In this study, we explore the event-triggered control of a flexible three-dimensional (3D) Euler-Bernoulli beam modeled by partial differential equation (PDEs). A novel event-triggered control strategy is developed which can minimize the communication burden in the process of signal transmission. A larger threshold value can be selected when the control input signal value is large to limit the communication burden; a smaller threshold value can be selected when the control input signal value is close to zero in order to improve the control accuracy. The threshold is time-varying, which further preserves the system resources. The proposed control laws can realize both vibration and event-triggered control. All the system signals can be guaranteed as uniform ultimate bounds. The effectiveness of this approach is verified in a series of simulations.