0
Design and Analysis

# Limit Load Solutions for Cracked Elbows Subjected to Internal Pressure and In-Plane Bending

[+] Author and Article Information
C. Hari Manoj Simha1

AMEC NSS, 393 University Avenue, 4th Floor, Toronto, ON M5G 1E6, Canada

1

Present address: CANMET Materials, 183 Longwood Rd. South, Hamilton ON L89 0A5.

J. Pressure Vessel Technol 134(4), 041201 (Jul 09, 2012) (11 pages) doi:10.1115/1.4005867 History: Received September 19, 2010; Revised December 19, 2011; Online July 09, 2012; Published July 26, 2012

## Abstract

In this article, limit load solutions for cracked elbows containing through-wall and part through-wall axial and circumferential cracks under internal pressure and in-plane bending loading are presented. For elbows with axial cracks, limit pressure solutions are presented, and modifications to existing limit moment solutions are proposed. The foregoing limit pressure and limit moment solutions are used in conjunction with a novel interaction curve to obtain limit load solutions for elbows with axial cracks under combined pressure and moment loading. If the applied moment and pressure are within (outside) the envelope of the interaction curve, no failure (failure) is indicated. Furthermore, limit pressure and limit moment solutions for circumferentially cracked elbows are developed using the same interaction curve. Limit loads computed with the solutions presented in this work are compared with experimental results and the agreement is found to be within acceptable limits after accounting for the uncertainties in the experimental results.

<>

## Figures

Figure 1

Schematic of elbow geometry, loading, and nomenclature: θ = 0 is the cheek, θ = π/2 is the extrados, and θ = −π/2 is the intrados

Figure 2

Schematic of elbow with axial and circumferential cracks. (a), (b) Axial through-wall and part through-wall cracks. (c), (d) Circumferential through-wall and part through-wall cracks.

Figure 3

Definitions of limit load for experimental results and finite element analysis

Figure 4

Plot of relative uncertainty associated with limit pressures for elbows with through-wall axial cracks at intrados

Figure 5

Crack free elbow: internal pressure and in-plane bending moment. Comparison of interaction equation Eq. 6 and finite element results for limit loads of crack free elbows loaded by internal pressure and in-plane bending moment. Finite element results and the dashed line are from the article by Kim and Oh [8]. The dotted line is the envelope proposed by Konosu and Mukaimachi [20].

Figure 6

Figure 7

Section of pipe wall with semi-elliptical crack. The gray area is obtained by constructing the trapezoid, and is the effective load-bearing area. Schematic is similar to the one presented by Scarth and Merkle [27].

Figure 8

Axial part through-wall crack: pressure–moment interaction diagram. Triangles, squares, and circles are internal pressure loading, data from GE, Stuttgart from the ELBOWCK database [15], and the data of Duan [28]. Diamonds—in-plane bending moment, data are from Yahiaoui [14].

Figure 9

Circumferential through-wall crack: internal pressure loading. The squares are finite element analysis results and taken from Yahiaoui [2]. All of the cracks were at the intrados. The solid line is obtained from Eq. 16 and with σp  = σf .

Figure 10

Circumferential through-wall crack: pressure–moment interaction diagram. Open circles and triangles are moment data from Yahiaoui [14] and Chattopadhyay [3]. Filled squares are moment + pressure data from Ref. [29].

Figure 11

Circumferential part through-wall crack: internal pressure loading. The squares are finite element analysis results and taken from Yahiaoui [2]. The solid line is obtained from Eq. 18 and is for the deeper a/t = 0.75 crack. The dotted line is for the shallow a/t = 0.5 crack. All of the cracks were at the intrados.

Figure 12

Circumferential part through-wall crack: pressure–moment loading diagram. Filled squares are moment data from Yahiaoui [14]. Filled diamonds are moment + pressure data from Ref. [31].

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections