Pounding Effects in Simply Supported Bridges Accounting for Spatial Variability of Ground Motion: A Case Study

<table>Coherency function modulus obtained for different correlation levels corresponding to a set of 4 values of parameters <svg height="16.299999" id="M47" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 30.025 16.299999" width="30.025" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,12.013)"><path d="M457 332q0 -81 -41 -161.5t-105.5 -131.5t-129.5 -51q-46 0 -79 30.5t-33 86.5q0 18 7 51q18 95 46 187q6 19 6 33q0 7 -7 7q-24 0 -78 -64l-20 23q32 48 73 77t78 29q33 0 33 -46q0 -38 -10 -70q-28 -92 -39 -152q-7 -38 -7 -57q0 -78 69 -78q68 0 118 75.5t50 194.5
q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D463"></path></g>
<g transform="matrix(.012,0,0,-.012,8.225,16.088)"><path d="M352 391q0 -31 -27 -44q-14 -7 -24 6q-39 48 -84 48q-23 0 -39.5 -15t-16.5 -40q0 -43 73 -90q49 -32 70 -58t21 -57q0 -58 -62 -105.5t-129 -47.5q-40 0 -75.5 25t-35.5 52q0 28 32 46q7 4 15 3t11 -6q19 -31 48.5 -50.5t54.5 -19.5q34 0 54 19.5t20 42.5q0 43 -65 81
q-97 56 -97 123q0 50 51 96q19 17 58 32.5t62 15.5q37 0 61 -18t24 -39z" id="x1D460"></path></g>
<g transform="matrix(.017,0,0,-.017,13.313,12.013)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g><g transform="matrix(.017,0,0,-.017,20.316,12.013)"><path d="M545 106q-67 -118 -134 -118q-24 0 -40 37.5t-30 129.5h-2q-47 -72 -103 -119.5t-108 -47.5q-47 0 -76 45.5t-29 119.5q0 113 85 204t174 91q47 0 70 -33.5t43 -119.5h3q32 47 80 140l55 13l10 -9q-47 -80 -138 -201q17 -99 27.5 -136t22.5 -37q23 0 69 61zM333 204
q-14 98 -31 149.5t-50 51.5q-49 0 -94 -70t-45 -164q0 -55 15.5 -86t40.5 -31q70 0 164 150z" id="x1D6FC"></path></g>
</svg> e <svg height="14.675" id="M48" style="vertical-align:-5.56917pt" version="1.1" viewbox="0 0 26.237499 14.675" width="26.237499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,7.675)"><path d="M457 332q0 -81 -41 -161.5t-105.5 -131.5t-129.5 -51q-46 0 -79 30.5t-33 86.5q0 18 7 51q18 95 46 187q6 19 6 33q0 7 -7 7q-24 0 -78 -64l-20 23q32 48 73 77t78 29q33 0 33 -46q0 -38 -10 -70q-28 -92 -39 -152q-7 -38 -7 -57q0 -78 69 -78q68 0 118 75.5t50 194.5
q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D463"></path></g>
<g transform="matrix(.012,0,0,-.012,8.225,11.763)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5
t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g><g transform="matrix(.012,0,0,-.012,13.222,11.763)"><path d="M169 380l92 53q26 16 49 16q80 0 128.5 -56t48.5 -133q0 -108 -72.5 -180.5t-176.5 -91.5q-38 1 -69 18v-131q0 -57 13 -70t71 -18v-27h-236v27q49 5 61 17t12 61v452q0 48 -9.5 58.5t-56.5 16.5v24q66 11 145 43v-79zM169 346v-270q37 -39 94 -39q63 0 101.5 50
t38.5 134q0 78 -38.5 123t-95.5 45q-45 0 -100 -43z" id="x70"></path></g><g transform="matrix(.012,0,0,-.012,19.327,11.763)"><path d="M169 380l92 53q26 16 49 16q80 0 128.5 -56t48.5 -133q0 -108 -72.5 -180.5t-176.5 -91.5q-38 1 -69 18v-131q0 -57 13 -70t71 -18v-27h-236v27q49 5 61 17t12 61v452q0 48 -9.5 58.5t-56.5 16.5v24q66 11 145 43v-79zM169 346v-270q37 -39 94 -39q63 0 101.5 50
t38.5 134q0 78 -38.5 123t-95.5 45q-45 0 -100 -43z" id="x70"></path></g>
</svg> (formulation by Luco and Wong).</table>

Advances in Civil Engineering

fig10

Figure 10

Figure 10: Pounding Effects in Simply Supported Bridges Accounting for Spatial Variability of Ground Motion: A Case Study 