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RESEARCH PAPERS

# Theoretical Stress Analysis of Intersecting Cylindrical Shells Subjected to External Forces on Nozzle

[+] Author and Article Information
Ming-De Xue1

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R.Chinaxuemd@mail.tsinghua.edu.cn

Qing-Hai Du, Dong-Feng Li, Keh-Chih Hwang

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R.China

1

Corresponding author.

J. Pressure Vessel Technol 128(1), 71-83 (Oct 18, 2005) (13 pages) doi:10.1115/1.2138065 History: Received August 25, 2005; Revised October 18, 2005

## Abstract

The stress analysis based on thin shell theory is presented for a cylindrical shell with a normally intersecting nozzle subjected to three kinds of branch pipe forces, which are tension and two shear forces. The basic mechanical models for the three load cases are presented in order to obtain the solutions independent of the length of the main shell and branch pipe. The applicable range of the present solution is expanded up to $d∕D⩽0.8$ and $λ=d∕DT⩽12$ by means of the accurate cylindrical shell equations and continuity conditions and the improved numerical method. The theoretical results are verified by test and three-dimensional (3D) finite element method (FEM) results. The maximum stress for tension force case are in good agreement with WRC Bulletin No. 297 when $λ$ is small. The comparison between the present results and WRC Bulletin No. 107 shows that the latter needs improvement.

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## Figures

Figure 1

(a) Five coordinate systems; (b) six kinds of branch pipe loads

Figure 3

Decomposition for load case Pxb. (a) Model (a) for Pxb; (b) Basic model (b) for Pxb; (c) Model (c) for Pxb.

Figure 4

Decomposition for load case Pyb. (a) Model (a) for Pyb; (b) Basic model (b) for Pyb; (c) Model (c) for Pyb.

Figure 7

Branch pipe subjected to external loads

Figure 8

A main shell subjected to branch pipe forces

Figure 9

The analyzed mechanical model of the particular solution for main shell

Figure 10

Variation of dimensionless stresses for the ORNL-1 Model subjected to Pzb. (a) k at θ=90° on the outer surface; (b) k at θ=90° on the inner surface; (c) maximum principal stress ratios on the nozzle around the junction.

Figure 19

The dimensionless shear stresses in the main shell subjected to branch pipe shear force Pyb (t∕T=2, τ0=Pyb∕πrT)

Figure 2

Decomposition for load case Pzb. (a) Model (a) for Pzb; (b) Basic model (b) for Pzb; (c) Model (c) for Pzb.

Figure 5

The decomposition of basic model for Pzb (Case 1). (a) Basic model for Case 1; (b) Categor 1A; (c) Category 1B.

Figure 6

The decomposition of basic model for Pyb (Case 4). (a) Basic model for Case 4; (b) Category 4A; (c) Category 4B.

Figure 11

Variation of dimensionless stresses for the ORNL-1 Model subjected to Pxb. (a) k at θ=0° on the outer surface; (b) k at θ=0° on the inner surface; (c) maximum principal stress ratios on the nozzle around the junction.

Figure 12

Variation of dimensionless stresses for the ORNL-1 Model subjected to Pyb. (a) k at θ=90° on the outer surface; (b) k at θ=90° on the inner surface; (c) maximum principal stress ratios on the nozzle around the junction.

Figure 13

Distribution of k at θ=90deg on the outer and inner surfaces of the Basic Model subjected to Pzb with parameters d∕D=0.8, D∕T=225, t∕T=1(σ0=Pzb∕2πrT)

Figure 14

Comparison of k of the Basic Model subjected to Pxb with parameters d∕D=0.8, D∕T=225, t∕T=1(τ0=Pxb∕πrT). (a) distribution of k at θ=0° on the outer surfaces; (b) distribution of kmax at Γ on the main shell.

Figure 15

Comparison of k at θ=90deg of the Basic Model subjected to Pyb with parameters d∕D=0.8, D∕T=225, t∕T=1(τ0=Pyb∕πrT)

Figure 16

The comparison of dimensionless resultant forces and moments at the junction of the main shell for case 1 (d∕t=50, t∕T=2)

Figure 17

The dimensionless stress intensities for branch pipe extension Pzb (t∕T=2, σ0=Pzb∕2πrT)

Figure 18

The dimensionless shear stresses in the main shell subjected to branch pipe shear force Pxb (t∕T=2, τ0=Pxb∕πrT)

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