Transformation of dynamic loads into equivalent static loads based on modal analysis

All the forces in the real-world act dynamically on structures. Since dynamic loads are extremely di$cult to handle in analysis and design, static loads are usually utilized with dynamic factors. Static loads are especially exploited well in structural optimization where many analyses are carried out. However, the dynamic factors are not determined logically. Therefore, structural engineers often come up with unreliable solutions. An analytical method based on modal analysis is proposed for the transformation of dynamic loads into Equivalent Static Loads (ESLs). The ESLs are calculated to generate an identical displacement "eld with that from dynamic loads at a certain time. The process is derived and evaluated mathematically by using the modal analysis. Since the exact solution is extremely expensive, some approximation methods are proposed. Error analyses have been conducted for the approximation methods. Standard examples for structural design are selected and solved by the proposed method. Applications of the method to structural optimization are discussed