The classical system reliability theory only involves random static load with constant value，which cannot provide reasonable estimation for the structure under random static load with variable value，and underestimates the risk of the structure. In view of this，a global reliability evaluation method for framed structures under static load with variable value is proposed，which is based on the shakedown theory with the shakedown state defined as the limit state. Firstly，a single performance function is proposed，and two implementations for calculating the performance function are introduced；Secondly，based on the probability density evolution method (PDEM)，a generalized density evolution equation of the performance function is derived，and its approximate solution is obtained by introducing Dirac δ sequence algorithm，and then the global reliability of the structure can be obtained by the one-dimensional integral of the probability density of performance function. Finally，several examples are investigated to verify the proposed method. The results show that: 1) the proposed method is of high accuracy and efficiency；2) The global reliability obtained by the proposed method can evaluate the safety of the structure under static load with variable value more rationally.