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This article studies the distributed constrained optimization problems for the discrete-time second-order multiagent systems (MASs), in which each agent privately owns local cost function and nonidentical convex set constraints. To solve this problem, a projection-based distributed event-triggered algorithm is developed via the constant step-sizes, which achieves an ergodic convergence rate $O(1/k)$ for the general convex functions. By applying the event-triggered mechanism, the proposed algorithm can avoid unnecessary communication among the agents. Moreover, it is shown that the introduced event-triggered component does not sacrifice the convergence rate. Finally, a simulation example is carried out to demonstrate the theoretical results.