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

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left">Property</td><td align="center">Notation</td><td align="center">Value</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left">Density</td><td align="center"><span style="width: 7.9749999px;"><svg height="9.875" id="M417" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.9749999 9.875" width="7.9749999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜌</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><svg height="11.1" id="M418" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 33.987499 11.1" width="33.987499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="18.754499" y="0">0</tspan>
</text>
</g>
</g>
</svg>kg/m<sup>3</sup></td></tr><tr><td align="left">Poisson’s ratio</td><td align="center"><span style="width: 7.9749999px;"><svg height="7.2375002" id="M419" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 7.9749999 7.2375002" width="7.9749999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.2375)">
<g transform="translate(72,-66.21)">
<text transform="matrix(1,0,0,-1,-71.95,66.37)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜈</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center">
												0.33
											</td></tr><tr><td align="left">Yield stress</td><td align="center"><span style="width: 14.6125px;"><svg height="10.875" id="M420" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 14.6125 10.875" width="14.6125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.875)">
<g transform="translate(72,-63.3)">
<text transform="matrix(1,0,0,-1,-71.95,66.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜎</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.24,63.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><svg height="10.9125" id="M421" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 26.174999 10.9125" width="26.174999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">0</tspan>
</text>
</g>
</g>
</svg>MPa</td></tr><tr><td align="left">Young’s modulus</td><td align="center"><span style="width: 19.950001px;"><svg height="14.2375" id="M422" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 19.950001 14.2375" width="19.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐸</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.02,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑌</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><svg height="10.9125" id="M423" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 52.224998 10.9125" width="52.224998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="20.829998" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="27.081497" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="33.332996" y="0">0</tspan>
</text>
</g>
</g>
</svg>MPa</td></tr><tr><td align="left">Tangent modulus</td><td align="center"><span style="width: 19.674999px;"><svg height="14.2375" id="M424" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 19.674999 14.2375" width="19.674999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐸</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.02,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑇</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><svg height="10.9125" id="M425" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 33.987499 10.9125" width="33.987499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="18.754499" y="0">8</tspan>
</text>
</g>
</g>
</svg>MPa</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Useful properties for defining the material law of steel.

Journal of Applied Mathematics

tab4

Table 4

Table 4: Simplified Analytical Method for Estimating the Resistance of Lock Gates to Ship Impacts 