Civil Engineering March 2022 | Vol 30 No 2

34 March 2022 Civil Engineering amplification due to resonance is not applicable at ultimate limit state. This is because resonance is typically caused by single vehicle crossings on medium and long span bridges which do not correspond to the load scenarios that cause the highest load effects. It can thus be concluded that dynamic amplification at ultimate limit state is considerably less than at serviceability limit state for ductile failures. Studies show that the DAF can be taken as 1.0 at ultimate limit state for ductile failures. For brittle failures with small deformations, for example shear, the energy dissipation is not as pronounced as for ductile failures with larger deformation capacity. For these cases the author proposes a DAF which starts at 1.3 up to a 5 m span and reduces linearly to 1.0 for spans in excess of 40 m. INTERNATIONAL CODES OF PRACTICE Great variation exists in the formulation of DAFs in different design codes. In this sec- tion DAFs for the most widely used codes are discussed as well as the DAF in TMH7. 1. TMH7 Dynamic amplification is included in NA and NB loading in accordance with the Swiss formula and is dependent on equivalent span length, L s . It is not clear from the code what is meant by “equiva- lent span length” and the Swiss formula is unreferenced. DAF = 0.05 ⎫ ⎪ ⎭ 100 + L s 10 + L s ⎫ ⎪ ⎭ (3) Equation 3 leads to a DAF of 1.35 for a span length of 5 m which reduces linearly to 1.125 for a span length of 50 m. 2. AASHTO AASHTO (1992) specified the dynamic impact factor (IM) as a function of the bridge span length in metres. AASHTO (1994) replaced the IM with a dynamic load allowance (DLA) which is a function of the limit states and com- ponents. The DLA is independent of the span length and is not applied to the lane load. For ULS and SLS global effects the DLA is specified as 33%. 3. Eurocode In Eurocode 1991-2 the DAF is not stated explicitly but is already included in the load model proposed in the code. The DAF was determined using a medium quality pavement and a pneumatic vehicle suspension and is a function of span length, number of loaded lanes and load effect. For single lane bridges the included DAF is given separately for bending and shear. For bending the DAF is specified as 1.7 for span lengths smaller than 5 m and reduces to 1.4 for span lengths larger than 15 m. For shear the DAF is specified as 1.4 for span lengths smaller than 5 m to 1.2 for span lengths larger than 25 m. For two lane bridges the included DAF is equal for bending and shear. The DAF reduces linearly from 1.3 for a span length of 0 m to 1.1 for a span length of 50 m. There is no further reduction beyond 50 m. For four lane bridges the DAF is specified as 1.1 for both bending and shear. 4. Australian standard In AS5100 the DAF is applied to both truck loads and UDLs and is a function of the load configuration. For the M1600 load, which is a moving load, the DAF is specified as 0.3. For S1600 loading, which is static, the DAF is specified as 0, as expected. 5. Canadian standard The Canadian Highway Bridge Design Code specifies an idealised five axle truck, referred to as CL-W. The standard specifies that axles that cause favourable load effects shall be neglected, hence it is possible to have a truck loading with fewer than five axles. Dynamic allowance is only applied to the truck load and is a function of the number of axles causing the most onerous load effect. The dy- namic load allowance is prescribed as 0.4 for single axle loading, 0.3 for two-axle loading and 0.25 when three or more axles are loaded. It is clear from the analysis above that great variation exists between codes regarding the governing parameters, the recommended DAF values, and the way they were derived. Further to this, subsequent research and experiments show that the DAFs that have historically been assumed in design codes may not be as high as originally thought. ARCHES REPORT The ARCHES project (Assessment and Rehabilitation of Central European Highway Structures) was commissioned to reduce the gap between the standard of highway infrastructure in Central and Eastern European countries. More specifi- cally, ARCHES report D10 deals with the dynamic amplification to be applied in the assessment of existing structures, thereby reducing the conservative values typically provided in design codes. The study performed site measure- ments as well as simulation together with finite element analyses and, for the specific cases analysed in the report, the authors show that the dynamic amplifica- tion can be as low as 6% at characteristic load effect level. This is determined using the ADR concept and the study confirms findings that heavier vehicles cause lower dynamic amplification. ARCHES makes recommendations for dynamic allowance for bridge assess- ment, but these can also be extended to the design of new bridges. The dynamic allowance is a function of the road surface roughness as prescribed in ISO 8608. For ISO road class A, a DAF of 1.3 is prescribed for a span length of 5 m and reduces linearly to 1.15 for a 15 m bridge. For ISO road class B, the DAF is given as 1.4 for a span length of 5 m reducing to 1.2 at 15 m. Beyond 15 m the DAFs remain constant. These recommendations are valid for one- and two-lane bridges and for both bending and shear load effects. It can thus be concluded that dynamic amplification at ultimate limit state is considerably less than at serviceability limit state for ductile failures. Studies show that the DAF can be taken as 1.0 at ultimate limit state for ductile failures. For brittle failures with small deformations, for example shear, the energy dissipation is not as pronounced as for ductile failures with larger deformation capacity. For these cases the author proposes a DAF which starts at 1.3 up to a 5 m span and reduces linearly to 1.0 for spans in excess of 40 m.