PSI - Issue 64

Edward Steeves et al. / Procedia Structural Integrity 64 (2024) 1975–1982 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

1979

5

3.3. Structural redundancy index from Steeves and Oudah (2024) = [ ∑ == 1 −∑ 1 == 1 −∑ == 1

∑ ( , ) == 1 −∑ 1 == 1 ] ∙ [ ∑

== 1 −∑ == 1 ∑ == 1 ]

(5)

The first term relates to the external loads, and the second term contains utilization ratios. This index does not distinguish between damaged and intact systems, and as such is applied separately to both. As per the definitions cited previously , Eq. (5) accounts for the structure’s ability to carry additional load after element failure along with force redistribution after damage and is, therefore, able to reward systems with element-level ductility. 4. Upgrade of existing truss bridge utilizing indices from Steeves and Oudah (2024) The holistic structural robustness index and associated structural redundancy index from Steeves and Oudah (2024) are employed to evaluate and upgrade a steel truss bridge subjected to a 75-year corrosion level applied to the entire system (ISO 9223; ISO 9224); corrosion has been identified as being the major cause of deterioration in steel bridges (AASHTO 2018), while 75 years corresponds to the design service life of a new bridge as per the Canadian Highway Bridge Design Code, CSA S6:19 (CSA 2019). The truss bridge is based off an existing structure built in 1930 and located in rural NB, Canada. Fig. 1 illustrates an FE model of the truss in SAP2000 where each of the members have been labeled; the height of the truss is 6.096 m with each bay measuring 5.22 m, and section properties for each member are summarized in Table 1.

2

5

3

4

21

20

19

18

1

6

15

16

14

17

13

8

9

10

12

7

11

Fig. 1. Truss structure based of existing bridge in rural NB built in 1930.

Table 1. Section properties associated with structural members from truss bridge shown in Fig. 1. Member Type Section Properties (inches) Top Chord – 2, 3, 4, 5 2 – 8 x 2 3/8 x 5/16 C @ 13.75 lb/ft spaced at 8 7/8 End Diagonal – 1, 6 2 – 8 x 2 3/8 x 3/8 C @ 16.25 lb/ft spaced at 8 7/8 Diagonal – 18, 19, 20, 21 8 x 6 1/2 M @ 30.5 lb/ft Vertical – 13, 14, 15, 16, 17 8 x 6 1/2 M @ 30.5 lb/ft Bottom Chord – 7, 8, 9, 10, 11, 12 8 x 6 1/2 M @ 30.5 lb/ft

To perform the evaluation, the member and local connection capacities were calculated following guidance from CSA S6:19 and the Manual for Bridge Evaluation (CSA 2019; AASHTO 2018); connection and member geometry were obtained from the existing drawings, while material properties were taken from CSA S6:19 (CSA 2019). Hinge definitions from ASCE 41-17 were used for member capacities, with simple brittle hinge definitions used for the connections (ASCE 2017). The member hinges were assigned at the middle of the member, and the connection hinges were assigned at the ends. SAP2000 was used to perform the progressive collapse simulations, and the bridge was pushed to collapse using a uniformly distributed load idealized as point loads applied to the bottom chord.