Whether you use closed-form or numerical integration, the deflection at the free end of a laterally loaded linear-elastic, prismatic column is known to be . This result is easily verified in OpenSees with either an
elasticBeamColumn element or a material nonlinear element with elastic sections.
Now suppose we philosophized a bit then posited the following modeling approach…
Instead of a single element for that column, let’s use a series of zero length rotational springs connected by flexurally rigid segments. The rotational springs are collocated with the integration points from whatever quadrature rule you like, e.g., three-point Gauss-Legendre or four-point Gauss-Lobatto as shown below, or any other integration option.
My question is, what stiffness should be assigned to each rotational spring in order to compute the correct free end deflection, , using a springs and rigid segments model?
F. None of the above
In options D and E, wi is the integration weight on the column domain [0,L] associated with quadrature point/spring location xi, meaning the stiffness is not the same for each spring.
Post your answer with an explanation in the comments section below. I will explain the correct answer in a follow up post. Responses are due by May 31, 2022.
While you can develop a model in OpenSees or use good ‘ol pencil and paper to figure out the correct answer, I don’t recommend you use this modeling approach anywhere else. As usual, complicated is not better.