 1 due to the
Gateway Project, specifically offer many opportunities for new bridge construction in the immediate area. The design of bridges can be quite an involved and arduous procedure. The Canadian
Highway Bridge Design Code or CAN/CSA-S6-00, issued in 2000, provides comprehensive and up-to-date requirements for new as well as existing highway bridges. It combines and replaces two previous publications: Design of Highway Bridges (CAN/CSA-S6-
88) and the Ontario Highway Bridge Design Code (1991). The use of its “Simplified Method of Analysis” provides designers and bridge engineers with a very practical and useful method of analysis, which greatly simplifies the overall procedure.
According to the CSA, the CHBDC’s underlying principle is to:
“support the implementation of a national transportation system with uniform minimum standards and design loads for bridges on interprovincial highways. The consistency makes it easier and more cost-effective to design, construct and maintain interprovincial highways, and to transport goods between jurisdictions.”
Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 Andrew Chad
Topics included in this code include: Durability, Loads, Seismic
Design, Methods of Analysis, Buried Structures, Movable Bridges,
Fiber Reinforced Structures, etc (CSA Website, 2006).
This paper provides a synopsis of common loading and load combinations applicable to the design of a new slab on steel girder bridge according to the Canadian Highway Bridge Design Code, hereafter referred to as the CHBDC or the code.
A formatted spreadsheet is also provided which acts as a tool for bridge designers and engineers to organize and summarize the multitude of loading cases, conditions and actual loads required by the code for the design of new bridge structures.
In most general terms, bridge failure occurs when the structure is no longer able to fulfill its primary function, that is, to transmit primary loads comfortably across an opening. Building codes attempt to minimize the possibility of failure primarily through the use of three primary design philosophies, namely, Design at
Working Loads or Allowable Stress Design, Design for Collapse and Limit States Design. The Canadian Highway Bridge Design
Code is based on the Limit States method.
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CIVL 511 Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00
The Limit States Design Method, as currently used in the CHBDC has two basic characteristics:
1. It tries to consider all possible limit states
2. It is based on probabilistic methods.
The chief advantages of this probability-based, Limit States Design
Method are:
1. The recognition of different variabilities for various loads, such as the dead load versus the live load. This differs from the working stress method in that it would encompass both loads into one factor of safety.
2. The recognition of a range of limit states
3. The promise of uniformity by the use of statistical methods to relate all to the probabilities of failure.
As amazing as it sounds, the limit states design method is not without its flaws. This method’s chief disadvantages, deals with the necessity to choose an acceptable risk of failure. Quantifying risk is a fine science, as how does one put a number to a chance of collapse that involves only structural failure versus one that leads to a loss of life? Also, this probability of failure must be delegated to events and loading conditions that may or may not occur during the lifetime of the bridge (O’Connor, 2000). In the CHBDC, default bridge design life is set at 75 years, there is an inherent
Andrew Chad difficulty in predicting a loading condition or event that may not occur until this time has almost elapsed.
The Ontario Highway bridge design code (OHBDC) was a pioneer in the use of this Limit States design philosophy for bridges; it has also influenced heavily the American AASHTO (American
Association of Highway Transportation Officials) specifications.
The AASHTO Code has changed its primary design philosophy from ASD to LRFD and as of May 2005, 17 states have fully implemented this procedure, with many more close to full implementation (AASHTO Website, 2006). A major advancement of the OHBDC code was the linkage of design loads to the legal capacity limits for trucks in Ontario. Theoretically though, these limits spread beyond Ontario as one cannot drive through Canada without passing through the province. The truck geometry, wheel placement and overall length for the 1979 OHBDC were also of major importance, both with regards to the development of the limit states format and in its methodology for the choice of a design vehicle and associated legal limits (O’Connor, 2000).
