Simplified Analytical Method for Estimating the Resistance of Lock Gates to Ship Impacts

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left"></td><td align="center">Simulation 1</td><td align="center">Simulation 2</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left" rowspan="2">Gate 1</td><td align="center"><svg height="14.7875" id="M440" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 70.900002 14.7875" width="70.900002" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝑋</tspan>
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<text transform="matrix(1,0,0,-1,-62.07,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐸</tspan>
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<text transform="matrix(1,0,0,-1,-51.33,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
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<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="27.656635" y="0">5</tspan>
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</svg>m</td><td align="center"><svg height="14.7875" id="M441" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 70.900002 14.7875" width="70.900002" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-60.17)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑋</tspan>
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<text transform="matrix(1,0,0,-1,-62.07,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐸</tspan>
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<text transform="matrix(1,0,0,-1,-51.33,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="27.656635" y="0">5</tspan>
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</g>
</svg>m</td></tr><tr><td align="center"><svg height="14.6" id="M442" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 47.387501 14.6" width="47.387501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑌</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.26,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐸</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.52,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">8</tspan>
</text>
</g>
</g>
</svg>m</td><td align="center"><svg height="14.6" id="M443" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 66.925003 14.6" width="66.925003" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑌</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.26,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐸</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.52,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="18.291889" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="24.543388" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="27.66914" y="0">1</tspan>
</text>
</g>
</g>
</svg>m</td></tr><tr><td align="left" colspan="3"><hr/></td></tr><tr><td align="left" rowspan="2">Gate 2</td><td align="center"><svg height="14.7875" id="M444" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 70.900002 14.7875" width="70.900002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7875)">
<g transform="translate(72,-60.17)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑋</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.07,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐸</tspan>
</text>
<text transform="matrix(1,0,0,-1,-51.33,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="27.656635" y="0">5</tspan>
</text>
</g>
</g>
</svg>m</td><td align="center"><svg height="14.7875" id="M445" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 70.900002 14.7875" width="70.900002" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-60.17)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑋</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.07,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐸</tspan>
</text>
<text transform="matrix(1,0,0,-1,-51.33,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="27.656635" y="0">5</tspan>
</text>
</g>
</g>
</svg>m</td></tr><tr><td align="center"><svg height="14.7875" id="M446" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 59.099998 14.7875" width="59.099998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7875)">
<g transform="translate(72,-60.17)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑌</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.26,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐸</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.52,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="18.291889" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.417639" y="0">5</tspan>
</text>
</g>
</g>
</svg>m</td><td align="center"><svg height="14.7875" id="M447" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 74.737503 14.7875" width="74.737503" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7875)">
<g transform="translate(72,-60.17)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑌</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.26,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐸</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.52,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="18.291889" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="24.543388" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="27.66914" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="33.920639" y="0">5</tspan>
</text>
</g>
</g>
</svg>m</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Journal of Applied Mathematics

tab5

Table 5

Table 5: Simplified Analytical Method for Estimating the Resistance of Lock Gates to Ship Impacts 