1.1 The SABLE omputer program will be used to find the stiffness of a one-story, single bay portal frame for comparison with results obtained experimentally using a signal analyzer. The program is available in the Civil Engineering Computer-Aided Design Laboratory, Room 213 Carrier Hall. The signal analyzer is located in the Sturctural Dynamics Laborattory in Room 121M Carrier Hall. In addition, the PCModal software package available on one of the PC's in the Structural Dynamics Laboratory will be used to visualize and animate the fundamental mode of vibration of the frame using a classical modes model that is based on the measured data from the spectrum analyzer.
1.2 The objective is to use finite element and vibrational analysis methods to determine the transverse stiffness of the frame.
2.1 Definitions.
2.2 Analysis
Estimate the stiffness of the portal frame in the transverse direction at the level of the beam, i.e., the top of the columns. Use any statically indeterminate frame analysis method. First analyze the system as a single fixed-fixed column (i.e., lump the two columns into one and assume infinite flexural rigidity of the beam), then as a rigidly connected frame neglecting the axial deformation of the beam and columns.. Finally, compute the solution using beam elements available in the SABLE finite element software described in Experiment 8. Note that the axial rigidity is included in the beam element stiffness matrix
Elementary vibration theory (see, e.g., Hibbeler, Engineering Mechanics, 7th ed., Prentice-Hall) states that the frequency of a single DOF may be computed as follows:
w = 2* pi * f = ( k/m ) ^(1/2)
where f = frequency in Hz and w= circular frequency in rad/s
Note that direct computation of stiffness could be obtained using a linear variable differential transformer (LVDT). The vibrational technique, however, is 1) very versatile, 2) very sensitive, and 3) nondestructive, 4) usefil in finding many other quantities relating to vibrating system besides stiffness.
The Bruel and Kjaer Type 2034 dual channel signal analyzer. is shown in the figure below along with the Bruel and Kjaer Type 8202 impact hammer and a schematic of the operational setup for forced vibration. Not shown is the Bruel and Kjaer Type 4375 accelerometer to be placed on the portal frame or the frame itself. The frame is mad out of one long piece of steel bar having a rectangular cross-section which is bent in the two one-third length positions and welded at each end to a thick steel base plate.
Verify that hammer and accelerometer are hooked up to analyzer as shown above and place the accelerometer somewhere on the portal frame. Set the spectrum analyzer to record the frequency response function, H2, and strike the portal frame on the side near the top
Record the frequency in cycles per second or Hertz (Hz) of the first noticeable peak on the frequency response function curve.
Compare this frequency with that shown for Mode 1 on the PCModal model which was developed for this frame by others. Animate the modal response for Mode 1 and compare with the static deformed plot produced with your SABLE model.
Comment on sources of error and random variation in the recorded data. Comment
on possible explanations of differences between recorded data, numerical
predictions, and theoretical predictions.
State what you accomplished through the experiment. Were your measurements reasonable? Was the apparatus well suited for this measurement? Do you have any suggestions to improve the procedure?