The Canadian Highway Bridge Design Code Limit States Design philosophy involves the satisfaction three limit states criteria;
Ultimate Limit States (ULS), Fatigue Limit States (FLS) and
Serviceability Limit States (SLS).
The Ultimate Limit States deals with the overall strength of the structure. This criterion ensures that the overall and component
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CIVL 511 Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 factored bridge strength and stability is able to withstand statistically significant loading conditions over its design life.
The Fatigue Limit States deals with strength degradation with sustained cyclic loading. It can be seen as the imposition of repeated cycles that cause repetitive and reversed plasticity at some point in a material. This eventually causes a crack, initiating at an internal defect or notch, that spreads and in worse case causes failure through either a brittle mechanism or ductile.
The Serviceability Limit State outlines maximum deflections and vibrations for safe use and pedestrian comfort among others.
Acceptable vibration criteria, deflection vs. first flexural frequency is outlined in the code in Clause 3.4.4 and shown below in Figure
1. Further serviceability requirements to be met include acceptable crack widths, stress and deformations.
Andrew Chad
Figure 1 – Deflection Limitations for Highway Bridge
Superstructure Vibration
As stated earlier, there is a multitude of loads that must be taken into account for the design of a new bridge structure in Canada.
According to limit states theory, these loads are combined in a manner for ULS, SLS and FLS that is statistically significant. The
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CIVL 511
CHBDC outlines twelve of these appropriate load combinations in table 3.5.1(a) shown below as table 1. Further, load amplification or de-amplification factors are given for the individual load cases.
Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 Andrew Chad
The bridge consists of a 9” reinforced concrete deck on 5 steel girders spanning continuously over two 20m spans. Spacing between girders is 3.5m with deck overhangs of 1.0m on either side. This type of structure is representative of a typical highway overpass structure. A cross section is shown in fig. 2. The bridge is to be idealized as a beam as shown in figure 3.
Table 1 – CHBDC Load Factors and Load Combinations
Before proceeding any further, due the nature of this report, a case study bridge is defined in this section. For the purposes of illustrating load and analysis characteristics and explaining the formatted spreadsheet which accompanies this paper a 4 lane highway bridge was chosen as an aid.
1m 3.5m
Figure 2 – Design Aid Bridge Cross Section
20m 20m
Figure 3 –Idealized Beam of Design Aid Example
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CIVL 511
Prior to summarizing the loading conditions, it is important to keep in mind the methods of analysis that will be used by engineers to practically design the bridge described in above. Section 5 of the
CAN/CSA-S6 provides guidance as to what types of analysis should be performed and when.
It is not coincidental that the bridge described in section 3.0 appears to fall into the category where one could apply the
“Simplified Method of Analysis” as specified by the code. For both dead loads and live loads, if a structure satisfies the criteria outlined in sections 5.6 and 5.7, the method is available for use.
Outlined below is a summary of the necessary criteria and the method of analysis to be used should the criteria be met.
The benefits of being able to use the simplified method of analysis for dead load takedown and calculations are substantial. If the criteria are met, bridge designers have the ability to employ the
“Beam Analogy Method” as outlined in Cl. 5.6.1.2. As is stated in this clause, “it is permitted to the whole of the bridge superstructure, or part contained between two parallel vertical planes running in the longitudinal direction, as a beam, for the purposes of obtaining the longitudinal moments, longitudinal
Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 Andrew Chad vertical shears, and deflections due to dead load. The dead load of a cast deck and superimposed dead load shall be distributed using engineering judgement and in such a manner as to satisfy overall equilibrium”. The use of the “Beam Analogy Method” is permitted if the following conditions are met:

