## 2 Experimental Studies of Spherical Shells
### Experimental Studies of Steel Spherical Shells Performed by [PERSON]  
The experimental studies conducted at the Department of Construction at the University of Liverpool, authored by [PERSON], included the results in a paper entitled \"Buckling of Shallow Spherical Caps Subjected to External Pressure\" [12]. The research involved six shallow spherical shells composed of mild steel alloys. These shells were precisely machined using CNC numerically controlled lathes, resulting in near-perfect geometries. The studied series of spherical shells (D1-D6) were characterized by an almost constant base radius _Di_, varying nominal radius of curvature of the shell \(R\), and different thickness values \(t\) and heights \(H\). The shells were rigidly fixed in the base, and their ideal shape is shown in Figure 7.  
The exact geometric data of each of the tested samples are presented in [12]. The material parameters of the tested shells were determined experimentally: elastic modulus \(E\) = 207.0 GPa, yield strength _fjk_ = 303.5 MPa, and [PERSON]'s ratio \(v\) = 0.28. Figure 6: Comparison of the test results of [PERSON] and [PERSON] [11] with proposed B&M buckling capacity curves. Figure 7: Idealized geometry diagram of the tested spherical shells. According to [12]. A comparison of the results from the tests with the proposed B&M procedure for estimating the buckling capacity is shown in Figure 8. These results show very good convergence. This proves the correctness of the proposed calculation formulas. It is worth noting that the spherical shells tested covered a wide range of slenderness, as measured by the R/t ratio. The value of the critical pressure causing the buckling of the tested shell was in each case higher than the buckling capacity determined by the proposed procedure, taking into account any manufacturing quality parameter Q. Experimental Studies of Steel Spherical Shells Performed by [PERSON] and [PERSON]  
In 2018, a paper was published [13] presenting experimental studies of shallow spherical shells of steel. This work is part of [PERSON]'s doctoral dissertation entitled \"Experimental evaluation of buckling capacity of steel spherical shells loaded with external pressure\". The research program included the testing of twenty spherical shell specimens composed of steel sheets of DC04 grade according to EN10130, which has excellent parameters for plastic processing. The shell models were decided to be created by the Spinning Metal Forming method on a modern numerically controlled machine. The geometry of the shells was chosen to obtain the \(R\)/\(t\) ratios most commonly encountered in engineering practice. Samples were composed of sheet metal with four nominal thicknesses \(t\) of 0.50; 0.80; 1.00; and 1.50 mm. The radius of the support perimeter in each case was 125 mm, and the nominal heights of \(H\) were 15.87; 15.86; 15.86; and 15.85 mm, respectively. The nominal radii \(R\) were 500.25; 500.40; 500.50; and 500.75 mm, resulting in the following \(R\)/\(t\) ratios = 1000.50; 625.50; 500.50; and 333.86. It is worth noting that each series was characterized by a different yield strength value _fjk_, but [PERSON]'s modulus \(E\) = 210 GP and [PERSON]'s ratio \(v\) = 0.3 had constant values. The main component of the test stand was a pressure chamber, shown in Figure 9. A strain gauge pressure transducer coupled to a computerized recording unit was used to measure the pressure in the chamber. A non-contact optical displacement measurement  
Figure 8: Comparison of the test results of [PERSON] [12] with proposed B&M buckling capacity curves. system was used to measure displacement. The details of the test apparatus and measuring station are presented in [13; 14]. The test program included the testing of twenty spherical shell samples with radius \(a=125\) mm and nominal inner surface radius \(R=500\).