## 4 Discussion  
### Overturning and Stabilizing Moments Assumed for Gantry Crane According to ISO 4302  
Using the resulting coefficients for the box and truss girder model, detailed calculations of the actual ZREMB SB-8 and SBS-4.5 gantry crane stabilities were conducted. The maximum overturning moment \(M_{O}\) and the stabilizing moment \(M_{S}\) were determined concerning the tipping line, which is shown in Figure 16a,b. In the case of a gantry crane, the overturning line is between the supports, i.e., at the circle contact of the crane and rail contact widths. Calculations were conducted for the least favorable wind direction (Figure 16a,b). It was assumed that a crane operating outdoors is affected by a wind pressure of 245 N/m\({}^{2}\), which corresponds to a wind speed of 20 m/s. According to Figure 16a,b, for the stationary gantry crane example with the wheels locked but not coupled to the rail, all loads and forces that can act simultaneously are considered in their most unfavorable combinations. The effective area \(A_{n\!ref}\) for the real objects was calculated and yielded the following results for the gantry crane: \(A_{n\!refB}=A_{n\!refB1}+A_{n\!refB2}+A_{n\!refB3}=40.24\) m\({}^{2}\) for the box girder and \(A_{n\!ref}=A_{n\!ref1}+A_{n\!ref2}+A_{n\!ref3}=13.05\) m\({}^{2}\) for the truss girder. The effective area was calculated as an area of the perpendicular projection of the structure on the plane, which is perpendicular to the wind direction. The angle attack of the wind was not taken into account. The self-weight, the components of the effective area, and all the assumed technical parameters of the actual object are presented in Table 5. The masses of the gantry crane elements are assumed as static structural loads \(Q\) (stationary), with a factor equal to 1. For dynamic loads, like wind load \(W\), the taken factor is 1.1, according to [48]. Taking the above into account, for the gantry crane to remain stable, the following conditions must be met:  
\[M_{S}>M_{O}, \tag{5}\]  
where \(M_{S}\) is the sum of stabilizing moments; \(M_{O}\) is the sum of overturning moments. The stabilizing moments for box girder B gantry crane \(M_{SB}\) include the following:  
\[M_{SB}=M_{SB1}+M_{SB2}+M_{SB3}. \tag{6}\]  
Figure 16: The gantry crane: (a) ZREMB SB-8 box girder “B”; (b) ZREMB SBS-4.5 truss girder “T”. \(M_{SB1}=625\),878.00 Nm, \(M_{SB2}=2209.02\) Nm, and \(M_{SB3}=5687.84\) Nm are moments resulting from the product of structural loadings \(Q_{B1}\), \(Q_{B2}\), and \(Q_{B3}\), and distances \(l_{B1}\), \(l_{B2}\), and \(l_{B3}\) are those from the tipping line (according to Table 5). The overturning moments include the following:  
\[M_{OB}=M_{OB1}+M_{OB2}+M_{OB3}, \tag{7}\]  
\(M_{OB1}=90\),538.67 Nm, \(M_{OB2}=1746.70\) Nm, and \(M_{OB3}=10\),579.27 Nm are moments resulting from the product of wind loadings \(W_{B1}\), \(W_{B2}\), and \(W_{B3}\) acting at distances \(h_{B1}\), \(h_{B2}\), and \(h_{B3}\). Considering the above data, Condition (5) for a box girder B crane for a wind speed of 20 m/s is as follows:  
\[M_{S}=628,087.02\text{ Nm}>M_{O}=102,864.65\text{ Nm}, \tag{8}\]  
The condition for the stability of the gantry crane is satisfied. Similarly, the stabilizing moments for the truss girder T gantry crane include the following:  
\[M_{ST}=M_{ST1}+M_{ST2}. \tag{9}\]  
where \(M_{ST1}=Q_{ST1}\cdot l_{T1}=141,631.88\) Nm; \(M_{ST2}=Q_{ST2}\cdot l_{T2}=141,631.88\) Nm. The overturning moments include the following:  
\[M_{OT}=M_{OT1}+M_{OT2}+M_{OT3}, \tag{10}\]  
where \(M_{OT1}=W_{T1}\cdot h_{T1}=20,640.13\) Nm; \(M_{OT2}=W_{T2}\cdot h_{T2}=1164.54\) Nm; \(M_{OT3}=W_{T3}\cdot h_{T3}=4031.98\) Nm.