The width is constant

The support conditions are closely equivalent to line support, both at the ends of the bridge and, in the case of multispan bridges, at intermediate supports
 For slab and voided slab bridges the skew parameter ε does not exceed 1/6 and for slab-on-girder bridges built with shored construction, the skew parameter does not exceed
1/18. For slab-on-girder bridges built with unshored construction, no limitation on the value of skew parameter,
ε applies (see Cl. 5.6.1.1 for definition of ε).

For bridges that are curved in plan and that are built with shored construction, the radius of curvature, span and width satisfy the requirements of A5.1(b)(ii)

A solid or voided slab is of substantial uniform depth across a transverse section, or tapered in the vicinity of a free edge provided that the length of the taper in the transverse direction does not exceed 2.5m

For a bridge having longitudinal girders and an overhanging deck slab, the overhang does not exceed 60% of the mean spacing between longitudinal girders or the
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CIVL 511 spacing of the two outermost adjacent webs for box girder bridges, and, also, is not more than 1.80m
The code also provides an escape clause in the case that all of these conditions are not fully met. Engineering judgement may be employed to judge whether the bridge meets the criteria of the simplified method sufficiently closely. If, according to the designers judgement, the bridge sufficiently meets the criteria, the
“beam analogy” method may be employed.
If a short to medium span bridge does not meet the criteria for simplified analysis, a more refined method than the beam analogy method is required. These analysis techniques are defined in section 5.9 and include:
Grillage analogy
Orthotropic plate theory
Finite element
Finite strip
Folded plate
Semi-continuum
These methods fall beyond the scope of this report but would be useful in the iteration and refining of the results from the beam analogy method.
Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 Andrew Chad
Although somewhat more involved, the simplified method of analysis for live loads also provides a relatively easy method for determining longitudinal shears, moments and deflections.
The simplified method criteria closely parallels that of the dead load method and requires:

The bridge width is constant

The support conditions are closely equivalent to line support, both at the ends of the bridge and, in the case of multispan bridges, at intermediate supports
 For slab and slab on girder bridges with skew, the provisions of A5.1(b)(i) are met

For bridges that are curved in plan, the radius of curvature, span, and width satisfy the relative requirements of
A5.1(b)(ii)

A solid or voided slab is of substantial uniform depth across a transverse section, or tapered in the vicinity of a free edge provided that the length of the taper in the transverse direction does not exceed 2.5m

For slab-on-girder bridges, there shall be at least three longitudinal girders that are of equal flexural rigidity and
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CIVL 511 Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 equally spaced, or with variations from the mean of not more than 10% in each case

For a bridge having longitudinal girders and an overhanging deck slab, the overhang does not exceed 60% of the mean spacing between the longitudinal girders or the spacing of the two outermost adjacent webs for box girders, and, also, is not more than 1.8m

For a continuous span bridge, the provisions of A5.1(a) shall apply
 In the case of multispine bridges, each spin has only two webs. Also, the conditions of Cl. 10.12.5.1 shall apply for steel and steel-composite multispine bridges.
The live load simplified method differs from that of the dead load in that there is possibility for transverse variation in the load placement. As such, longitudinal bending moment and shear diagrams are obtained, treating the bridge as a beam and subsequently adjusted with amplification factors, F m
and F v
, to account for the transverse variation in bending moment and shear values respectively. This method differs from the previously used method of Load Fractions to determine each girder’s share of moment and shear forces.
Andrew Chad
For slab-on-girder bridges, F m
and F v
factors are functions of:

