# Monte Carlo Analysis of the Intensification Factor of Design Response Spectra for Hoisted Loads
## 1 Introduction  
In the design of large infrastructures, such as facilities for international scientific experiments, one of the critical requirements is the earthquake-induced acceleration. The particle accelerators built by the High Energy Accelerator Research Organization (KEK) in Japan [1] and the European Southern Observatory's Extremely Large Telescope (ESO's ELT) [2, 3] are two very meaningful examples. Notably, the ELT is located in Armazones, Chile, near the region affected by the most potent recorded earthquake to date, the Valdivia Earthquake of 22 May 1960. Earthquake requirements also significantly influence the design of nuclear power plants in multiple countries.  
The design process of structures against seismic loads is extensively studied by national norms, such as Eurocode 8 [4] for the European Union. These norms thoroughly cover the design and verification procedures for structures and buildings and offer both linear and non-linear approaches. In the linear case, the seismic design is based on the Acceleration Response Spectrum (RS) [5], a plot of the maximum absolute acceleration experienced by a simple oscillator, in response to a certain transient input load, as a function of the natural frequency of the 1-dof oscillator. This tool is common for studying the effect of transient vibrations or shocks. Except for structures entering the post-elastic regime, which can be analyzed with a pushover non-linear analysis [6], all the non-linear systemsare studied via time history transient simulations that are very system-specific and do not facilitate deriving general rules.  
Installing and maintaining the delicate assemblies that comprise an experiment require a daily use of cranes, which lift and move hoisted loads. This operation poses risks to personnel and to the integrity of often unique, expensive and schedule-critical systems. In the event of an earthquake, the crane rope can become temporarily slack (i.e., it loses its tension) and then determine an increased acceleration to the lifted systems once the rope regains its tension [7]. This type of oscillation is highly non-linear, and the acceleration experienced by the hoisted load is not properly forecast by linear techniques.  
This paper generalizes the response of hoisted loads and estimates the intensification factor in the acceleration experienced with respect to the one of a given linear design RS. The result is based on a large number of parametric simulations with a Monte Carlo approach, which is suitable for capturing the uncertainties and variability inherent in seismic events. The Monte Carlo method allows for exploring a wide range of potential scenarios, which is essential for preliminary design considerations.  
To obtain a generic parameter-free result, we implement a first-order model of the hoisted load and generate statistical earthquake load histories with a simple, but established, approach. The use of older references is justified as they are foundational works that established key concepts in the field. While newer references can provide an additional context, these classic works remain relevant and are regularly used in design work. We also note that a hoist crane is a sub-system hosted by a structure, which transfers an input ground earthquake into an interface load and decouples this study from detailed knowledge of ground earthquakes.  
In Section 1, we see the process of generating a realistic earthquake time history compliant with a certain RS. In Section 2, we discuss the hoisted load's simple mathematical model and the typical values of the physical parameters. In Section 3, we discuss the effect of damping on the RS. Finally, in the last section, we collect and discuss the results, providing an upper value for the intensification factor.