The Structural Engineer's Corner

Eng. Onorio Francesco Salvatore

Dynamic to static deflection ratio in beam analysis

Written By: Francesco Salvatore Onorio - May• 13•12

If a force moves at uniform speed across a beam, its effects in terms of maximum deflection can exceed the static deflection.

So, assuming a beam with simply supported ends, if v represents the velocity of the force, l the span, ω the lowest natural vibration frequency of the unloaded beam, we will have that the maximum value of the ratio of dynamic to static deflection is 1.74.
This result occurs for

v = ωl/1.64π

and at the instant when the force has progressed at a distance 0.757 l along the span.

The measure v is called critical velocity.

Let’s now consider another case. Let’s assume we have a constant mass W moving across a simple beam of relatively negligible mass, then the maximum ratio of dynamic to static deflection is:

So, we could analyze our beams (bridge decks, for example) taking into account the design velocity and compare it with critical velocity in order to evaluate dynamic effects. Of course, critical velocity isn’t always the same because it depends on the natural frequencies, so it depends on the configuration of our structure.

That’s all, for now.



For guidance, reports and more you can contact the author at:

Eng. Onorio Francesco Salvatore

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