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RESEARCH PAPERS

# A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments

[+] Author and Article Information
M. D. Xue, D. F. Li, K. C. Hwang

Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, People’s Republic of China

J. Pressure Vessel Technol 127(4), 357-368 (Jun 05, 2005) (12 pages) doi:10.1115/1.2042471 History: Received March 16, 2004; Revised June 05, 2005

## Abstract

A theoretical solution is presented for cylindrical shells with normally intersecting nozzles subjected to three kinds of external branch pipe moments. The improved double trigonometric series solution is used for the particular solution of main shell subjected to distributed forces, and the modified Morley equation instead of the Donnell shallow shell equation is used for the homogeneous solution of the shell with cutout. The Goldenveizer equation instead of Timoshenko’s is used for the nozzle with a nonplanar end. The accurate continuity conditions at the intersection curve are adopted instead of approximate ones. The presented results are in good agreement with those obtained by tests and by 3D FEM and with WRC Bulletin 297 when $d∕D$ is small. The theoretical solution can be applied to $d∕D⩽0.8$, $λ=d∕DT⩽8$, and $d∕D⩽t∕T⩽2$ successfully.

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## Figures

Figure 14

The stress concentration factors versus λ and t∕T(ρ0=0.7). (a) Kyb for in-plane bending moment Myb; (b) Kxb for out-of-plane bending moment Mxb; (c) Kzb for torsion moment Mzb.

Figure 13

The comparison of dimensionless resultant forces and moments in the main shell with WRCB 297 due to Mxb. (a) d∕t=30, t∕T=1, due to Mxb; (b) d∕t=100, t∕T=1, due to Mxb.

Figure 12

The comparison of dimensionless resultant forces and moments in the main shell with WRCB 297 due to Myb. (a) d∕t=30, t∕T=1, due to Myb; (b) d∕t=100, t∕T=1, due to Myb.

Figure 11

Distribution of stress ratios along the line θ=90deg of the model d∕D=0.8 subjected to Mxb. (a) On the outer surface; (b) on the inner surface.

Figure 10

Distribution of stress ratios along the line θ=0deg of the model d∕D=0.8 subjected to Myb. (a) On the outer surface; (b) on the inner surface.

Figure 9

Maximum principal stress ratios around the junction of ORNL-1 subjected to Mzb

Figure 8

Distribution of k along the line θ=60deg on the outer surface of Model ORNL-1 subjected to Mzb

Figure 7

Maximum principal stress ratios around the junction of ORNL-1 subjected to Mxb

Figure 6

Distribution of k along the line θ=90deg on the outer surface of Model ORNL-1 subjected to Mxb

Figure 5

Maximum principal stress ratios around the junction of ORNL-1 subjected to Myb

Figure 4

Distribution of k along the line θ=0deg on the outer surface of Model ORNL-1 subjected to Myb

Figure 3

The analyzed models of the particular solution in the load case Mxb. (a) The distributed force system qz equivalent to Mxb; (b) the distributed force qn used by Bijlaard; (c) the area on the developed surface of the main shell where is applied the distributed forces.

Figure 2

Mxb load case is decomposed into two categories (b) and (c): (a) the basic model; (b) simply supported main shell under branch pipe moment Mxb; and (c) main shell subjected to torsion moment Mxb∕2.

Figure 1

Calculated model and five coordinate systems

## Errata

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