HLR Section 6.2
Detailed Assessment Methodology
CONTENTS
| 6.2.1 Assessment Methodology 6.2.2 Structures with Capacities and Girders 6.2.3 Structures with Capacities but without Girders 6.2.4 Simply Supported Structures 6.2.5 Continuous Structures with Capacities 6.2.6 Continuous Structures without Capacities 6.2.7 Shear & Reaction Checks Flowchart of the Assessment Process
| Other Links: | Main Index | No Capacities | Ratio Method | K-Factors |
6.2.1 Assessment Methodology
| This section describes in detail the underlying methodology on which the heavy load assessment is based. An outline of the system is also summarised in Section 1.2 and a flowchart of the assessment process may be viewed by clicking here. Once job ID, vehicle and route data have been entered and a number of analysis options selected, the analysis can commence. Outline of the Assessment Process Each structure along the specified route is first checked for height, width or other imposed restrictions. If no restrictions are found HLR will attempt to calculate the maximum moments induced by the heavy load vehicle and compare them with the working stress or ultimate live load moment capacities of the structure as stored on the structure database. In the case of a selected list of structures the program will check and report on both height-width clearances as well as structural sufficiency. If capacities do not exist a modfied moment ratio method is employed for simply supported structures or a direct comparison is made with design vehicle moment envelopes for continuous structures (refer to Section 6.9 for details). In each case the comparison is done for three notional vehicle travel conditions giving, in effect, three comparative HL vehicle moments (M1, M2 and M3 - refer to Section 6.2.2 for a description of these conditions and moments). A brief overview of the data entry and analysis process is also given in Section 1 (Program Overview). When calculating the effects due to the HL vehicle, two primary superstructure cases are differentiated by HLR, depending on the type of deck being analysed. If girders exist (i.e. girder spacings are specified in the structure data file), HLR assumes that the capacity check is based on individual girder moments (refer to Section 6.2.2 below). Otherwise, if girders are not present, (Girder spacing = 0), the check is performed on the full superstructure cross-section (refer to Section 6.2.3 for a more complete discussion). The detailed procedure used to check each structure along the designated route is described below and a summary flowchart of the process may be viewed by clicking here. (NOTE: After navigating to another section or link in this manual use the Back arrow on the browser to return to the last spot in this section). 1. Calculation of the heavy load effects The program first checks if the current structure is simply supported or continuous. Although the same assessment principles are used to check continuous and simply supported structures a few differences do exist. Refer to Section 6.2.4 for a discussion of simply supported structures and Section 6.2.5 for continuous structures.
Width Modified Axle Loads
An option has been provided in HLR to modify heavy vehicle axle loads according to axle width (Wa) and the type of structure being loaded (i.e. timber or concrete). If any of the axle widths in the heavy load vehicle exceed the limits specified on the Vehicles tab (and in the Options/ Defaults Settings form), HLR will multiply each axle load by the relevant factor (refer to the document "Width-Modified Axle Loads.pdf" for further details). The modified axle loads will then be used to determine the heavy vehicle moment and shear effects. Note that modified axle loads will only be used if "Use reduced axle loads in the analysis" is ticked in the Analysis Option tab. If the bridge is a Northern Territory (Type 9) structure, HLR will obtain the axle load reduction factor from the table specified under Options/NT-Factors and apply them to the heavy vehicle axle loads. This will occur irrespective of whether the analysis option "Use reduced axle loads in the analysis" is ticked or not. (Refer to Section 6.5 and Section 8.6 for a discussion of NT factors).
Calculation of moments due to the heavy load vehicle (M hl)
HLR calculates the maximum moments (and shears) induced in the structure by the heavy load vehicle using conventional structural beam theory. Refer to Section 6.2.4 for the analysis of simply supported structures and Section 6.2.5 for continuous structures.