Girder Spacing

Girder Span

Number of Design Lanes

Lane Width

Multilane Loading Reduction
Figure 4 provides an illustration of this variation showing extreme variations in truck placements on bridge.
Figure 4 – Transverse Moment Distribution Simplified Method of
Analysis ULS & SLS
For slab-on-girder bridges, M g
, or adjusted bending moment per girder is obtained from the following equations as outlined in
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CIVL 511 Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 clause 5.7.1.2 “Longitudinal Bending moments in shallow superstructures”. For ultimate limit states and serviceability limit states, procedure for ULS and SLS is outlined below:
M g
= F m
M gavg
Where:
M gavg
=nM
T
R
L
/N
M
T
= max moment per design lane
R
L
= modification factor for multilane loading
F m
= Amplification factor for moments
F m
= SN/F(1+ mewC f
/100) greater than or equal 1.05
S = Girder Spacing
N = Number of Girders
F = Width dimension given in table A5.7.1.2.1
(1+μC f
/100) = lane width correction factor
C f
= given in Table A5.7.1.2.1
For fatigue limit states, F m
and F v
also account for Truck Location in a travel lane; as well, D ve
, a reduction for wide girder spacing, is applied. Figure 5 shows truck placement with respect to bridge edge to achieve maximum design moments and shear for the fatigue limit state.
Andrew Chad
Figure 5 – Transverse Moment Distribution Simplified Method of
Analysis FLS
For fatigue limit states:
M g
= F m
M gavg
Where:
M gavg
=M
T
/N
M
T
= max moment for one truck at the point of the span that creates the maximum result. This load is then shared equally among all girders.
F m
= Amplification factor for moments
F m
= SN/F(1+ mewC f
/100+C e
/100) greater than or equal
1.05
S = Girder Spacing
N = Number of Girders
F = Width dimension given in table A5.7.1.2.2(a)
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CIVL 511
(1+μC f
/100+C e
/100) = lane width correction factor
C f
= correction factor given in Table A5.7.1.2.2(b)
C e
= correction factor for vehicle edge distance from table
A5.7.1.2.2(a)
This simplified method of analysis is demonstrated in the design example formatted spreadsheet in appendix a.
The determination of longitudinal vertical shears is very similar to that of longitudinal vertical moments. Longitudinal shear diagrams should be obtained treating the bridge as a beam for two load cases. The first load case comprises one truck, consisting of two lines of CL-625 wheel loads, the second load case comprises the
CL-W lane load to be specified in section 5.2 of this report and
3.8.3.2 of the code. Each of these load cases includes the multiplication of the dynamic load allowance factor where applicable to be discussed in section 5.2 and Clause 3.8.4.5 of the code. For slab-on-girder bridges meeting the criteria of the simplified method of analysis, the longitudinal vertical shear per girder, V g
, is obtained form the following equations:
V g
= F v
V gavg
Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 Andrew Chad
Where:
V gavg
= the average shear per girder determined by sharing equally the total shear on the bridge cross section among all girders in the cross section.
V gavg
= nV
T
R
L
/N
V
T
= the maximum shear per lane at the point of span under consideration n = number of design lanes in accordance with Clause 3.8.2
R
L
= the modification factor for multilane loading in accordance with Clause 3.8.4.2 or 14.8.4.2
N = the number of girders or longitudinal wood beams in the bridge deck B
F v
= an amplification factor to account for the transverse variation in maximum longitudinal shear intensity, as compared to the average longitudinal shear intensity.
F v
= SN/F
S = center to center girder spacing
F = a width dimension that characterizes load distribution for a bridge. For bridges having up to four design lanes, F, shall be obtained from table 5.7.1.4.1 according to the type of bridge and and the number of design lanes in the bridge.
For girder type bridges and voided slabs, where the spacing
S of longitudinal girders or longitudinal web lines in voided slabs is less than 2.00 m, the value of F obtained from table
5.7.1.4.1 shall be multiplied by the following reduction factor (S/2.00)
0.25
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CIVL 511
The simplified method for longitudinal vertical shear for fatigue limit states shall be calculated in the same manner as that of the ultimate and serviceability limit states. The value of F however shall be obtained from table 5.7.1.4.2 and V
T
shall be calculated using a single truck on the bridge, in one lane only.
There are a multitude of forces that bridges built in Canada must now be built to withstand. In the CHBDC these are separated into three categories; Permanent Loads, Transitory Loads and
Exceptional Loads. Permanent Loads include:

Dead loads (D)

Loads due to earth pressure and hydrostatic pressure including surcharges other than dead load (E)

Secondary prestress effects (P)
Transitory Loads should only be included in an analysis if there is a possibility that their inclusion increases the total factored load effect. They include:
Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 Andrew Chad

Live load including dynamic load allowance when applicable, based on CL-625 Truck or Lane (L)

All strains, deformations, displacements, and their effects, including the effects of their restraint and those of friction or stiffness in bearings. Strains and deformation include those due to temperature change and temperature differential, concrete shrinkage, differential shrinkageand creep; but not elastic strains (K)

Wind load on structure (W)

Wind load on traffic (V)

Load due to differential settlement and/or movement of the foundation (S)
Exceptional loads, appropriately named, involve lower probability higher consequence loading. They too should only be included if they increase the total factored load effect.

