Virtual Crotch Plate

Abstract

Crotch-plate design has become an exercise in reading curves and/or meticulously solving equations, rather than providing a design with a substantial understanding of the interaction between crotch-plates and the connecting pipeline. This is a result of technology available in the early 1900 s where the bulk of today's standards originated. Without a substantial understanding of the mechanics involved, the engineer does not have the means to provide a refined design. However, through the use of modern computing, crotch-plate design has become faster, easier and more comprehensive. By the use of curves and equations, Blair and Swanson of the 40 s and 50 s, respectively, have provided a means to conservatively size crotch-plates for many applications. The process typically begins by sizing plates with nomographs; curves based on empirical data obtained from a small diameter pipeline. The designer, if he chooses, may then progress to solving structural determinate equations for the structurally indeterminate crotch-plate system. Unfortunately, as with nomographs, this also only provides a portion of the real picture. However, by using the modern personal computer and commercially available 3-D finite element (FE) software, understanding of structural interaction is greatly improved, calculations are efficient, and refinement is achieved. This method was applied to the 4.3 m (14 ft) fittings of the P-l Pumping Plant at the Diamond Valley Lake located near Hemet, California. The subject analysis method pursues the use of both the 3-D FE and traditional numerical methods, while limiting the use of nomographs. Although FE is the author's choice for designing crotch-plates, the traditional method is maintained due to its reasonable accuracy and availability. Even though stresses and deflections may be obtained through traditional methods, they only provide an understanding of the structural interaction problem allowed by the limiting assumptions of the governing equations. Generally, understanding of the three-dimensional structure is confined to a two-dimensional system. Presented in this paper is an explanation of three-dimensional stresses as they relate to both global and local deflections. Design for plastic behavior is given and shown to be present through traditional methods. A discussion is provided describing why traditional calculations are conservative, and an outline is given describing the pitfalls to avoid when modeling with the 3-D FE method.