Ultimate Seismic Resistance Capacity for Long Span Lattice Structures under Vertical Ground Motions

<table>Rise amount <svg height="12.4375" id="M123" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 13.7625 12.4375" width="13.7625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M452 333q0 -82 -46 -164t-116 -128q-81 -53 -158 -53q-26 0 -51 13t-37 32q-26 41 -6 134l91 431q7 40 2.5 47t-34.5 7h-33l2 25q36 4 72.5 13t58.5 15.5t28 6.5q10 0 4 -29l-91 -391h2q65 77 130 116.5t105 39.5q36 0 56.5 -32t20.5 -83zM365 316q0 76 -35 76
q-31 0 -93.5 -49t-107.5 -110q-12 -37 -17 -70q-9 -65 12 -96.5t59 -31.5q31 0 56 14q53 29 89.5 105t36.5 162z" id="x1D44F"></path></g>
</svg>and <svg height="17.700001" id="M124" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 27.9375 17.700001" width="27.9375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,13.55)"><path d="M600 0h-557v24l268 633l28 8l261 -641v-24zM497 50l-194 489l-196 -489h390z" id="x394"></path></g><g transform="matrix(.017,-0,0,-.017,10.959,13.55)"><path d="M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5
l14 20.5t15 23.5t13.5 21.5l29 -10q-52 -129 -71 -163h-500l6 28q66 4 83 17.5t28 73.5l77 409q11 61 -0.5 75.5t-78.5 18.5l10 28h467z" id="x1D438"></path></g>
<g transform="matrix(.012,-0,0,-.012,21.7,5.388)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g>
</svg>/<svg height="18.4375" id="M125" style="vertical-align:-3.86845pt" version="1.1" viewbox="0 0 22.125 18.4375" width="22.125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.012,-0,0,-.012,.062,17.638)"><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,-.017,5.15,13.55)"><path d="M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5
l14 20.5t15 23.5t13.5 21.5l29 -10q-52 -129 -71 -163h-500l6 28q66 4 83 17.5t28 73.5l77 409q11 61 -0.5 75.5t-78.5 18.5l10 28h467z" id="x1D438"></path></g>
<g transform="matrix(.012,-0,0,-.012,15.888,5.388)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g>
</svg>,  and  <svg height="15.65" id="M126" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 33.837502 15.65" width="33.837502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.362)"><path d="M600 0h-557v24l268 633l28 8l261 -641v-24zM497 50l-194 489l-196 -489h390z" id="x394"></path></g><g transform="matrix(.017,-0,0,-.017,10.959,11.362)"><path d="M1004 650l-6 -29q-54 -6 -71 -19.5t-51 -74.5l-271 -539h-33l-98 506h-3l-258 -506h-30l-78 532q-10 67 -21.5 80t-66.5 21l6 29h241l-8 -29l-26 -5q-34 -6 -41 -16t-3 -47l59 -425h4l251 510h31l102 -510h2q150 299 198 423q14 40 8.5 48.5t-47.5 16.5l-28 5l7 29h231z
" id="x1D44A"></path></g>
<g transform="matrix(.012,-0,0,-.012,28.225,15.45)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g>
</svg>/<svg height="15.4" id="M127" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 28.025 15.4" width="28.025" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.012,-0,0,-.012,.062,15.187)"><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,-.017,5.15,11.112)"><path d="M1004 650l-6 -29q-54 -6 -71 -19.5t-51 -74.5l-271 -539h-33l-98 506h-3l-258 -506h-30l-78 532q-10 67 -21.5 80t-66.5 21l6 29h241l-8 -29l-26 -5q-34 -6 -41 -16t-3 -47l59 -425h4l251 510h31l102 -510h2q150 299 198 423q14 40 8.5 48.5t-47.5 16.5l-28 5l7 29h231z
" id="x1D44A"></path></g>
<g transform="matrix(.012,-0,0,-.012,22.412,15.187)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g>
</svg>, <svg height="18.5625" id="M128" style="vertical-align:-5.73167pt" version="1.1" viewbox="0 0 35.974998 18.5625" width="35.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path d="M600 0h-557v24l268 633l28 8l261 -641v-24zM497 50l-194 489l-196 -489h390z" id="x394"></path></g><g transform="matrix(.017,-0,0,-.017,10.959,11.363)"><path d="M1004 650l-6 -29q-54 -6 -71 -19.5t-51 -74.5l-271 -539h-33l-98 506h-3l-258 -506h-30l-78 532q-10 67 -21.5 80t-66.5 21l6 29h241l-8 -29l-26 -5q-34 -6 -41 -16t-3 -47l59 -425h4l251 510h31l102 -510h2q150 299 198 423q14 40 8.5 48.5t-47.5 16.5l-28 5l7 29h231z
" id="x1D44A"></path></g>
<g transform="matrix(.012,-0,0,-.012,28.225,15.45)"><path d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" id="x1D45D"></path></g>
</svg>/<svg height="19.049999" id="M129" style="vertical-align:-6.32408pt" version="1.1" viewbox="0 0 30.1625 19.049999" width="30.1625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.012,-0,0,-.012,.062,15.187)"><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,-.017,5.15,11.112)"><path d="M1004 650l-6 -29q-54 -6 -71 -19.5t-51 -74.5l-271 -539h-33l-98 506h-3l-258 -506h-30l-78 532q-10 67 -21.5 80t-66.5 21l6 29h241l-8 -29l-26 -5q-34 -6 -41 -16t-3 -47l59 -425h4l251 510h31l102 -510h2q150 299 198 423q14 40 8.5 48.5t-47.5 16.5l-28 5l7 29h231z
" id="x1D44A"></path></g>
<g transform="matrix(.012,-0,0,-.012,22.412,15.925)"><path d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" id="x1D45D"></path></g>
</svg>.</table>

Journal of Structures

fig10

Figure 10

Figure 10: Ultimate Seismic Resistance Capacity for Long Span Lattice Structures under Vertical Ground Motions 