Earthquake loads (EQ)

Loads due to stream pressure and ice forces, or debris torrents (F)

Ice Accretion Load (A)

Collision load arising from highway vehicles or vessels (H)
For the purposes of this report, due to its focus on the bridge superstructure, and the case-by-case specificity required for several load types, five of the aforementioned load types will be discussed
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CIVL 511 Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 in further detail in this. These are: Dead Loads, Live Loads, Wind load on Structure, Wind Load on Traffic and Earthquake Loading.
Dead loads are defined in CSA/CAN-S6 as “the load from material that is supported by the structure and is not subject to movement.”
This loading includes the weight of all components and appendages affixed to the structure including wearing surface, earth cover and utilities. With the absence of more precise information, table 2 as defined in the code as table 3.6, provides the unit material weights for use in design.
The CHBDC’s approach becomes quite thorough with respect to the load factors associated with dead loads. Through calibration of an annual reliability index, Β, of 3.75 and a service life of 75 years for a new bridge, minimum and maximum load factors have been provided as shown in table 3 (Table 3.5.1(b) in code). Minimum and maximum values of α have been calibrated according to the relative confidence and variability of the load in question. For instance, factory produced components, with a greater degree of quality control, and a lesser degree of variability have an α load factor which varies by only 14% vs. wearing surfaces which vary by 57%, ranging from 0.65 to 1.5. Wearing surfaces are a special case dead load, in that, they are expected to vary in weight over the life of the bridge.
Andrew Chad
Table 2 –Unit Material Weights Specified in the Code
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CIVL 511 Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00
Table 3 - Maximum and Minimum Alpha Load Factors for ULS
Loading
Dead load inclusion in the attached formatted spreadsheet is fairly straight forward. The program assumes that the bridge is qualified to use the “beam analogy method” as outlined in section 4.1. By entering bridge geometry, deck, barrier and sidewalk thicknesses the spreadsheet provides design values for interior and exterior girders and associated range in alpha load factors through the beam idealization of the structure. The program calculates the tributary width for interior girders by taking the area between two vertical planes between exterior girders & the first interior girders. See
Andrew Chad attached program in Appendix 1 for example calculations and further explanations.
Live loading and analysis, which includes, traffic, maintenance and pedestrians makes up a large portion of the CHBDC. It is vehicle loading though that typically governs the design of a highway bridge in Canada. Live loading of highway bridges in Canada is based on the CL-W truck load as well as the CL-W Lane Load.
These loads provide designers and engineers with the minimum analysis values for design. Loading of lesser or greater magnitude may be stipulated by provincial authorities or appropriate localized traffic conditions.
A CL-W truck is the idealized five axle vehicle as shown in figure
6. Load values, wheel placement and lengths as shown in this figure have been specifically calibrated for a 625kN truck, the current legal limit in Canada. This truck is encompassed in a 3m x
3m clearance envelope with 1.8 m wheel to wheel spacing as shown in section in figure 7.
Originally, the design of bridges in Canada was based upon loading prescribed by the AASHTO. By 1978 these prescribed loadings were changed to the legal limits observed by all provinces. In 1998 a 600 kN load was assigned as the legal truck
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CIVL 511 Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 load limit for inter-provincial trucking routes. This was raised to
625kN in 2000, as well, the associated live load factor was raised to the current 1.7. Canadian values differed originally from those of Ontario, in that, the latter were based on MOL (maximum observed loads) versus preset legal limits in Canada. In today’s code, although a 625kN weight is used throughout the country, there still remains a discrepancy between Ontarian truck wheel placement and axle weight distribution compared to that a CL-W truck prescribed for the rest of Canada. The CL-625-ON truck can be found in appendix A3.4 of the CHBDC and is to be used for the design of bridges in Ontario.
Figure 6 – CL-W Truck Load Layout and Distribution
Andrew Chad
Figure 7 – CL-W Truck Section Envelope
The CL-W lane load consists of a CL-W truck load with each axle reduced to 80% of the values given in figure 6 superimposed with a 9kN/m lane load applied over an area 3m wide. It is important to note that this load need not be applied where it reduces the overall load effects. For example, where bridge girders are continuous over supports, applying the lane load over the entire superstructure would result in lower maximum positive bending moments at midspans; not unlike the technique used for snow or live loading in buildings, pattern loading yields the critical results. This 9kN/m lane load is based on work done by Taylor based on observations at the Vancouver Second Narrows Bridge (O’Connor, 2000). This loading also dictates the informal lane load for the design of an
ASCE bridge.
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CIVL 511 Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00
Figure 8 – CL-W Lane Load Distribution
Both the truck and lane load cases shall be factored according to the 12 load cases stipulated in table 1. Further, a dynamic load allowance factor shall increase loads where applicable. While these factors would typically produce higher critical results on smaller components such as manhole covers and deck joints, a designer must remain fully aware of their presence for overall bridge superstructure design. Dynamic load allowance factors, in percent, are stipulated in Cl. 3.8.4.5.3 as: a.
0.50 for deck joints b.
0.40 where only one axle of the CL-W truck is used, except for deck joints c.
0.30 where any two axles of the CL-W truck are used, or axles 1,2 and 3 are used; or d.
0.25 where three axles of the CL-W Truck, except for axles 1,2 and 3 or more than 3 axles are used.
These factors need not be applied to the CL-W lane load nor to its associated reduced wheel loads, these provisions essentially
Andrew Chad stipulate that where a full truck or more than 3 axles are used, the wheel and axle loads shown in figure 6 be increased by at least
25%.
The application of live loads is subject to the provisions of clause
3.8.4., this clause stipulates:

