pressure vessel

STATIC STRUCTURAL ANALYSIS OF BOILER SHELL WITH RIVETED JOINTS USING ANSYS

Department of Mechanical Engineering, BEC, Bagalkot. Page 1

I. INTRODUCTION

The pressure vessels (i.e. cylinders or tanks) are used to store fluids under pressure. The fluid

being stored may undergo a change of state inside the pressure vessel as incase of steam boilers

or it may combine with other reagents as in a chemical plant. The pressure vessels are designed

with great care because rupture of a pressure vessel means an explosion which may cause loss of

life and property. The material of pressure vessels may be brittle such as cast-iron, or ductile

such as mild steel. When a thin cylindrical shell is subjected to an internal pressure, it is likely to

fail in the following two ways:

1. It may fail along the longitudinal section (i.e. circumferentially) splitting the cylinder into two

troughs, as shown in Fig. 1(a).

2. It may fail across the transverse section (i.e. longitudinally) splitting the cylinder into two

cylindrical shells, as shown in Fig. 1(b).

Figure 1(a) Failure of cylindrical shell Figure 1(b) Failure of cylindrical shell

along longitudinal section. along the transverse section.

Thus the wall of a cylindrical shell subjected to an internal pressure has to withstand tensile

stresses of the following two types:

(a) Circumferential or hoop stress, and

(b) Longitudinal stress.



CIRCUMFERENTIAL OR HOOP STRESS (σH):

Consider a thin cylindrical shell subjected to an internal pressure as shown in Figure. 2 (a) and

(b). Tensile stress acting in a direction tangential to the circumference is called Circumferential

or Hoop Stress.

Figure 2(a) View of Shell Figure 2(b) Cross Section of Shell

Let, p= Intensity of internal pressure,

d= Internal diameter of the cylindrical shell,

t = Thickness of the cylindrical shell, and

σH= Circumferential or hoop stress.

l = Length of the cylindrical shell

The Hoop stress is given by,

σH=�∗�

�� (1)

LONGITUDINAL STRESS (σL):

Consider a closed thin cylindrical shell subjected to an internal pressure as shown in Fig. 3 (a)

and (b). Tensile stress acting in the direction of the axis is called Longitudinal Stress.



Figure 3(a) View of Shell. Figure 3(b)Cross Section of Shell.

The Longitudinal stress is given,

σL=�∗�

�� (2)

The longitudinal joint bears hoop stress (σH) and circumferential joint bears longitudinal

stress (σL). As σH = 2 ( σL), the longitudinal joint will have to be two times as strong as

circumferential joint[1]. Rivets are used to make permanent fastening between the plates

such as in bridges, tanks and boiler shells. The riveted joints are widely used for joining light

metals. The boiler and pressure vessels are cylindrical in shape and withstand high

internal pressure. Steel plates of only particular lengths and widths are available. Hence

whenever larger size cylinder is required a number of plates are connected. This is achieved by

using riveting in circumferential and longitudinal directions as shown in figure 4. The

longitudinal joint is called Butt Riveting and the circumferential joint is called as Lap Riveting

[2].

Figure 4.



II. LITERATURE SURVEY

Farah Kamil Abid Muslim and Dr. Essam L. Esmail developed a software with the objective

of their work as to establish software programs for designing and analyzing rivets for boiler

shells as an example to use rivets in industry [3].

David Heckman studied finite element analysis of pressure vessel using finite element analysis

(FEA) a practical tool in the study of pressure vessels, especially in determining stresses in local

areas such as penetrations, O-ring grooves and other areas difficult to analyze by hand. His

project set out to explore applicable methods using finite element analysis in pressure vessel

analysis. Having tested three dimensional, symmetric and axis symmetric models, the

preliminary conclusion is that finite element analysis is an extremely powerful tool that offer

faster run times and less error [4].

Nidhi Dwivedi and Veerendra Kumar, showed burst pressure prediction of pressure vessel

using FEA. They proposed various types of finite element methods used for the

calculation of burst strength of pressure vessel [5].

