25.5 : 叠加法

The method of superposition is used in structural engineering to calculate the slope and deflection of beams subjected to multiple loads.

When a beam experiences various concentrated or distributed loads, it's often more practical to compute the slope and deflection caused by each load separately.

The principle of superposition is then applied, adding together the values of slope or deflection corresponding to each load to determine the total effect.

Consider a supported beam subjected to distributed and concentrated loads.

First, the slope and deflection caused by the concentrated load are determined, followed by the deflection due to the distributed load, using an elastic curve equation.

The slope equation is obtained by differentiating the deflection equation. The slopes and deflections caused by both distributed and concentrated loads are then combined, resulting in the overall deflection and slope of the beam.

The method of superposition simplifies complex load scenarios, providing accurate calculations for beam deflection and slope, which is essential for safe and effective structural design.