HLR Section 6.3
Ratio Method - Moment Capacities Not Available
CONTENTS
| 6.3.1 General Overview of Procedure 6.3.2 Detailed Description of the Ratio Method
| Other Links: | Main Index | Analysis Options | Capacities Exist |
6.3.1 General Overview of Procedure
| The Load Ratio method is only used for simply supported structures that have no moment capacities. (Continuous structures with no capacities are dealt with in a slightly different way - refer to Section 6.2.5). The technique essentially compares the maximum moment generated by the heavy load vehicle with that of the original design vehicle specified in the structure data i.e., the analysis is based on a comparison of empirically derived moment ratios. A number of standard design vehicles have been incorporated into HLR including:- the Highways & Local Government truck (1927); the HS20 truck (NAASRA 1947-based on AASHTO); and the NAASRA (1976/1992) T44 vehicle. However, other "non-standard" design vehicles can also be created and stored in the database. Refer to Section 4.4 for details regarding the creation of design vehicles. For a detailed description of the rationale and equations used in the ratio method refer to Section 6.3.2. Ratios R 1, R 2, R 3 are calculated for three basic travel conditions viz: unrestricted vehicle position and speed restricted vehicle speed but not position (e.g. 10 kph travel anywhere on the deck) restricted vehicle speed and position (e.g. 5 kph along the centre of the deck) All three ratios are then compared to the allowable ratio R = Fw/100 , where Fw represents the Working Overload Factor (as a %) specified in the Analysis Options form. Note, however, that it is possible to specify a structure-specific working overstress factor by including an entry of the form: *WSF=... in the Comments field of the Structure Data form (refer also to Section 5.2 for further details). If a specification of this form is present it will over-ride the default value of Fw. Once R has been calculated the following criteria are applied to determined if any travel restrictions apply:
If | R 1 < R | No travel restrictions apply
If | R 2 < R <R 1 | A speed restriction is applied (e.g. 10 kph)
If | R 3 < R <R 2 | A speed and position restriction is applied (e.g. 5 kph down the bridge centreline)
If | R 3 > R | The structure may be overstressed - no travel is permitted
Note that the calculation of R 1 - R 3 is dependent on the type of structure being analysed - refer to the detailed explanation given below.
6.3.2 Ratio Method
| The moment ratio method employed in HLR is an attempt to cater for situations where bridge capacity data is unavailable. It is an empirical technique that allows the maximum moment generated by a heavy load vehicle to be compared with the moment generated by the original design vehicle. Inherent in this method is the basic assumption that this latter moment notionally represents the section capacity. However, for older bridges in particular, this simple live load ratio approach takes no account of the effect of dead load (DL) and consequently can be unnecessarily conservative. The methodology has therefore been modified in HLR to take DL into account. It may be summarised as follows: (1) When determining the heavy load vehicle effect, (LL hl), use the Dynamic Load Allowance factor (DLA hl) specified either in the DLA1 field on the Options/Load Effects form, or in the structure database or, if none exists, the method described in Section 6.6. For the design vehicle effect, (LL design), use the design Dynamic Load Allowance, DLA design, described in Section 6.6 or, for pre-1992 structures, a default design DLA of 16/(L+40) based on the old NAASRA code. (2) In order to obtain a more accurate indication of overloading, the conventional LLhl/LLdesign ratio is modified to incorporate the effect of dead load (DL). The modified ratio is given by: DL + LL hl x (1 + DLA hl) DL + LL design x (1 + DLA design) (3) A study of the load capacity of South Australian bridges carried out by Transport SA showed that for pre-1976 bridges the relationship between the dead load effect (DL) in a structure and its design live load effect (LLdesign) can be approximated using the expression:
DL LL design x (1 + DLA design) | = | Span Phi
where Phi is a statistically derived 95% probability factor determined for different design standards and structure types. In HLR they have been tabulated and saved to a text file that can be accessed and edited via the Options/Vehicle Phi Factors form. As an example, Phi factors compiled by TSA for South Australian beam or girder bridges are shown in the following table:
Design Standard | Phi | Comment
HLGD | 27 | Design vehicle for pre 1950 structures
HS20 | 42 | Design vehicle for 1950 - 1976 structures
T44 | 200 | Current Australian design vehicle (this value is conservative and has not yet been verified)
(4) Transposing the expression in clause (3) above gives:
DL | = | Span x LL design x (1 + DLA design) Phi
(5) Substituting for DL in expression (2) produces the following relationship for unrestricted travel speed and vehicle position on the bridge deck (where DLA hl = DLA1 - refer to point [1] above for details):
R 1 | = | Span/Phi x {LL design x (1 + DLA design)} + {LL hl x (1 + DLA hl)} (Span/Phi + 1) x {LL design x (1 + DLA design)}
(6) For travel at restricted speed (e.g. 10 kph) and no restriction imposed on the vehicle position on the bridge deck, the expression becomes:
R 2 | = | Span/Phi x {LL design x (1 + DLA design)} + {LL hl x (1 + DLA 2)} (Span/Phi + 1) x {LL design x (1 + DLA design)}
where the dynamic load allowance, DLA 2, is usually reduced to 0.05 (5%) or similar to account for the restricted speed. (DLA 2 is specified in the Options / Load Effects form).
(7) For travel restricted to an absolutely minimum speed (5kph, for example) and the vehicle required to travel in its most favourable position on the bridge deck (along the bridge centre-line, for example), the expression becomes:
R 3 | = | Span/Phi x {LL design x (1 + DLA design)} + {LL hl x (1 + DLA 3)} x D f2/Df1 (Span/Phi + 1) x LL design x (1 + DLA design)
At this highly restricted speed the dynamic load allowance, DLA 3, is usually reduced to 0.0 (0%). (DLA3 is specified in the Options / Load Effects form). For structures with beams and girders the general expression is modified to account for an improvement in load distribution due to dedicated centre-line travel of the HL vehicle. This is done via the parameters D f1 and D f2 where: Df 1 = An empirically derived girder factor for single lane analysis (e.g. 2.1) Df 2 = An empirically derived girder factor for multiple lane analysis (e.g. 1.7 ) If the HL vehicle exceeds the standard lane width, reduced axle loads are also used in the analysis. This effectively reduces the HL vehicle to the equivalent of a single lane load in order to enable direct comparison with the Design Vehicle loading.
(8) Box girder structures. To effectively model this type of structure insert the notation "[B]" into the span "Notes & Comments" field. HLR will not use the reduced (width-modified) axle loads in the analysis and will not apply the Df2/Df1 factor when calculating R3. This recognises the fact that the vehicle width is irrelevant in this structure type since the total vehicle load will be carried by the entire box section. (9) Culvert & armco type structures. HLR will also cater for precast culvert units (or similar). This type of structure would normally be designed using a design vehicle corresponding to a single line of wheels. By inserting the notation "[C]" into the span "Notes & Comments" field, HLR will use the reduced (width-modified) axle loads in the analysis but will not apply the Df2/Df1 factor when calculating R3. (10) Finally, the ratios R1, R2 and R3 are compared to the allowable ratio R = Fw/100, where Fw = specified working stress factor as a percentage. The governing travel condition is then set inaccordance with the relationships given in Section 6.3.1. If a unique working overstress factor has been specified for the structure (as a *WSF=... entry in the Comments field of the Structure Data form - refer to Section 5.2 for further details) it will over-ride the default value of Fw.