Effect of stereotomy on the lower bound value of minimum thickness of semi-circular masonry arches
Effect of stereotomy on the lower bound value of minimum thickness of semi-circular masonry arches
复制标题
立体切割对半圆形砌体拱最小厚度下界值的影响
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
I. Sajtos
中科院分区：
文献类型：
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作者：
O. Gáspár;A. Sipos;I. Sajtos
在整个建筑史沿着，以最小的构件横截面来建造结构体系是一个强大的动力。本文研究了立体切割对由砌体制成的半圆形拱的最小厚度值的影响：砌体是一种抗拉强度可以忽略不计的材料。该拱以其中心线建模，荷载根据拱长指定给该中心线。在这里，而不是一些标量参数，如断裂角和位置的中间铰链的内弧面，立体分割的几何形状与一个连续的功能。立体相关的约束条件，从工程的角度来看，保持可行的结果，它也表明，他们是必不可少的适定约束优化问题。考虑极限状态分析、无限摩擦和无张力材料模型的假设，解析推导出最小厚度值的非零下限的必要条件。厚度与半径之比（t/R）的下限为t/R = 0.0819。一个数值方法来证明存在一个有效的立体切割的下限。多个可接受的立体切割模式在各种最小厚度值（高于下限），以证明合适的立体切割固定（T/R）的比例是远远不是唯一的，一般来说，即使是中间铰链的位置和破裂角可能会有所不同。
ABSTRACT Constructing structural systems with the minimal required cross section of its members was a strong motivation for progress whole along the history of building. This article investigates the effect of stereotomy on the minimum thickness value of a semi-circular arch made of masonry: a material with negligible tensile strength. The arch is modeled with its center line to which the loading is assigned according to arch length. Here, instead of some scalar parameters such as the rupture angle and the location of the middle hinge on the intrados, the geometry of the stereotomy is associated with a continuous function. Stereotomy-related constraints are introduced to keep the results feasible from an engineering point of view, and it is also demonstrated that they are essential for a well-posed constrained optimization problem. The necessary condition for a non-vanishing lower bound of minimum thickness values is derived analytically considering the assumptions of limit state analysis, infinite friction, and a no-tension material model. The lower bound thickness to radius ratio (t/R) is found to be t/R = 0.0819. A numerical method is introduced to demonstrate the existence of a valid stereotomy at the lower bound. Multiple admissible stereotomy patterns are presented at various minimum thickness values (higher than the lower bound) to demonstrate that suitable stereotomy for a fixed (t/R) ratio is far not unique—in general even the location of the middle hinge and the rupture angle might vary.