Transformer models have revolutionized a wide spectrum of disciplines, especially in language processing. The recent success has proven that model size scalability is crucial for achieving superior performance metrics. However, training large transformer models is challenging even on modern hardware with powerful GPUs and high-speed interconnects. Existing studies primarily focus on optimizing model training distribution strategies to minimize memory footprint and enhance training speed, often overlooking the scalability challenges related to model size and hardware constraints. To address this oversight, we thoroughly investigate computational, memory, and network demands of training large transformers using the Fully Sharded Data Parallel (FSDP) distributed strategy across different hardware clusters. We explore the intricate relationships between model size and hardware setups to identify configurations that ensure maximum model and hardware efficiency, effective sequence length management, and optimal training throughput.A significant finding of our study is the critical interplay of the cluster's connection bandwidth and GPU memory size compared to the computational performance of GPUs. This interplay limits training efficiency, underscoring the role of both hardware characteristics as a possible bottleneck. By integrating theoretical analysis with simulations and empirical tests, we demonstrate how hardware limitations affect training efficacy, identifying key hardware thresholds and the impact of network connectivity. Our findings prompt a reassessment of training strategies guiding users on the way to finding hardware-optimal FSDP configurations, enhancing training efficiency for large-scale transformer models.