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Research Papers: Design and Analysis

# An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part II: Design Method

[+] Author and Article Information
Ming-De Xue, Keh-Chih Hwang, Zhi-Hai Xiang

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

Qing-Hai Du

China Ship Scientific Research Center, Wuxi, Jiangsu, 214082, P.R. China

The basic stress for internal pressure load is primary membrane stress and the counterparts for external nozzle load cases are equal or in proportion to the mean stresses transmitted through nozzle to the cutout in the shell.

In the Chinese code (13), the sizes of fillet welds are required as: $ws≥T/2$ and $wh≥t/2$. $ws$ and $wh$ are shown in Fig. 2.

J. Pressure Vessel Technol 132(3), 031207 (May 19, 2010) (8 pages) doi:10.1115/1.4001200 History: Received June 03, 2009; Revised January 17, 2010; Published May 19, 2010; Online May 19, 2010

## Abstract

A universal design method for pressurized cylindrical shells with attached nozzles subjected to external forces (moments) and internal pressure are presented, based on theoretical stress analysis. The applicable ranges of the presented design methods are extended to $ρ0=d/D≤0.9$ and $λ=d/(DT)1/2≤12$. As a first step of design, the required reinforcement thicknesses, both of the main shell and nozzle due to internal pressure, can be determined by the presented theoretical solutions. When the junction is subjected to external nozzle loads, the next step is to determine the absolute values of dimensionless longitudinal and circumferential, normal and shear, membrane and bending stresses in the shell at the junction subjected to internal pressure, and six external nozzle load components by reading out from a number of sets of curves calculated by the present theoretical method. Then the stress components at eight examination points are calculated and superimposed for the combined loads. Finally, the membrane and primary plus secondary stress intensities can be calculated, respectively, to meet the design criteria.

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## Figures

Figure 4

Reinforcement design curves (r/R=0.9)

Figure 2

(a) A model with fillet weld, (b) 3D FEM model, and (c) thin shell model

Figure 1

The basic mechanical model

Figure 9

(a) Curves VIc, kξm versus D/T, ρ0 due to Pyb(θ=90°, t/T=1.5); (b) curves VIb, kφb versus D/T, ρ0 due to Pyb(θ=90 deg, t/T=1.5)

Figure 10

Curves Va, kφm versus D/T, ρ0 due to Pxb(θ=0 deg,t/T=2.0)

Figure 11

Curves VIIa, kξφm versus D/T, ρ0 due to Pxb(θ=90 deg,t/T=2.0)

Figure 5

(a) Curves Ia, kφm versus D/T, ρ0 due to p(θ=0 deg,t/T=1); (b) curves Id, kξb versus D/T, due to p(θ=0 deg,t/T=1)

Figure 3

Reinforcement design curves (r/R=0.5)

Figure 6

(a) Curves IIg, kξm versus D/T, ρ0 due to pzb(θ=90 deg,t/T=0.5); (b) curves IIf, kφb versus D/T, ρ0 due to pzb(θ=90 deg, t/T=0.5)

Figure 7

(a) Curves IIIc, kξm versus D/T, ρ0 due to Mxb(θ=90 deg,t/T=1); (b) curves IIIb, kφb versus D/T, ρ0 due to Mxb(θ=90 deg,t/T=1)

Figure 8

(a) Curves IVa, kφm versus D/T, ρ0 due to Myb(θ=0 deg,t/T=0.7); (b) curves IVe, kξφm versus D/T, ρ0 due to Myb(θ=90 deg,t/T=0.7)

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