Faisal Aman , S. Hossein Cheraghi , Krishna K. Krishnan and Hamid Lankarani studied

the impact of riveting sequence, rivet pitch, and gap between sheets on the quality of riveted lap

joints using finite element method [6].

S. Hossein Cheraghi studied the effect of variations in the riveting process on the quality of

riveted joints [7].

Elzbieta Szymczyk, Jerzy Jachimowicz, Grzegorz Sławinski and Agnieszka Derewonkoa

studied the Influence of technological imperfections on residual stress fields in riveted joints [8].

A number of analyses have been performed on thin pressure vessels and riveted joints. But static

structural analysis of boiler shell with riveted joints(which is designed on the basis of thin

pressure vessel theory) using ANSYS has not been studied much. By using finite element

method, a stress analysis has been carried out under the application of pressure at the

inner surface of boiler shell. Using the two materials, structural steel and aluminum alloy,

stress values have been compared for same working conditions.



III. OBJECTIVES OF THE PRESENT STUDY

The objective of the present paper is:-

1. To model the boiler shell with riveted joints.

2. To import the modeled geometry to FEA software and carry out the stress analysis.

3. To determine the stresses(Maximum Principal, Minimum Principal, Von-Mises,

Maximum Shear) theoretically.

4. To obtain the stresses using FEA software.

5. To compare the obtained theoretical and FEA results.

6. To carry out the stress analysis with Aluminum Alloy for same working conditions.

7. To compare the obtained FEA results of Structural Steel and Aluminum Alloy



IV. PROBLEM MODELING

A double riveted lap joint has been analyzed. Geometry of the present problem is:

Diameter of the cylinder = 150mm.

Applied internal pressure = 10N/mm2.

Pitch of rivets = 105mm.

Thickness of cylinder = 10mm.

Hoop stress σH =�∗�

�� =

��∗��

�∗�� =75 N/mm2.

Longitudinal stress σL=�∗�

�� =

��∗��

�∗�� = 37.5 N/mm2.

Maximum Principal Stress (σ1) = 37.5 N/mm2.

Minimum Principal Stress (σ2) = 10N/mm2.

Von Mises Stress (σo) = [{(σ1- σ2)2+ (σ2- σ3)

2+ (σ3-σ1)2}/2]0.5

=33.63 N/mm2.

Maximum Shear Stress = (σ1- σ2)/2 = 13.75 N/mm2.



The problem is modeled in CATIA V5 and imported to ANSYS workbench as shown in Figure

5.

Figure 5. Geometry of boiler shell with riveted joints using symmetry.

The cylinder is subjected to internal pressure of 10 N/mm2 and the boundary condition is as

shown in Figure 6

Figure 6. Applied displacement supports.



Structural steel and Aluminum alloy have been used which are ductile in nature. The following

table shows the material property.

Table 1: Material Property of Structural Steel and Aluminum Alloy for Boiler Shell.

Property Structural Steel Aluminum Alloy

Young's Modulus, (E) 2×105MPa 7.1×104MPa

Poisson's Ratio 0.30 0.33

Tensile Ultimate Strength 460MPa 310MPa

Tensile Yield Strength 250MPa 280MPa

Compressive Yield Strength 250MPa 280MPa

Density 7850kg/m3 2770kg/m3

Behavior Isotropic Isotropic

.



V. RESULTS AND DISCUSSIONS

The Figure 7 shows the minimum principal stress at internal surface which is 9.83N/mm2 which

is in close agreement with applied pressure at inner surface.

Figure 7 Minimum principle stresses for each element in the Boiler Shell.

The Figure 8 shows the maximum principle stress which is found to be 35.747 N/mm2 which is

nearly close agreement with analytical value of 37.5 N/mm2.

Figure 8 Maximum principle stresses for each element in the boiler shell



The following Figure 9 shows the equivalent Von-Mises stress which is found to be

36.31N/mm2, which is at internal surface as shown by red color this includes local stress.