2. Dynamic Load Allowance A separate dynamic load allowance factor can be applied to each of the three notional travel conditions checked by HLR (refer to Section 6.2.2 for a description of these conditions). The DLA factors corresponding to travel at restricted speeds and/or location on the bridge deck (DLA2 and DLA3) are specified in the Options / Load Effects form and will be applied by HLR to all structures on the route being assessed. DLA1, representing the dynamic load allowance factor for vehicle travel at unrestricted speed, is treated differently. If a default DLA1 has been entered in the Options / Load Effects form this value will be used in calculating the maximum moment (M1) for all structures in the current route. If this value is zero HLR will check whether a dynamic load allowance factor has been specified in the database for each individual structure. If it has, that value will be used to modify the calculated HL vehicle moments for the effects of dynamic impact on that one structure only. (Note that for multi-span bridges each span can have a different DLA). If a DLA factor has not been specified in the structure database, HLR will calculate a value based on the empirical method described in Section 6.6. 3. Effective Girder Spacings For structures having beam members HLR will modify the calculated HL vehicle moments to allow for the distribution of these moments to individual girders in order that a direct comparison can be made with their capacities. The distribution factors have been derived from former NAASRA 1976 BDS expressions and are based on the effective girder spacing and an empirically derived parameter (refer to Section 6.2.2 for details). For structures with no girders the distribution factors are set to unity. Girder spacings are obtained from the first column of the structure span details table. Note that HLR also allows an alternative effective girder spacing to be used when calculating the HL effect for the third, very low-speed, travel condition. This condition will occur when the vehicle travels at crawl speed and is positioned at the most favourable location on the bridge deck, (usually 5kph down the centre-line of the structure). If this value is present in the structure data base it will be used to calculate the HL effect for this travel condition. Otherwise, the one girder spacing is used in all calculations. Although HLR also allows a specification of the form *E=... to be entered in the span Notes & Comments field to represent an alternative effective girder spacing for the low speed check, this is a remnant of the former DOS version of the program and is not recommended. 4. Distribution Factors During the analysis HLR will check if a distribution factors table is available for the structure being checked. If it is, the program will attempt to match the widest HL vehicle axle with the entries in the table (also using the value specified in the Number of Tyres per Axle field - which has yet to be included in the program). If a match is found, the appropriate distribution factors will be loaded. If an exact match cannot be made, the default girder factors currently embodied in the program will be used. Note, however, that if only a single row of DF data has been entered into the table and the Axle Width shown in the DF table is less than the width specified for the HL vehicle, the tabulated factors will over-ride the defaults. If the HLV axle width is less than the Axle Width the default system values will be used. (Refer also to Section 5.3, Structure Data). Structure-specific distribution factors are not used if the analysis is based on the ratio method - the default girder factors are invoked instead. For structures with beams and girders the default empirical distribution factor parameters (also referred to as girder factors) are taken from the Load Effects Factors tab (under the Options item in the menu bar). They can be changed to suit your own requirements. 5. Check if the Ultimate Strength Capacity Exists HLR allows both ultimate and working overload capacities to be checked for each structure in the one pass. If ultimate live load capacities exist, HLR will calculate the moment (and/or shear) effects due to the heavy load vehicle for three different travel conditions (M 1,M 2, M 3) using the values in items 1-4 above and the ultimate load factor from the Analysis Options tab. These values are then compared to the ultimate live load capacity of the structure, M uc. Once completed, the program will check for ultimate shear and/or reaction capacities then continue on to item 6. The methodology for this procedure is given in Section 6.2.2 for structures with girders and Section 6.2.3 for those without. If ultimate capacities do not exist, this check is automatically bypassed. 6. Verify if a Working Stress (Overload) Check is to be Performed If both Ultimate and Working Overload capacities are present for a structure, a working stress check will only be performed if the Check working stress flag in the structure database is set to Yes. If ultimate capacities are not available a working stress check is automatically undertaken (but see item 7 below). 