# An Assessment of the Impact of Protective Lifeline Safety Systems on Formwork Systems
## 3 Results
### Test 3 and 4--Arrester Hook  
During the fall using the formwork hook, a fall factor (FI) of 1.0 and 1.3 was used, which corresponds to the typical factor when moving or working with a formwork hook. Hook use may occur when the formwork system is not yet fully assembled, which means that the forces may cause the formwork elements to detach together while the person is working at height. The simulation results showed that the stresses were very short and exceeded the elastic range (Figure 12). Thus, when a structural element falls, it may undergo temporary elastic deformation but without permanent deformation. In the case of the repeated dynamic impact, the presence of high momentary elastic deformations may reduce the plasticity of the structure openings and initiate fatigue cracks in future operation. The design conditions of the formwork system make such a case unlikely. The reduced stresses that occur in the system are relatively high, approaching the yield point of the material (for S235 steel) and up to 235 MPa for FI = 1.3 and 128 MPa for FI = 1.0, respectively. These stresses correspond to the force acting on the formwork of 5.1 kN for a free fall of 1.2-1.4 m and 4.43 kN for a free fall of 1.0 m. Despite the fall, the hook was not deformed (destroyed) at FI = 1.3 and 1.0.  
Reducing FI from 1.3 to 1.0 reduces the impact force of the hook on the formwork and thus reduces the reduced stresses. However, the momentary stress values are significant and may lead to plastic deformation in the assembly holes and cross-beams when subjected to repeated dynamic effects (Table 1). The stress distributions are shown in Figures 13 and 14. Stress analysis was carried out in the complete fall arrest system due to the rigid structure of the hook and the absorption of fall energy only by the personal safety system. The results of the calculation indicate that the structural effort reaches up to 87% in the area where the hook is attached and is reduced to 9% in the side elements of the formwork (Figure 15). The FEM stress distribution indicates the stress concentration in the hole edge. The values in this area are above the tensile strength of steel, which could indicate the plastic deformation or fracture in this area (Figure 16), but such cross-beam material defects were not observed.  
Figure 11: FEM analysis—stress distribution in the cross-beam of frame: (a) isometric map view; (b) top surface; (c) front surface. A comma separates fractions.  
Figure 12: Framework arrester hook test with fall factors: (a) FI = 1.3; (b) FI = 1.0.  
Figure 14: Stress distributions over time during the fall of a 100 kg mass with an arrester hook-based delay system for FI = 1.0.  
Figure 13: Stress distributions over time during the fall of a 100 kg mass with an arrester hook-based delay system for FI = 1.3.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**FI = 1.3**} & \multicolumn{2}{c}{**FI = 1.0**} \\ \hline \multicolumn{2}{c}{Maximum stress matrix:} \\ \hline \(\begin{bmatrix}\sigma_{11}&\tau_{12}\\ \tau_{21}&\sigma_{22}\end{bmatrix}=\begin{bmatrix}212&12\\ 12&236\end{bmatrix}\) & MPa & \(\begin{bmatrix}\sigma_{11}&\tau_{12}\\ \tau_{21}&\sigma_{22}\end{bmatrix}=\begin{bmatrix}128&2\\ 2&124\end{bmatrix}\) & MPa \\ \hline \multicolumn{2}{c}{Maximum stress matrix in a plane stress state:} \\ \hline \(\begin{bmatrix}\sigma_{1}&\tau_{12}\\ \tau_{21}&\sigma_{2}\end{bmatrix}=\begin{bmatrix}207&0\\ 0&241\end{bmatrix}\) & MPa & \(\begin{bmatrix}\sigma_{1}&\tau_{12}\\ \tau_{21}&\sigma_{2}\end{bmatrix}=\begin{bmatrix}129&0\\ 0&123\end{bmatrix}\) & MPa \\ \hline \end{tabular}
\end{table}
Table 1: Stress matrices for fall factors 1.0 and 1.3.