Static Frame Based Exercises
Comparision of experimental and theoretical stiffness/flexibility
Comparison of experimental and theoretical stiffness/flexibility. Measure the flexibility matrix experimentally. This can best be achieved by applying a unit load at each floor in turn, and measuring the displacement. Each loading will give a single column of the flexibility matrix, for example, if the first floor is loaded, then:
- Is the measured flexibility matrix F symmetric?
- What is a sensible way to make it symmetric to remove experimental error?
- Determine the stiffness matrix from your experimental results, and also find the stiffness matrix theoretically. How does this compare?
- What may be the reasons for any discrepancy?
- Are there any experiments that you could do to confirm your hypothesis?
Effect of vertical loading on stiffness
Measure the flexibility matrix experimentally. This can best be achieved by applying a load at each floor in turn, and measuring the displacement. Each loading will give a single column of the flexibility matrix:
Now repeat the experiment with vertical loads applied to the structure (what pattern of loading do you wish to consider?).
- Does the stiffness vary?
- Find the effect on eigenvalues and eigenvectors of the stiffness matrix. Do the eigenvectors and eigenvalues change?
- Does this depend on the pattern of loading?
Prediction of buckling load
Measure the flexibility matrix experimentally. This can best be achieved by applying a load at each floor in turn, and measuring the displacement. Each loading will give a single column of the flexibility matrix:
Now repeat the loading with increasing vertical load applied to the top floor. Investigate the effect of load on the eigenvalues and eigenvectors. Note that the structure becomes less stiff - at what load does your experiment predict that the stiffness will become zero? How does this relate to the buckling load?
Buckling via vibration modes
One way to detect the approach to buckling is to track natural frequencies: the buckling threshold occurs when a frequency first reaches zero. Why is this so? Investigate the variation of natural frequencies as weights are added to the floors of the building and use this to predict the buckling load. How does it vary depending on the floor to which you add the weights?
Growth of imperfection under vertical load
Measure the horizontal displacement at all three floors as an increasing vertical load is applied to the top floor. Use the Southwell plot construction (see handout for experiment A2 and textbooks) to estimate the buckling load, and the size of any initial imperfection in the shape of the model structure. Repeat the experiment for other patterns of vertical loading.
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Last updated 8/1/2013 by hrs@eng