A random attractor which can capture the long-time behavior of nonlinear stochastic dynamical systems has been developed in the past decades.Consider a wide class of abstract stochastic equations for a nonlinear beam as following dut+(A2u+g(u,ut)+m(B‖1/2u‖)Bu)dt=σ(t)udW (1)With certain dissipative assumptions, it is shown that there exists a random attractor in the nonlinear system (1), which has a finite Hausdorffdimension.If σ(t) in Eq.(1) is a constant, the existence of the random attractor and its Hausdorff dimension estimation can be obtained easily.