ABSTRACT
The supports for pressure vessels can be of various types including lug support, support skirts, and saddle supports.
This is a common means of support for vertical vessels that are mounted on I-beams. Such a support is shown in Figure 10.1. If the vessel is made of carbon steel, the lugs may be directly welded to the vessel. Bijlaard’s classic assessment of local stresses in shells due to loadings on an attached lug is particularly noteworthy.1 That analysis forms the basis for the Welding Research Council Bulletin 1072 which has been used extensively for the design of lug attachments to pressure vessels. The method consists of determining the stresses in the vicinity of a support lug of height 2C1 and width 2C2 as shown in Figure 10.2. The maximum primary plus secondary stress in the shell wall is given as a combination of direct stress due to the thrust, W, bending stress due to longitudinal moment, ML, bending stress due to circumferential moment, MC, and the torsional shear stress due to the twisting moment, MT, with appropriate coefficients. The earlier work by Bijlaard1 involves representing ML, MC, and MT, by double Fourier series, which enables one to obtain the stresses and deformations in the form of the series. In other words, the series is capable of representing a load with dimensions in both the circumferential, ’, and the longitudinal, x, directions:
Vessels:
Pr ¼ X1
Pn;m cosn cos mx
L
ð10:1Þ
where L is the length of the shell, the term Pn,m is the loading term. This representation is used for different forms of vessel loadings, where the direct and moment loadings are expressed as double Fourier series and introduced into the shell equations to obtain the values of stress resultants and displacements. In order to represent the patch load from the lug it is often necessary to have a large number of terms (typically about 200) in both the circumferential and axial directions. This approach has been used to draw up the curves presented in WRC 107.2 When the attachment contact face is not rectangular, but maybe circular or elliptical, the design codes attempt to resolve the geometry into a rectangular patch. Mirza and Gupgupoglu3 have studied stresses and displacements in circular cylindrical shells having square and rectangular lugs separated 90 apart along the circumferential direction. They have utilized a finite-element technique using 17-node doubly curved shell elements. For values of C1 ¼ C2 ¼ 0.1 D, and D/t 40 (where D is the mean diameter of the shell, and t the thickness) there seems to be a good agreement of results between References 2, 3, and 4. However, for smaller values of C1 and C2 (typically less than 0.05 D), large variations occur between the finite-element results3
and closed-form predictions of References 2 and 4. However in spite of the variations in predicting the magnitude of the maximum stresses the methods agree on the direction of the maximum stress.3