7. Perform a Working Stress (Overload) Check A working stress check will only be performed if a working Overload moment is present in the second (middle) field of the structure capacity data base. If this live load moment capacity is not available HLR will attempt to perform a Moment Ratio check (see item 12 below). Although the working Overload value is usually assumed to be the 140% overload (overstress) moment, it can represent whatever overstress limit you wish. However, it should be consistent across all structures in the database. The Working Overload Factor specified in the Default Settings form essentially identifies and documents this overload limit. You should change it if it differs from 140%. If a working overload moment exists for the structure, HLR will calculate M1, M2 and M3 using the values in items 1-4 and a limit state factor of 1. Although the Working Overload Factor specified in the Analysis Options tab is not directly used in the working stress check it is, however, used in the following two special circumstances: Moment Ratio Check: The HL Vehicle/Design Vehicle moment ratios are checked against the value Overload Factor/100 (refer to item 13 below or Section 6.3 for details regarding the Moment-Ratio method). Reduced Capacity Check: Refer to item 8 below. 8. Reduced Overload Capacity Check HLR allows two types of Working Stress capacities to be specified for a structure:- a 100% capacity that refects the capacity at basic allowable stress levels; and a 140% over-load capacity that reflects the full overload condition. (Note, however, that the over-load capacity need not be strictly based on 140% stress levels, but may be based on some other full overload criteria). The serviceability check is normally based on the full working stress overload capacity (Transport SA assumes this to be 140% of the basic capacity). HLR allows the Working Stress Overload Factor (found on the Analysis Options panel) to be varied in the range 100% - 140%. If the factor is left at the default value of 140% the program will simply use the full working stress overload capacity when performing the moment comparison. No further factoring is performed. If, however, the factor is changed to a value between 100% and 140%, HLR will linearly interpolate between the basic allowable capacity and the full overload capacity. If either of these two capacities do not exist, HLR will default to a simple ratio check, since it is unable to perform the interpolation. Overstress factors larger than 140% are not allowed. The reduced working overload moment capacity is calculated using the expression: Mc = M wk + (M 140 - M wk)*(WOSF - 100)/40 where WOSF is the user-specified working overload factor and M140 the 140% Working Overload moment. Although in theory the above relationship allows the working stress factor to exceed the 140% overstress limit HLR will not permit this to happen. If the working stress capacity, Mwk, and the Ultimate Moment capacity, do not exist HLR will perform a moment ratio check (see item 12 below for simply supported structures and Section 6.9 for continuous structures). Structures for which a *WSF= specification has been entered into the Structure Data Comments field A reduced Working Stress Overload Factor is often specified for PSC structures without capacities (e.g., Transport SA specifies *WSF=1.25). This specification is entered into the Comments field on the Structure Data form (refer to Section 5.2.5 for details). Normally this factor will supercede the value specified in the Analysis Options tab. This can be a problem, however, in situations where an allowable overstress less than 40% is required (as, for example, in a network-wide assessment of B-Doubles, where 115% overstress is permitted). Since the *WSF=" specification applies to the full overload condition (which is equivalent to allowing 140% overstress), HLR "pro-rates" the structure-specific overstress with respect to the value given in the Analysis Options tab. This is done in the following way: When 140% overstress is specified for the Working Stress Overload Factor in the Analysis Options tab and a structure has a specification of the form "*WSF=" in the Comments field an allowable ratio of WSF is used. When 100% overstress is specified in the Analysis Options tab, an allowable ratio of 1.00 is used. The "pro-rata" formula adopted for other values of *WSF and Working Stress Overload Factor is: Rpsc = 1 + (WSOF - 100) * (WSF - 1) / 40 Where Rpsc = allowable ratio for structures having a unique *WSF specification (e.g., *WSF = 1.25) and WSOF = Working Stress Overload Factor (e.g. 140%). The above expression is essentially the equation of a straight line. For example, if WSOF = 115%, then Rpsc = 1.09375. Note that this formulation applies to both simply supported and continuous bridges with no capacities. 9. Apply the Vehicle Reduction Factor This option allows the heavy load moments, shears and reactions at the unrestricted travel speed to be optionally multiplied by a user defined vehicle reduction factor (VRF). It allows a check to be performed to determine if a legal vehicle of width 2.5m can concurrently occupy the bridge with the HL vehicle. In essence, it represents the Austroads 1992 Bridge Code Multiple Lane Modification Factor. For the structure being analysed the relationship Kerb-kerb width >= W+3.7 (in metres) must be satisfied, where W represents the overall width of the vehicle. If the structure width does not exist or is zero, or the VRF exclusion flag has been set (refer to Section 5.2.8 for a definition of this flag), the factor will not be applied. If the HL vehicle width (W) is entered as zero or is overlooked by the user the program will use a width equal to the maximum axle width. The factor is only applied to M1 where structure capacities are known, or only to the ratio R1 if not (i.e. the factor is not applied to M2, M3, R2 or R3). The factor is also applied to V1 (shear) and Reaction-1 if these capacities have been specified. 10. Comparison of Calculated HL Moments With Capacities Once the girder or structure live load capacity, Mc, has been determined, (either calculated as in item 8 above or read off the structure database), it is finally compared to the calculated HL vehicle moments (M 1,M 2, M 3), where M 1,M 2, M 3 are based on the algorithms described in Sections 6.2.2 and 6.2.3 for structures with, and without, girders respectively.