Truck Axles that reduce the load effect shall be neglected

The uniformly distributed portion of the lane load shall not be applied to those parts of a design lane where its application decreases the total load effect

For fatigue limit state, and for the superstructure vibration serviceability limit state (combination 2), the traffic load shall be one truck load increased by the dynamic load allowance or the lane load, whichever produces the maximum load effect. The truck width shall not project beyond the design lane except as specified in clause 3.8.4.3(d). The lane load shall not project beyond the edge of a design lane, nor shall the
CL-W truck clearance envelope, except as specified in clause 3.8.4.4.
Multiple Lane loading is taken into account in the CHBDC through the application of a modification factor which adjusts for the lesser probability of having more than one lane loaded with full CL-W truck or lane loading. These factors are shown in table 3.8.4.2 of the code, table 4 below
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CIVL 511 Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00
Number of Loaded Design Lanes Modification Factor
1 1.00
2
3
4
0.90
0.80
0.70
5
6 or More
0.60
0.55
Table 4 - Modification Factors for Multilane Loading
Since this report focuses on the design of multilane slab-on-girder highway bridges, several live load categories and load types have been omitted from this paper. While truck loading remains the forefront load of concern for this relatively simple structure, where applicable, the following loads must be applied:

CL-W Truck wheels on sidewalk

Centrifugal Force on curved bridges

Braking force

Curb Load

Traffic Barrier Loading

Pedestrian and Bicycle barrier loads

Pedestrian Loads

Maintenance Access loads

Maintenance Vehicle Loads
Andrew Chad
It is interesting to note that snow loads have not been included in the code as it was assumed that the occurrence of a considerable snow load would cause a compensating reduction in traffic load.
Organization of all possible live loading conditions is of utmost importance. For the most part, there are no reduction factors for live loads which occur at the same time, aside from the lane reduction factors from table 4.
The attached formatted spreadsheet requires users to input general bridge geometry and location. The program then outlines the loads to be input into an analysis program idealizing the bridge as a beam as described in section 3.0. With the results taken from this analysis program, users then re-input values into the formatted sheet which adjusts the values accordingly to account for transverse variation. The final values are then available for the designer to input into and factor according to the load combinations of table 1.
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CIVL 511
Dynamic wind loading has the ability to impart massive forces unto a structure. Section 3.10 of the CHBDC stipulates wind loads for all highway structures, with specific requirements for bridge substructures and superstructures. Since this report is concerned with the superstructure design, this section will focus on that feature. Clause 3.10 also provides guidance as to the level of superstructure aeroelastic instability a designer can expect per span length, bridge type and reference wind velocity.
5.3.1.1 Wind Load Application:
Clause 3.10.2.1 of the CHBDC states that the “Superstructure shall be designed for wind induced vertical and horizontal drag loads acting simultaneously”. These wind loads shall be applied uniformly and non-uniformly over the entire structure. The nonuniform load portion shall comprise 75% of the uniform load over any portion of the structure with 100% of the uniform load over the remainder. The horizontal drag load, defined below, is to be applied over the exposed frontal area of the superstructure. In the case of a slab on steel girder bridge, this would be represented by the span length multiplied by girder height, deck thickness and solid barrier height if present.
Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 Andrew Chad
The vertical load is to be applied over the exposed plan area and taken to act either upward or downward. Possible eccentricities in this load application are taken into account by applying total vertical wind load as an equivalent vertical line load at the windward quarter point of the transverse superstructure width.
Vertical and horizontal drag loads are defined as:
F h
=qC e
C g
C h
F v
=qC e
C g
C v
Where q,C e
,C g
,C v
, C h
are defined below: q = Reference wind pressure:
The reference wind pressure, q, mandated by the code is a
1/100 year wind for bridges spanning greater than 125m, and a 1/50 year wind for structures less than 125m. Also, if site topography can cause the wind to funnel, reference wind pressures are to be increased by 20%.
C g
= Gust Effect Coefficient:
For bridges that are not sensitive to wind action, which includes most bridges less than 125m, the gust effect coefficient, C g
, shall be taken as 2.0. For lighter and more slender structures such as pedestrian bridges, this coefficient shall be taken as 2.5. The gust effect approach is
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CIVL 511 Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 to be replaced with a detailed analysis of dynamic wind action for structures that are sensitive to wind action.
C e
= Exposure Coefficient:
The exposure coefficient is proportional to reference height, H, of the structure. It shall not be less than 1,0 and can be calculated from the equation below or taken from table 3.10.1.3 of the code.
C e
= (0.1H)
0.2
C h
, C v
= Drag Coefficients:
C h
and C v
for use in design equations above are to be taken as 2.0 and 1.0 respectively.
This code section also includes a clause that enables a designer to use representative wind tunnel tests or other more detailed methods of analysis to establish loads and design criteria. This would be an appropriate approach for longer slab-on-girder structures or those built in areas where continual high winds are expected.
The wind load on traffic is calculated in the same manner as the horizontal wind load calculation. The load is applied to the exposed area of traffic or any portion thereof which produces critical results. For a highway bridge this area is represented by a
Andrew Chad solid height of 3m representing truck traffic across the span of the bridge. The area of solid highway barriers is to be neglected in this calculation. Also, a value of 1.2 is to be taken for horizontal drag coefficient, C h
.
Given the proven aeroelastic stability of slab-on-girder bridges, the calculation of wind loads is a relatively straightforward procedure; relatively few variable calculations are required. See formatted spreadsheet in Appendix A for example design calculations, references to the corresponding code clauses and further explanation to the use of the procedure outlined in section 5.3.1.1.
Earthquake loading is described in substantial detail in CAN/CSA-
S6-00 Section 4. A detailed seismic loading summary is slightly beyond the scope of this report. However, a synopsis of the procedure is provided in this section.
Effectively, the horizontal seismic forces acting upon a bridge are dependant on the elastic seismic response coefficient, C sm
, as well as the effective weight of the structure.
The minimum analysis required for specific bridge types is specified in Clauses 4.4.5.2 and 4.4.5.3 of the code. While no
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CIVL 511 Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 seismic analysis is required for single span bridges (except single span truss structures), the multispan analysis consists of one of:

None

Uniform Load Method (UL)

Single Mode Spectral Method (SM)

Multimode Spectral Method (MM)

