What is Lateral Stiffness? Examples and Formulas

Lateral stiffness is a way to define the ability of a frame or beam to resist lateral loads, such as wind loads or seismic loads. Different systems (e.g. moment frames, braced frames, etc.) have different derivations of lateral stiffness.

What is Lateral Stiffness?

Lateral stiffness is not the same as axial or bending stiffness, which apply to individual members. Lateral stiffness defines the ability of a system of members to resist lateral loads. By knowing the lateral stiffness and applying some force, we can calculate the deflection of said frame.

Cantilever Column with End Applied Load

Lateral Stiffness is the same as a cantilever beam with an applied load at the end:

Lateral stiffness,

For example, if you have a moment frame with fixed supports, and the beam has almost no bending stiffness, then the system behaves as two cantilevered columns.

Fixed-Fixed Column in a Moment Frame

The lateral stiffness is:same as a cantilever beam with an applied load at the end:

Lateral stiffness, 

Braced Frame Lateral Stiffness

For a braced frame where only one diagonal is acting...

Lateral stiffness, 

Note that the lateral stiffness of this bracing arrangement is greatest when the bracing angle, θ = 45 degrees. This represents the most optimal bracing angle. Other bracing angles will provide lower stiffness.

Moment Frame Lateral Stiffness

The lateral stiffness of a moment frame with a fixed base can be calculated as:

Lateral Stiffness, 

Where ρ is the beam-to-column stiffness ratio, defined as:

When the beam has near zero bending stiffness, the row term tends to zero, and the equation becomes 6EIc/H^3, which is essentially the lateral stiffness of two cantilever columns (2 x 3EIc/H^3). When the beam is infinitely rigid, the right term of the lateral stiffness equation tends to 1.0, and the lateral stiffness is 24EIc/H^3, which corresponds to 2 fixed-fixed columns (2 x 12EIc/H^3).