If | Mc > M l | No travel restrictions apply
If | M 2<Mc<M l | Travel speed is restricted but not the vehicle position (e.g. 10kph)
If | M 3<Mc<M 2 | Travel speed and vehicle position are both restricted (e.g. 5 kph down centre)
If | Mc < M 3 | The structure may be overstressed - no travel is permitted
Refer to Section 6.2.2 below for a detailed description of the expressions for M 1,M 2, M 3 and the factors used there-in. Note that HLR also allows the second capacity set, Mc 5 (if it has been specified for the structure), to be used for the highly restricted third level check (usually 5kph down the centreline of the bridge). 11. Check for a Second Set of Moment Capacities HLR has the facility for checking the structure for an alternative girder configuration. If a second set of girder spacings and live load capacities is included in the structure database the assessment procedure described it steps 3-9 will be repeated for this alternative data set. 12. Shear & Reaction Checks If shear and/or reaction live load capacities have been specified in the database they too will be checked. Shear (and reaction) effects (V 1,V 2, V 3) due to the heavy load vehicle will be calculated in the same way as for moments and the comparison then performed using the same criteria indicated in item 9 above. Refer also to Section 6.2.6 for a more complete discussion of shear/reaction checking. 13. Moment Ratio Check If neither Ultimate moment capacities nor Working Overload moments exist for a structure, HLR will attempt to perform a moment ratio check if the structure is simply supported (refer to Section 6.3 for details) or, for a continuous structure, a comparison of the moment envelopes produced by both the heavy load vehicle and the original design vehicle (Section 6.2.5). However, for this to be possible, the name of the design vehicle must be entered into the structure database and the vehicle itself must already exist in the Design Vehicle database. Once the ratio check has been completed, HLR will check for shear and/or reaction capacities then continue on to the next structure.
6.2.2 Structures with girders and capacities (Gspacing > 0)
| As described in Section 6.2.1 above, the maximum heavy load moment, Mhl, is calculated for each span group using reduced axle loads (where appropriate) then factored to produce a set of equivalent girder moments, (M1, M2, M3) representing three possible travel conditions viz: Girder Factors GF 1, GF 2, GF 3 are used:
M l = M hl * 0.5 * G spacing * (1 + DLA 1) * LSf / GF 1 | Unrestricted travel speed
M 2 = M hl * 0.5 * G spacing * (1 + DLA 2) * LSf / GF 2 | Restricted travel speed but not position
M 3 = M hl * 0.5 * G spacing * (1 + DLA 3) * LSf / GF 3 | Restricted travel speed and position
Structure-Specific Distribution Factors DF 1, DF 2, DF 3 are used:
M l = M hl * (1 + DLA 1) * LSf * DF 1 | Unrestricted travel speed
M 2 = M hl * (1 + DLA 2) * LSf * DF 2 | Restricted travel speed but not position
M 3 = M hl * (1 + DLA 3) * LSf * DF 3 | Restricted travel speed and position
LSf represents the ultimate strength (Limit State) factor, usually set to a value in the range 1.5 - 2. It is entered by the user prior to the analysis and is set to 1.0 for working stress checks. Gspacing represents the equivalent girder spacing and GF i and DF i are girder factors that reflect the various positions on the bridge deck that may be traversed by the heavy vehicle. The DLAi factors represent dynamic load allowances for the three possible vehicle travel conditions. DLA and GFi factors are specified on the Options / Load Effects form while distribution factors DF1, DF2, DF3 are entered with structure data. M l assumes that neither speed nor positional restrictions will be imposed on the vehicle. DLA1 is a dynamic load allowance (impact factor) to allow for the dynamic effects of vehicular loading at unrestricted travel speed (refer to Section 6.6 for details). The girder distribution factor, 0.5*Gspacing/GF 1, is based on the assumption that the structure has two or