To improve the spectral efficiency in long-term evolution systems, the resource blocks (RBs) are shared among different cells/base stations (BSs) resulting in interference among the cells/BSs on each RB, although all the sub-carriers (SCs) in an RB may not be used in a cell. Defining the load of a given BS per RB as the fraction of the active SCs in that RB, in this paper, we present a generalized signal-to-interference-and-noise-ratio (SINR) model for downlink users on a given RB. This model considers both the transmit powers of the BSs and the loads of the cells over that RB. Under this load-coupled SINR model, to study the feasibility of a given rate demand vector for users, we formulate an optimization problem of minimizing the total load of the BSs on the RBs. Then, for two different scenarios of feasible and infeasible demand vectors, respectively, we study the load management problem (i.e., minimizing the total load of the BSs on the RBs) and admission control problem (i.e., finding the sub-set of users with maximum cardinality whose demands can be concurrently satisfied), respectively. Our theoretical investigations, which provide guidelines for designing radio resource management methods for load-coupled OFDMA networks, are complemented through Monte Carlo simulations.