By introducing the relay capability, the IEEE 802.16j standard is developed to improve the WiMAX performance. Under the transparent mode, existing studies aim at improving network throughput by increasing the transmission rates of mobile stations (MSs). However, we show that using higher rates will let MSs consume more energy. In the paper, we define an energy-conserved uplink resource allocation (EURA) problem in 802.16j networks under the transparent mode, which asks how to arrange the uplink resource to 1) satisfy MSs' requests and 2) minimize their energy consumption. Objective 1 is necessary while objective 2 should be achieved when objective 1 is met. The above bi-objective problem is especially important when the network is nonsaturated. The EURA problem is NP-hard and we propose a heuristic with two key designs. First, we exploit relay stations to allow more concurrent uplink transmissions to fully use the frame space. Second, we reduce MSs' transmission powers by adjusting their rates and paths. Simulation results show that our heuristic can save up to 80% of MSs' energy as compared with existing work.