more design lanes. A typical value for GF 1 (and the one used as a default in HLR) is 1.7 (based on the old NAASRA 1976 Bridge Design Specification). M 2 assumes the vehicle speed is restricted in order to reduce the effect of dynamic impact. Transport SA, for example, imposes a 10 kph speed limit, but no restriction is placed on the position of the vehicle on the bridge deck. The dynamic effect, DLA2, is reduced to a minimum level (usually set by TSA to 0.05 or 5%) and the girder factor GF 2 is assumed to be the same as for Ml (to recognise that concurrent multi-lane loading is still possible). M 3 assumes that both vehicle travel speed and vehicle position on the bridge deck are highly restricted (e.g. to 5 kph along the centreline of the bridge - equivalent, therefore, to one effective design lane). As a conseqence, the girder distribution factor, 0.5*Gspacing/GF3, can often be reduced, generally by using a different girder factor (GF3). A value of 2.1 is typically used by TSA for GF3 while the dynamic imapact effect, DLA1, is considered to be negligible and is usually set to zero. Gspacing: HLR allows an alternative effective girder spacing to be used when calculating M 3. This is done by either specifying a second value for the girder spacing in the structure database (Section 5.3) or by including a specification of the form: *E5=… or *E5S2=… in the general (or span) comments fields of the structure data. VRF: As a last step the heavy load moments, shears and reactions at the unrestricted travel speed (i.e., M1, V1) can be optionally multiplied by a user defined vehicle reduction factor (Section 6.1.7). This, in effect, emulates the provisions of the Austroads 1992 Bridge Code Multiple Lane Modification Factor. The calculated girder moments M 1, M 2, M 3 are finally compared to the girder moment capacity, Mc, and the appropriate travel restriction is determined in accordance with the following criteria.
If | Mc > M 1 | No travel restrictions apply
If | M 2<Mc<M 1 | Travel speed is restricted but not the vehicle position (e.g. 10kph)
If | M 3<Mc<M 2 | Travel speed and vehicle position are both restricted (e.g. 5 kph down centre)
If | Mc < M 3 | The structure may be overstressed - no travel is permitted
Default values for GF 1-3 and DLA 1-3 may be changed via the Options/Load Effect Factors facility on the main menu bar.
6.2.3 Structures with capacities but without girders (Gspacing = 0)
| This case normally applies to structures that cannot be modelled with beam or girder elements (such as slab structures or wide box girders with only a few cells). The analytical procedure is essentially the same as that described in Section 6.2.2 above but with the difference that: The full vehicle axle loads, (not the width-modified or reduced loads), are used in calculating the maximum moment (Mhl) M hl is not modified by the transverse load distribution factors or wheel factor i.e. G spacing and GFi are all set to 1.0 and the factor 0.5 is removed from the expressions for Ml, M2, M3.
6.2.4 Simply Supported Structures
| Simply supported structures are checked for sufficiency by comparing moments at a single section within the maximum midspan region. The point at which the maximum moment occurs is determined by performing a statics analysis at 18 span sections in the range 0.3L - 0.7L (i.e. the spacing between sections is L/40), where L = Span length. All span groups are checked if more than one group has been specified for the structure. If live load moment capacities are not available, an empirical moment ratio method based on the original design standard for the structure is used (refer to Section 6.3 for details). Ratios are calculated for each of the three notional travel conditions and compared with the specified working stress (overload) factor. HLR also caters for a special class of single lane bridges used in the Northern Territory. Refer to Section 6.5 for details.
| Return to Section 6.2.1 for a detailed description of the methodology or click here for a summary flowchart.
