PSI - Issue 52

282 Govardhan Polepally et al. / Procedia Structural Integrity 52 (2024) 280–292 Govardhan Polepally/ Structural Integrity Procedia 00 (2019) 000 – 000 ሺ ሻ ൌ ̅ ሺ ሻ ሺ ሻ ሺ ሻ (1) Š‡ ”‡•’‘•‡ ƒ† ‹’—– •’‡ –”ƒŽ †‡•‹–› ˆ— –‹‘• ƒ”‡ †‡‘–‡† ƒ• ›› (jω) and G šš (jω), respectively. The Frequency Response Function (FRF) matrix is represented by H(jω), where T denotes the complex conjugate ‘” –”ƒ•’‘•‡Ǥ › ‡šƒ‹‹‰ –Š‡ •’‡ –”ƒŽ †‡•‹–› ’Ž‘– –Šƒ– •Š‘™• ˜‡”•—• ˆ”‡“—‡ ›ǡ ‘‡ ƒ ƒ’’”‘š‹ƒ–‡ the mode shape φ by analyzing the PSD function near its peak, as well as the singular vectors for the ˆƒ””‡‘“——‡† –›Š ‡Ž ‹  ‡ • • — ”ˆ —” ‘ — –‹ †‘ ‹  ‰’ –‡Šƒ‡ •• ƒ ƒ ‡ ’„‡ ‡ƒ  —Ǥ • ‡Š†‡ – ‘‹  ‰‡Ž •‡– ‹ ‡ ƒ‰ –”‡‡ ‡– Š‘ ‡ˆ ” ‡ƒ ‡– —†”‘ƒŽ ˆሺ” ‡ “ — ‡ ሻ †›‡ ƒ•‹ –†› ˆ†—ƒ–’‹ ‘‹ ‰ ‘ „ˆ ‘– ”ƒ ‹ – Š‡ †‡ ‘””‡•’‘†‹‰ ‘†‡ •Šƒ’‡•Ǥ 3.2. Stochastic Subspace Identification (SSI) SSI is a technique used for identifying operational modal parameters, which operates directly on time-domain data, eliminating the need for converting them to correlations or spectra. This approach is particularly well-suited for output-only analysis (Peeters, B., et al 2000, Londono, N. A 2004). ȗ ̈ ሺ–ሻ൅ ȗ ̇ ሺ–ሻ൅ȗ—ሺ–ሻ ൌ ˆሺ–ሻ ൌ ”ȗ’ሺ–ሻ (2) The system comprises mass, damping, and stiffness matrices denoted by M, C, and K, respectively. Additionally, the excitation force is represented by f(t), while the displacement vector at continuous time t is denoted by u(t). To factorize the force vector f(t), it is split into a matrix r that describes the inputs in space and a vector u(t). 4. Case study 4.1. Bridge details The study focused on a 93-year-old rail composite bridge (Fig. 1) that is a part of the extensive Indian railway network. The bridge is made up of 44 steel girders resting on 43 stone masonry piers and two end abutments, with a total length of 1.2 km. The steel girders are 24.4 m in length and are supported by masonry piers measuring 13 m in height. Fig.1 gives the bridge overview and geometric details of the bridge can be seen Fig. 2 and Fig. 3. The load bearing system of the bridge transfers the load to the piers via simply supported beam action, with the piers made of stone masonry and supported by riveted plate girders. 3

Fig. 1. Different views of masonry bridge (a) Complete masonry bridge; (b) Steel girders; (c) Side elevation of masonry piers; (d) I girder with bearing ;(e) Steel box girder with cross-bracings.