In Static analysis users assume that loads are applied slowly. This is distinguished from Dynamic analysis, which does not force users to make this assumption. If the load is applied quickly, this can excite the structure as shown in the video below.
But how slow must the load be applied for our static assumption to be a reasonable one? I decided to test out a variety of load rates to get an idea of how to answer this question.
First, I setup a simple beam. I designed the beam such that when I apply a load of 100lb very carefully and slowly to the beam, it would deflect by 100.0mm. This way, I can compare the changes very easily when I apply the load faster. The results of this Static analysis are shown in Figure 1 below.
Then I slowly increased the same 100lb load from 0-100% over the course of 3 seconds (which I thought was fairly slow) in a Dynamic analysis. The reaction is depicted in the graph in Figure 2 which shows that the maximum displacement was still about 100mm, but without any damping the model vibrated as the wave-like curve indicates.
Next, I decided to apply the load faster to see how this would affect displacements. This time the load is increased the same way as before, but this time over the course of only 0.2 seconds. The results of this study are depicted in Figure 3.
Now the vibrations are much more substantial and the maximum displacement is close to 20% larger (120mm) than before. This scenario seemed to oscillate around a 100mm average. Other tests were performed with various loading times. The results are summarized in the two graphics below.
From these results, we might therefore have an insight into our initial question:
“How slow must the load be applied for our Static assumption to be a reasonable one?“
In this particular model, it seems that if it takes greater than 0.3 seconds to apply the full load, we might assume that the load is a static load. I also decided to run a frequency analysis on the structure and determined that the period of the first fundamental frequency was 0.15 seconds. Is there a relationship here?
Finally, the left portion of the curve in Figure 5 above seems to show a maximum asymptote at 200mm meaning that even if the load were applied instantaneously, this could only yield a maximum dynamic displacement equal to twice the static displacement (200mm/100mm).