Alternative Support Systems for Cantilever - National Transportation ...

To accurately determine the rotational stiffness of the concrete shaft, a system with 11
LVDTs was arranged. The arrangement of the LVDTs is detailed in Figure 4-12 through Figure
4-15. There will be one LVDT 6” from the point of applied force. There will be 4 LVDTs on the
base plate, 3 measuring vertical displacement, 1 measuring horizontal displacement (See Figure
4-12). The measurement from D4 (as seen in Figure 4-12) will measure the horizontal
displacement of the base plate. The rotation of the base plate was calculated using Equation 4-1.
⎛ ⎞
−1⎜
D1
+ D3
R = tan ⎟
(4-1)
⎜ ⎟
⎝ Dgage
⎠
Where
R = base plate rotation (rad)
D1 = displacement of LVDT D1 (in.)
D3 = displacement of LVDT D3 (in.)
= distance between LVDTs D1 and D3 (in.)
Dgage
Figure 4-13 shows the arrangement of the LVDTs on the top of the concrete shaft. Figure
4-14 shows the arrangement of the LVDTs on the bottom of the concrete shaft, where the
concrete shaft meets the block. The purpose of these LVDTs was to measure the rotation of the
concrete shaft relative to the base plate. Figure 4-15 shows the LVDT 6” from the load location.
Figure 4-12. Arrangement of the LVDTs on base plate
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