Structures experience large vibrations and stress variations during their life cycles. This causes reduction in their load-carrying capacity which is the main design criteria for many structures. Therefore, it is important to accurately establish the performance of structures after construction that often needs full-field strain or stress measurements. Many traditional inspection methods collect strain measurements by using wired strain gauges. These strain gauges carry a high installation cost and have high power demand. In contrast, this paper introduces a new methodology to replace this high cost with utilizing inexpensive data coming from wireless sensor networks. The study proposes to collect acceleration responses coming from a structure and give them as an input to deep learning framework to estimate the stress or strain responses. The obtained stress or strain time series then can be used in many applications to better understand the conditions of the structures. In this paper, designed deep learning architecture consists of multi-layer neural networks and Long Short-Term Memory (LSTM). The network achieves to learn the relationship between input and output by exploiting the temporal dependencies of them. In the evaluation of the method, a three-story steel building is simulated by using various dynamic wind and earthquake loading scenarios. The acceleration time histories under these loading cases are utilized to predict the stress time series. The learned architecture is tested on acceleration time series that the structure has never experienced.