6.2.5 Continuous Structures With Capacities
| The methodology for the analysis of continuous structures depends on whether live load moment capacities are stored in the structure database or not. Refer to Section 6.2.5 for the assessment of continuous structures for which capacities are not available. (a) Modelling the vehicle movement across structures Vehicles are moved across continuous structures in increments that are based on the overall length of the bridge. After each increment a continuous beam analysis is performed and the results are then enveloped. The vehicle movement increment, Xi, is calculated as follows: Xi = Total length of bridge / (Number of increments per span * Number of spans) The number of increments per span is internally fixed at 30. If spans differ significantly in length the shorter spans will consequently have far fewer increments than the longer spans. For geometrically symmetrical structures, or for uni-directional travel only, this may not pose a problem. However, in structures that have significantly different end (or internal) span lengths the moment envelopes for travel in the forward and reverse directions may be quite different. (b) Assessment process A full heavy vehicle envelope is generated of maximum positive (sagging) and negative (hogging) moments at tenth points along the entire structure. Moments and shears at every section are then factored in accordance with the empirical equations given in Sections 6.2.2 and 6.2.3 and compared to the capacities at those sections for which non-zero values exist. Note that a shear envelope will only be created if a shear check is required for the structure (this is flagged to HLR by including a specification of the form *V=... in the structure database notes & comments fields - refer to Section 6.2.6). Moment and shear envelopes are retained for all continuous structures and may be individually viewed and printed (if required) once the analysis of the entire route has been completed. However, these envelopes are deleted by the system when HLR is exited or if another run is performed. If you wish to save any of the envelopes, use Windows Explorer to navigate to the ..\TemFiles subfolder and copy the required factored envelope (.ENV) or raw results ( .OUT) files to other folders. Note that all spans in the structure are analysed, irrespective of the nature and type of symmetry. Although results are calculated at tenth points along each span the heavy load vehicle is moved along the structure in smaller increments to ensure that an accurate envelope is obtained. The vehicle movement increment is calculated by HLR as follows: Total length of the structure / (No. increments per span * Number of spans) The number of increments per span is currently set to 30. (Return to Section 6.2.1 for a detailed description of the analysis methodology).
6.2.6 Continuous Structures Without Capacities
| (a) Modelling the vehicle movement across structures Vehicles are moved across continuous structures in increments that are based on the overall length of the bridge. After each increment a continuous beam analysis is performed and the results are then enveloped. The vehicle movement increment, Xi, is calculated as follows: Xi = Total length of bridge / (Number of increments per span * Number of spans) The number of increments per span is internally fixed at 30. If spans differ significantly in length the shorter spans will consequently have far fewer increments than the longer spans. For geometrically symmetrical structures, or for uni-directional travel only, this may not pose a problem. However, in structures that have significantly different end (or internal) span lengths the moment envelopes for travel in the forward and reverse directions may be quite different. (b) Assessment methodology A full heavy vehicle envelope is generated of maximum positive (sagging) and negative (hogging) moments at tenth points along the entire structure. For a detailed description of the assessment methodology please refer to Section 6.9. Note that a shear envelope will only be created if a shear check is required for the structure (this is flagged to HLR by including a specification of the form *V=... in the structure database notes & comments fields - refer to Section 6.2.6).
6.2.7 Shear & Reaction Checks
| Shear force and support reaction capacity checks will only be performed if a specification of the form *V=… or *R=… is present in the general structure comments field or a span comments field (refer to the description of structure data in Section 5.6 for details of the exact format that must be used). Note that it is only shear and reaction due to live load that can be checked by the program. Shears and reactions are treated by HLR in much the same way as moment capacities i.e. the same methodology described in Section 6.2.1 is used. Shears and reactions induced by the HL vehicle are factored with the appropriate impact, distribution, ultimate and/or working stress factors to give a set of equivalent beam shears or reactions that are then compared to corresponding capacities from the structure database viz:
V l = V hl * 0.5 * G spacing * (1 + DLA 1) * LSf / GF 1 | Unrestricted travel speed
V 2 = V hl * 0.5 * G spacing * (1 + DLA 2) * LSf / GF 2 | Restricted travel speed but not position
V 3 = V hl * 0.5 * G spacing * (1 + DLA 3) * LSf / GF 3 | Restricted travel speed and position
Note that the Windows version of HLR calculates reactions on a girder basis if girder spacings are specified in the structure database. This differs from the DOS version, which only calculated the total (pier) reaction in all cases. To force HLR to calculate the total reaction use the specification: *Rt=& (refer to Section 5.6 for further details).