ZPA Method

To take into account missing effective masses

The ZPA method (Zero-Period-Acceleration) is one way of taking missing effective masses into account when using the response spectrum method. Assuming that the higher-order modes that are not detected have no dynamic amplification, this method can be useful.

Earthquake check of a bridge pier

Bridge piers, 1st and 2nd eigenmode
Bridge piers, 1st and 2nd eigenmode

The illustrated bridge pier will be used to demonstrate the response spectrum method using the ZPA method.

In this system, 9 eigenmodes already excite 100% of the eigenmasses. This can therefore be regarded as a reference solution.

In a calculation with 2 eigenmodes, only 75.8% of the masses are excited, which does not meet the standard requirement for 90% excitation.

In a comparative calculation with the ZPA method, the effect of the missing effective masses is now taken into account by an additional static load case (also called correction load case). In this way, 100% of the dead masses are now already taken into account with 2 eigenmodes and the ZPA method. The result shows a good approximation to the reference solution with 9 eigenmodes.

Superimposed internal forces, 1.+2. eigenmode, 1.+2. eigenmode + ZPA, reference solution