Time History Method (TH)
The exact analysis procedure is based on the importance category of the structure as well as the seismic performance zone in which it lies.
The importance categories as outlined in the CHBDC are: Lifeline bridges, Emergency-Route Bridges, and Other bridges. Lifeline bridges are those which must remain open to all traffic after a seismic event with a 10% probability of exceedance in 50 years and a return period of 475 years. These bridges must also remain usable by security and emergency vehicles after a larger 1/1000 year return event. Emergency route bridges are those which should, at a minimum remain open to emergency vehicles immediately after the design earthquake.
Bridges are assigned to one of four seismic zones based on this importance category and in accordance with the zonal acceleration ratio, taken from environmental data, and table 4.4.4.1 of the code, for the location the bridge is to be constructed.
Andrew Chad
Based on the seismic performance zone, importance category and whether the bridge is defined as “regular” or “irregular” according to Cl. 4.4.5.3.2 of the code, one of the aforementioned minimum analysis requirements is specified in table 4.4.5.3.1. This table shown is below as table 5.
Table 5 – Minimum Analysis Requirements for Multispan Bridges
According to Cl. 4.4.9.1 of the code, the structure is to be analyzed in both the longitudinal and transverse directions. The two load cases shall consist of 100% of the absolute value of the analysis load in one direction combined with 30% of the force effects of analysis in the other direction. An interesting note is that the vertical earthquake motions are taken into account by not eliminating the use of a dead load factor. For Canadian building design, the National Building Code of Canada requires that the vertical motions and forces be calculated using a similar procedure to the horizontal motions.
With respect to the design example outlined in section 3, assuming this is a “lifeline” bridge located in an area with a zonal
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CIVL 511 acceleration ratio of 0.2, table 5 defines the minimum analysis as multimode spectral.
This multimode spectral analysis would then bide by the same linear dynamic analysis principles as any multi degree of freedom structure. Cl. 4.5.3.3 of the code stipulates that the number of modes required for analysis shall be such that 90% of mass participation in the direction under consideration be achieved.
These modes and associated forces shall then be combined using an accepted modal combination procedure. For closely spaced modes, less than 10% difference with respect to the natural frequency, the Complete Quadratic Combination or absolute sum of the modal quantities methods shall be used.
Keeping the above in mind, the majority of publicized steel bridge failures during seismic events tend to be localized near or around the supports or bearings. With that said, improper design and detailing of a slab-on-steel girder system certainly has the potential for failure during a seismic event. With proper detailing, the concrete slab has the ability to perform extremely well as a transverse stiffening element; focus should be applied to the proper detailing of connections and bearings.
Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00 Andrew Chad
With respect to load, load cases and load analysis, the CHBDC provides a comprehensive, realistic and procedural outline to be followed by designers and engineers.
The CHBDC was based on the original OHBDC which was revolutionary in its use of Limit States Design and the use of a design vehicle based on prescribed legal limits. Outlined in this report is the general procedure for load summation, determination and simple analysis for bridges meeting the criteria of the
CHBDC’s “Simplified Method of Analysis”; specifically, detailed procedures were provided for Dead Loads, Live Loads, Wind on
Structure and Wind on Traffic. With that said, the CHBDC is nonetheless a complicated but well written code. Many loads were omitted for the relatively simple bridge example discussed in this report, as well as the attached formatted spreadsheet and only a very basic analysis was performed. Even with this “simple” bridge, the author found much room for confusion and the inclusion of
“small” mistakes. The Simplified Method of design provides the designer with an excellent base procedure and organization but vigilance is still required on their part. An interesting study would involve the vigilance of the current practice of bridge design in
Canada and its general compliance with this procedure, especially given the volume of new bridges to be designed in the immediate area in the near future.
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CIVL 511
Design of Slab-on-Girder Steel Highway Bridges According to CAN/CSA-S6-00
AASHTO Subcomitee on Bridges and Structures. 2006.
Information Retrieved from: http://bridges.transportation.org/?siteid=34&pageid=229
CAN/CSA-S6_00. 2000. Canadian Highway Bridge Design
Code , Canadian Standards Association, Toronto, Ontario, Canada.
CSA Website. 2006. Information retrieved March 1 from: http://www.csa.ca/products/construction/Default.asp?articleID=44
22&language=english
NBC- National Building Code of Canada . 2005, National Research
Council Canada. Ottawa, Ontario, Canada.
O’Connor, C., Shaw, P. 2000.
Bridge Loads:
An International Perspective , Taylor and Francis Group, London,
England.
Lwin, M. Myint.1999.
Why the AASTHO Load and Resistance
Factor Design Specifications?. Transportation Research Record.
Formatted Spreadsheet see attached electronic version.
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Andrew Chad
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