Eccentrically Loaded Bolt Groups

Tables 7-6 through 7-13 of the AISC Steel Manual contain values for C, the effective number of bolts that resist shear in eccentrically loaded bolt groups. For example, in a bolt group with three vertical rows of 4 bolts spaced s=3 inch with srow=3 inch row spacing and a load at $latex \theta$=30 degrees from … Continue reading Eccentrically Loaded Bolt Groups

Geometric Transformation

OpenSees offers three types of transformations between the basic system and global system for frame (beam-column) elements: Linear - small displacement assumptions for compatibility and equilibrium PDelta - small displacement assumption for compatibility with the $latex P-\Delta$ term included in equilibrium Corotational - large displacement assumption for compatibility and equilibrium Use the geomTransf command to … Continue reading Geometric Transformation

Pseudo-Time Is Not the Load Factor

In a nonlinear static analysis, the time series associated with lateral loads is typically linear: ops.timeSeries('Linear',1) In this case, the load factor, $latex \lambda$, associated with the time series is equal to the pseudo-time in the domain, i.e., $latex \lambda(t)=t$. Then, when you use the '-time' option in the node and element recorders, you get … Continue reading Pseudo-Time Is Not the Load Factor

Non-Convergence Is Not Structural Collapse

Legend has it that some published research results based on nonlinear dynamic analysis--incremental dynamic analyses, seismic fragility curves, Monte Carlo simulations, etc.--considered a non-convergent OpenSees model to indicate structural collapse or failure. Let's think about this for a minute. Here is the displacement response in two orthogonal directions at the top of a nearly 50 … Continue reading Non-Convergence Is Not Structural Collapse

Two Paths You Can Go By

I am confident we can use OpenSees to solve every truss, beam, and frame problem from any statics or structural analysis textbook as well as every single degree-of-freedom and rigid shear frame problem from a structural dynamics textbook. We can also solve any reasonable problem from a finite element textbook. My confidence starts to wane … Continue reading Two Paths You Can Go By

Finite Differences

A previous post showed how to compute response sensitivity by the DDM, or direct differentiation method. Comparisons with finite difference calculations verified that the DDM results were correct. In this post, I'll dig a little deeper into finite differences. The advantage of the finite difference method (FDM) is it will work for any model parameter--you … Continue reading Finite Differences

Monte Carlo Simulation

The uncertainty associated with a finite element analysis is as important, if not more important, than the results of the analysis itself. Thanks to Terje Haukaas, OpenSees has several modules for finite element reliability analysis: FORM, FOSM, SORM, and several other methods to quantify uncertainty. Unfortunately, those methods have not yet made their way into … Continue reading Monte Carlo Simulation

Eigenvalues During an Analysis

How to compute the eigenvalues (natural periods) of a structural model during an analysis, as the stiffness changes due to yielding, unloading, reloading, large displacement, etc., is a common question. In general, periods elongate during yielding events, then shorten again upon unloading. The extent and duration of period change depends on the constitutive models and … Continue reading Eigenvalues During an Analysis