Experimental Work on Tin Cans to Study Behavior of Thin Shell Cylindrical Tanks Under Axial Compression

Experimental Work on Tin Cans to Study Behavior of Thin Shell Cylindrical Tanks Under Axial Compression

Zalakkumar R. Chhaya

Assistant Professor, Civil Department,

L. D. College of Engineering, Ahmedabad-15

Abstract In this paper cold drink cans are taken for the experimentation to get idea of buckling occurred under axial compression. The experimentation is carried out in three phases. In the first phase, two empty cans are observed to see the buckling pattern and to calculate the buckling stress. In second phase, buckling pattern is observed after the total collapse of tin cans. The load is applied by the foot pressure. While in the third phase, the cans are incorporated with horizontal and vertical imperfections representing weld failure at the joints. In the first and third phases the load is applied by the universal compression testing machine. The purpose of the study to have primary idea of behavior of buckling in different conditions as mentioned above. This study may help in exploring other aspects of experimental or analytical work.

Keywords Thin shell; liquid tanks; shell buckling

1. INTRODUCTION

   Steel tanks for the storage of oil or other liquid are having very small average thickness compared to height and diameter of the tanks. These tanks are thin shell structures. Due to the circular geometry, hoop stresses can be balanced at the lower thickness. However, the tanks observed buckling in earthquakes due to increase of axial stress.

   The soft drink cans are also made of thin shells comprises full capacity drinks and also vulnerable of buckling. Therefore, it is decided to carry out experimental tests on such tin cans to study the primary behavior and the characteristics of damages.

   So far there are two popular codes in practice. One is API 650[1] and the other is NZSEE[2]. API 650 is developed by the American petroleum Institute while NZSEE is developed by the New Zealand group of researchers. NZSEE has provided some provisions and checks against buckling in designs.

   Researchers like Rinne[3] and Manos[4] have attempted to estimate realistic value of impulsive acceleration in terms of coefficient to get the difference between design acceleration and the one derived from the their formulas. For particular aspect ratios the formulas observed sound in perfect prediction of buckling.

2. EXPERIMENTAL TEST SETUP FOR PHASE 2

   First phase of experimental test was carried out with Two tonne compression testing machine. Two tin cans were used to

   observed critical load and buckling characteristics. The details are as follows in the table 1.

   TABLE 1. TIN CANS PROPERTIES AND BUCKLING DETAILS

   Sr. No.	Samples	Dimension (cm)	Thickness (mm)	Buckling load (Ton)
   1	Tin can 1	5 x 10	0.102	0.125
   2	Tin can 1	5 x 10	0.102	0.125

   Fig. 1. Compression testing machine (2 Ton)

   Observations: gradual axial load applied until failure, is observed. The first specimen is buckled with around 0.1-ton load with two diamond shaped buckling occurred at 3 cm from top (Fig. 1).

   While the second specimen (Fig. 2) is observed buckled under 0.125-ton load, in which diamond shaped buckling was observed at 5 cm (i.e. mid portion) from the top.

   Fig. 2 (Test specimen I), (a) & (b) D.S. buckling observed around 3 cm from top

   Fig. 3 (Test specimen II), D.S. buckling observed around 5 cm from top

   A. Calculation of critical stress and comparison with Timoshenkos theoretical buckling formula

   Timoshenko [5] have worked on developing analytical and empirical formulations along with the experimental work on thin shells. Timoshenkos Critical stress formula is

   Where, E- Young modulus of shell material, h- thickness of shell, a- radius of the tank, – poissons ratio of the material

   TABLE 2. COMPARISON OF ACTUAL CRITICAL STRESS AND THEORETICAL CRITICAL STRESS

   No.		(MPa)	(MPa)	Theoratical (%)
   1	Tin specimen 1	47.62	383.87	12.4
   2	Tin specimen 2	59.52	383.87	15.5

   It is very clear from the table 2 that actual critical stress is very less compared to the theoretical stress.

3. STUDY OF BUCKLING BY APPLYING THE FOOT LOAD

   Commonly without any mean of experimental setup axial stress can be applied by the foot pressure also. However, it is not precise way to know the critical load but buckling characteristics can be known. A tin can was tested under the foot load. Before applying the foot load, markings are placed (as shown in fig.4) at the top and bottom so as both will be in single plane.

   Fig. 4. Test specimen with Top and bottom marking

   Sr.

