## 2 Experimental Studies of Spherical Shells  
The latest methods of testing spherical shells mostly rely on laser scanning to obtain the exact geometry of the component. Advanced numerical analyses that take into account the scanned geometry of the shell are then carried out [6; 7; 8], and the results obtained are compared with the experimental results. The convergence of the results obtained is very satisfactory; however, these are research works and not design formulas. The analytical formulas are intended to provide engineers the ability to estimate the load carrying capacity of a spherical shell in an easy way, with the greatest possible convergence of the results between the analytical calculations and the actual behavior of the spherical shell. The obtained results of the analytical calculations according to the above procedure are characterized by high accuracy in reproducing the behavior of real spherical shells regardless of their geometry and the material used in their manufacture. This is confirmed by comparing the results obtained from the analytical calculations with the results of selected experimental tests. This comparison is all the more valuable because these studies have been conducted over the past 70 years, at different research centers, using different materials, different spherical shell fabrication techniques, and different measurement methods. Experimental Studies of Magnesium Alloy Spherical Shells Performed by [PERSON] and [PERSON]  
In August 1954, a paper entitled \"National Advisory Committee for Aeronautics, Technical Note 3212\" [9] was published in the journal. \"A nonlinear theory of bending and buckling of thin elastic shallow spherical shells\", whose authors were [PERSON] and [PERSON]. This work contained both theoretical considerations and the results of the experimental studies conducted. These tests were conducted on a series of shallow spherical shells with a base radius of 4 inches, nominal shell radii of curvature of 20 and 30 inches, and shell thicknesses ranging from 0.029 to 0.102 inches. The shells were rigidly fixed in the base and composed of a material designated QQ-M-44, which is a magnesium alloy. The material parameters were elastic modulus \(E=6.5\cdot 10^{6}\) psi and Poisson's ratio \(v=0.32\). The shell fabrication process was based on the \"spinning\" method, which involves rapidly rotating a flat sheet of metal while forming the curvature of the shell. Two types of pressure gauges were used in the study: a mercury gauge to measure pressures below 20 psi and a Bourdon tube gauge to measure when pressures exceeded 20 psi. The view of the test fixture is shown below in Figure 1.  
Figure 1: View of testing fixture. According to [9]. The experimental results, in their original form and expressed in Anglo Saxon units, were converted to SI units. In addition, when comparing these results with the proposed procedure for estimating buckling capacity, material parameters corresponding to those used in the experimental studies were used to ensure that the comparisons were correct and relevant. Figure 2 shows buckling capacity curves for different classes of manufacturing quality using material parameters corresponding to the QQ-M-44 alloy used in the experimental tests. The parameter values are \(E\) = 44,815.92 MPa, \(f_{\text{yk}}\) = 206.15 MPa, and \(v\) = 0.32. The results of the experimental tests are shown as points on a graph, where each point corresponds to one test trial. The comparison of the results clearly shows that the experimental results are consistent with those obtained using the proposed B&M procedure for estimating buckling capacity. In most cases, the experimental results were slightly higher than the buckling capacity curve for the manufacturing quality parameter \(Q\) = 40. Only in two cases did the experimental results fall between the curves for the parameter \(Q\) = 25 and \(Q\) = 40. This suggests that the proposed procedure accurately approximates the buckling capacity, taking into account the material used in the experimental tests.