| 1 | -1.6 | 0.79588 |
| 2 | 20 | 1.30103 |
| 3 | 53 | 1.724276 |
| 4 | 102 | 2.0086 |
| 5 | 300 | 2.477121 |
Jim:
Table is five equally spaced locations so integers are ok, next column is stress in MPa and next column is log. (See below about the 0.975 )
I have a steel block and we see strains and stresses, that vary with the daily temperature - this is about 25 days
I was asked why
It turns out the manufacture of the block and the rest of the stuff probably allows a rocking mechanism with temperature, the peak stress point migrates back and forward across the block as the bridge warms and we measure strain at one location on the side. A simple FEM model shows the expected result. The strain gauge on the other side failed, so if we averaged we would be ok.
I have estimated the stress in MPA at the five locations across the top for the point load and get a nice set of numbers, if I plot them I get
simple fourth order equation, the lowest number is -1.6
If I take the log of the last four numbers I get
So -1.6 plots as 0.8.
If I take 0.8 from 1 I get 0.2 and that is log of 1.6. Anything below the one line is negative log calculator so to speak. It breaks down pretty quickly
Thoughts, PS this is just for fun.
John
Link Copied
John,
A lot is not said about your setup.
The object under test... you state you have a steel block. Where do you place your strain gauges? On the side that faces the sun?, shade side?.. Is the block painted?
If in your second chart (blue and orange dots), I assume time is your X axis, and Y reflects a factor of strain. I count ~21 cycles.
It may help you understand what is going on, had you had temperature sensors (of steel) in proximity of the strain gauges. Also to have a measurement of solar radiation in proximity of the strain gauges. As well as ambient temperature indicated on chart.
I find three things of interest:
- The slope up is (generally) not as steep as the slope down.
- There tends to be a jiggle (1) on the slopes up
- There is a change in slope up (2)
Why?
Are there other external factors that might affect thermal radiation? e.g. shadow from trees, road sign, buildings, window reflections from buildings, traffic, ...?
Jim
The FFT is a statistical signal. We look at all frequencies across a range up until 500 Hz. There is nothing interesting above 500 Hz.
We work on bridges, so the average unique bridge signal for the average road bridge is about 5 seconds whether clean or with traffic. FFT works best on short signals if have the statistical routines in Fortran or C or C#.
So if we call all the signals the set of all signals and each is actually 8.192 seconds, (2000 times data/second * 8.192 seconds) we have the old 16384 FFT. 1000 Hz, with 8192 frequencies.
Each signal has Gaussian thermal data, which is 1/f to some small power say 1.5 which tells us the temperature and nothing else.
Each signal has non-Gaussian data that is not related to the damping, the damping is not constant and is not worth measuring.
One stores the interesting non-Gaussian data, which is about 30 data points every 8 seconds in a MySQL database and after a day you have about 10000 records after a year 3 million. You mine that data it is not complicated, just best done with a super fast language. You do not have enough space to store more without huge cost.
All modes degrade from the end of construction, they degrade whether there is traffic or no. You can fail a bridge by hitting it with an overload, we lose some bridges this way, but if you wait 80 years you have a problem from the daily change, because the DOT's are good at controlling load, so the 80 years is the problem for most bridges.
There is no such thing as a fundamental frequency that can described using only X Y and Z , there is a fundamental quaternion as well.
So if some one tells you the fundamental frequency of the world's longest cable stayed bridge is about 0.1 Hz sway in the transverse direction, then they are almost correct, but not quite. There is a recent paper on this topic.
Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell.
— W. Thompson, Lord Kelvin (1892)[59]
... quaternions appear to exude an air of nineteenth century decay, as a rather unsuccessful species in the struggle-for-life of mathematical ideas. Mathematicians, admittedly, still keep a warm place in their hearts for the remarkable algebraic properties of quaternions but, alas, such enthusiasm means little to the harder-headed physical scientist.
— Simon L. Altmann (1986)[page needed]
Altman and Thompson are wrong, but it took the invention of the silicon transistor and then a lot of fine people doing a lot of interesting work in the last 50 years to get to a stage where the data can give you much more than (https://doi.org/10.2514/3.57251)?
The only question of any interest is how long will my bridge last. So I understand Thompson and Altman, and then I look at my data and I realize there is a need for a better way to explain it to people whose math skills ended at high school, visually.
I spend many hours explaining this stuff to engineers.
Here are two relevant papers. They have my email address if you want more specific answers we need to stop boring these people.
We have a new accelerometer that I am just writing the analysis code for at the moment. This is the first pass at the FFT from a skinny sample. It is a high thick stone wall, the first true frequency is the 50 Hz, I can model that in 10 minutes with Strand7 that works nicely with Intel Fortran. I get a stone Young's modulus of 20 GPa, about right given the age of the wall.
Every thing below 0.1 mg is likely thermal, permanent and Gaussian -- but you have to prove that statistically. And it is not possible to prove Gaussian with less than 50 results, it is not difficult to show with a Fortran RNG.
This is essentially one data point, when we have say 300,000 we can draw reasonable statistical conclusions up to that stage you are just guessing.
This is the rotation angle on the FFT assuming real X and img Y. It is not random, the standard assumption made by Boore in developing the USGS software, I showed this to him on several occasions, but to little avail. There will be a "constant" rate of rotation of the angle.
In the 1890's there was a lot of really good testing, if you can find the book by Ira O Baker on masonry, it is worth the read.
Little changed until the 1990s in terms of testing.
We have a long way to go, and a lot of well trained engineers from the 1980s to now who are in the road. I have a Structural Master's student who cannot write in any computer language.
So I spend my time doing this stuff, talking to a few people and having the best time here.
