The maximum width calculation method for evaluating the geometrical compatibility of grid strut-tie model.Â This concept employed here originates from a rule stating that the overlaps of areas (or widths) of neighboring components are not allowed.

In thisÂ approach, the method employed in the 2-D grid strut-tie model approach is extended.Â Namely, in addition to the strut-tie model approaches of current design codes, the maximum cross-sectional areas of struts and ties are defined as the maximum areas that struts and ties can take without overlaps in a grid element.

The maximum cross-sectional area of a component of a grid element is determined by multiplying two maximum widths of the component evaluated on the componentâ€™s two orthogonal planes.Â For example,Â the maximum cross-sectional area of the x-directional component of length *l*_{x1} is determined by multiplying the z-directional maximum width *W _{HE}* and the y-directional maximum width

*W*.Â Here, the maximum width

_{VE}*W*is taken as 0.2

_{HE}*l*

_{z1}+0.2

*l*

_{z2}, whereÂ

*l*

_{z1}and

*l*

_{z2}Â are the lengths of the z-directional components connected to the ends of the x-directional component.Â In the same way, the maximum width

*W*is defined asÂ 0.2

_{VE}*l*

_{y1}+0.2

*l*

_{y2}, whereÂ

*l*

_{y1}and

*l*

_{y2}areÂ lengths of the y-directional components connected to the ends of the x-directional component.

The maximum cross-sectional area of an inclined plane component of a grid element is determined in the same manner.Â For example,Â the maximum cross-sectional area of the inclined plane component of x-directional lengthÂ *l*_{x1} in the xy-plane is determined by multiplying the maximum width *W _{IPE}* of the xy-plane and the maximum width

*W*Â of the plane orthogonal to the xy-plane.Â The maximum width

_{HEZ}*W*of the xz-plane areÂ taken as the length of theÂ perpendicular lines connecting the points (a, b, c, d),Â which are determined by considering the maximum widths of the neighboring horizontal and vertical elements.Â Following the methods,Â the maximum widthsÂ

_{IPE}*W*andÂ

_{IPE}*W*of the xy-plane and its orthogonal planes, respectively, are expressed as

_{HEZ}The cross-sectional area of an inclined space component that exists only in a 3-D grid element is defined as the area excluding all the cross-sectional areas of horizontal components, vertical components, and inclined plane components in a grid element. For example,Â the maximum cross-sectional area of the space component is determined by multiplying the maximum widthÂ *W _{IPE}* of the xz-plane and the maximum width

*W*of the yz-plane rotated about the y-axis. The maximum widthsÂ

_{ISE}*W*andÂ

_{IPE}*W*are expressed as

_{ISE}In the grid strut-tie model approach, a component of a grid element is assumed to fail if its maximum cross-sectional area is less than that required for carrying the cross-sectional force. To reflect more precisely the characteristics of the load transfer mechanism in a grid element, the modified maximum cross-sectional area of a component that is determined by considering the required cross-sectional areas of neighboring components (instead of the maximum cross-sectional area defined above) is used for examining the geometrical compatibility.Â Here, the modified maximum cross-sectional area of a component is determined by multiplying two modified maximum widths of the component in two orthogonal planes.

Reference

- Kim, B. H. and Yun, Y. M. (2014) Strut-Tie Model Approach Associated with 3-Dimensional Grid Elements for Design of Structural Concrete – (I) Proposal of Approach,
*Journal of the Korean Society of Civil Engineers*, Vol. 34, No. 2, pp. 425-436.

Email : astruttie@aroad.co.kr

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