## Question

**How are Story Shear and Inertia Force calculated in response spectrum analysis?**

## Answer

**To calculate Story Shear Force and Inertia Force (Story Load) in response spectrum analysis, you first need to determine the mode base shear (Vm).**

The Story Load for each story can be found by multiplying the mode base shear (V_{m}) by the mode vertical distribution factor(C_{vxm}).

The Inertia Force for each story (x) is the square root sum of the story loads from all modes, as shown in the image. Additionally, for the first mode, the Story Shear Force for each story (x) is calculated by summing the Inertia Forces for all stories above that story, as shown in the diagram. Therefore, the Story Shear Force for each story (x) is the square root sum of the Story Shear Forces from each mode.

[Image-1] Mode Base Shear and Story Loads (Inertia Force)

This can be expressed mathematically as follows for the m-th mode base shear V_{m}

The mode seismic response factor Csm is determined by the following equation.

The mth order mode load Fxm of layer X is found by the following equation