   Specimen

   cr Actual

   cr

   Theoratical

   cr

   Actual/

   cr

   Fig. 5 (a) and (b). series of small Diamond shaped buckling formed along with twisting and axial bending due to foot loading

   As shown in the above figure 5, eccentricity has been observed during applying the foot load. In addition to it, slight twisting is also occurred as shown in the figure as both the markings are not in the same plane. There are series of small diamond shaped buckling has been observed. It is may be due to small hole at the top which shifts the shear center of the can outward. There should be provision of design eccentricity similar to the buildings described in the clause 7.8.2 of IS 1893:2016 (part 1)[6], Further analytical investigation can be made on shear stress due to the imperfection.

   Schematic sketch showing the action occurs while applying the foot load is demonstrated in the fig. 6. Where eccentricity may be due to the positioning of applying the foot load but twisting may be possible due to the weld deficiency or imperfection, material strength and the aspect ratio of the shell.

   Fig.6. schematic sketch showing bending and twisting of tin can after foot loading

4. STUDY OF IMPERFECTION IN SHELL

   The third round of the study is carried out in the computerized compression testing machine. The experiment was aimed to observe the critical load and buckling characteristics on the shells having defects. However, the minimum load (around 1 Ton along with plate having approx. 10 kg weight) in the testing machine is quite more to study the buckling load.

   Therefore, only buckling characteristics are considered in the study.

   Two shells with horizontal and vertical defects are considered for compression testing along with specimen with no defects for the study mainly to see if the twisting occurred on the cans. However, there is no any signal could be captured about the twisting as tins primarily failed in compression. The diamond shaped buckling was observed near the cuts (Fig. 7).

   Fig. 7. Buckling of test specimen with horizontal and vertical defects

   One specimen with full of liquid having some free board provisions is also considered for the testing (Fig. 8). In this case, buckling is observed at upper portion (nearly at the free board region) unlike the other cans as shown in the below. The bucklingobserved with relatively increased load in comparison with the load given to the other specimens. This clearly indicates that hoop stress due to hydrostatic load enhances the buckling stiffness considerably.

   Fig. 8. Buckling of test specimen with full of liquid

5. CONCLUSIONS AND DISCUSSIONS Some notable and important observations are made:

1. The critical stress observed are quite less compared to theoretical critical stress.

2. In all the test specimens, Diamond shaped buckling is observed. It means the diamond shaped buckling is first common damage occurred at the lower most critical stress value.

3. During the foot pressure some amount of twisting observed. Twisting can create shear stress. Further analytical study can be made accordingly.

4. It is interestingly observed that the can full of liquid had buckling at the upper portion where there is freeboard. It shows hoop stresses due to hydrostatic pressure increases stiffness against buckling.

5. Buckling observed at the portion of the cans where horizontal and vertical cuts are provided. This buckling may

   lead to progressive buckling surrounding to that portion. In addition of it, as stress concentration focused at the cuts, the critical stress limits are also increased.

6. Detailed experimentation can be made on steel shells with small specimens of different aspect ratios.

7. Most of tin cans are observed with the Diamond shaped buckling at the mid or just below the mid-level of the cans.

8. It can be believed that buckling is at the local level which occurs at very low value of axial stress. Therefore, it may possible that the buckling may occur at low seismic impulsive acceleration too.

9. It is common observation that the structures with thin shell like oil tanks need to strengthen or stiffened in order to make it earthquake resistant.

ACKNOWLEDGMENT

The study is part of Authors PhD work at IIT Roorkee. The Experimental work is carried out at IIT Roorkee and L. D. Engineering College respectively. The work is inspired and guided by the Authors supervisor Dr. Vipul Prakash, Professor, Civil Department, IIT Roorkee.

REFERENCES

[1] API 650.: Welded Tanks for Oil Storage American Petroleum Institute Standard,650. Twelth edition, (2013).

[2] NZSEE Seismic design of storage tanks – Recommendations of the New Zealand Society for Earthquake Engineering. no. November (2009).

[3] Rinne J. E. (1969), Oil storage tanks-The prince Willian Sound, Alaska, Earthquake of 1964, Vol. II-A, U.S. Department of commerce, Coast and Geodetic Survey, Washington, D.C.

[4] Manos, G. C. (1986), Earthquake tank-wall stability of unanchored tanks, Journal of structural Engineering, 112(8), 1863-1880.

[5] Timoshenko S. P., Gere J. M.: Theory of Elastic stability. Mc Graw hill education, Second Edition, (2014).

[6] IS 1893:2016 (Part 1).: Indian standard on criteria for earthquake resistant design of structures. Part 1- General provisions and building. Sixth revision (2016).