Excluding local stress its value is 32.27N/mm2 which is in the close agreement with

33.63N/mm2 (analytical value).

Figure 9 Equivalent (Von-Mises) stress for each element in the boiler shell

The Figure 10 shows the maximum shear stress which is 20.919N/mm2

Figure 10 Maximum shear stress for each element in the boiler shell.



The Figure 11 shows the total deformation

Figure 11 Total deformations for each element in the boiler shell.

The following Table 2 shows the comparison between analytical and FEA results.

Table 2: Comparison of Theoretical Results with FEA Software Results.

Sl.No. Stress Theoretical Results

(N/mm2)

FEA Results

(N/mm2) (Excluding

local stress)

1. Maximum

principle

stress

37.5 35.747

2. Minimum

principle

stress

10 9.823

3. Von-Mises

stress

33.63 32.278

4. Maximum

shear stress

13.75 18.598



Figures 12-16 show analysis of boiler shell with riveted joints using aluminum alloy.

Figure 12 Maximum principle stresses for each element in the boiler shell for aluminum alloy

Figure 13 Minimum principle stresses for each element in the boiler shell for aluminum alloy



Figure 14 Equivalent (Von- Mises) Stress for each element in t he boiler shell for aluminum

alloy

Figure 15 Maximum shear stress for each element in the boiler shell for Aluminum alloy.



Figure16 Total deformation for each element in the boiler shell for Aluminum alloy

Results have been compared for structural steel (shell as well as rivets) and aluminum

alloy (shell as well as rivets) as shown in Table 3.

Table 3: Comparison of Results for Structural Steel and Aluminum Alloy.

Sl.No. Parameter FEA results for

Structural Steel

FEA Results for

Aluminum Alloy

1. Equivalent Von Mises

Stress

32.278N/mm2 35.621 N/mm2

2. Maximum Shear

Stress

20.919 N/mm2 20.51 N/mm2

3. Total Deformation 0.0053085mm 0.013919mm



VI. CONCLUSIONS

The following conclusions can be drawn from analysis:

1. The maximum Von–Mises stresses (including local stress) in structural steel as well as

in aluminum alloy are less than as compared to their corresponding yield strengths as

well as maximum tensile strength. The models presented here are safe and under permissible

limit of stresses.

2. The results obtained are well in agreement with the analytical results.

3. Boiler shell with riveted joints made with structural steel is safer as compared to boiler

shell made with aluminum alloy.



REFERENCES

[1]Theory of Machine design, Khurmi, RS and Gupta, JK,2005,S. Chand.

[2]A Textbook of Strength Of Materials,SS Bhavikatti, 2008, New Age International. [3]Farah Kamil Abid Muslim and Dr. Essam L Esmail, Computer aided design of rivets for Steam Boiler Shell Al-Qadisiya Journal for Engineering Sciences, Vol. 5, No. 4, 377 -393, Year 2012. [4]David Heckman, Finite Element Analysis of Pressure Vessels, University of California, Davis Mentor: Gene Massion, Mark Greise Summer 1998. [5]Nidhi Dwivedi and Veerendra Kumar, Burst Pressure Prediction of Pressure Vessel using FEA, International Journal of Engineering Research & Technology (IJERT) ISSN: 2278 -0181, Vol. 1 Issue 7, September – 2012. [6]Faisal Aman, S. Hossein Cheraghi, Krishna K. Krishnan and Hamid Lankarani, Study of the impact of riveting sequence, rivet pitch, and gap between sheets on the quality of riveted lap joints using finite element method Springer-Verlag London Limited 2012. [7]S. Hossein Cheraghi, Effect of variations in the riveting process on the quality of riveted joints Springer-Verlag London Limited 2007. [8] Elzbieta Szymczyk, Jerzy Jachimowicz, Grzegorz Sławinski and Agnieszka Derewonkoa, Influence of technological imperfections on residual stress fields in riveted joints Military University of Technology, Sylwestra Kaliskiego 2, 00 -908 Warsaw, Poland.

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pressure vessel