Recogida y análisis de Datos conforme a Nivel Estudiante A. Análisis de Estudiantes de Primer Año

The geometric and material properties of the cantilever structure are given in Table 4.2-1. These were taken from the design calculations provided by IDOT and verified from field measurements.

Table 4.2-1 Member geometric and material properties of the cantilever structure

Member O.D.

(in.)

Wall

(in.) Material F_y (ksi)

E (ksi)

L_b (in.)

Chord 6.50 0.3125 Aluminum 35 10,100 48.00

(24.00)

Vertical 3.25 0.3125 Aluminum 35 10,100 59.50

Horizontal 3.25 0.3125 Aluminum 35 10,100 29.50

Vertical Diagonal 3.25 0.3125 Aluminum 35 10,100 72.54 Horizontal Diagonal 3.25 0.3125 Aluminum 35 10,100 50.92 Interior Diagonal 3.25 0.3125 Aluminum 35 10,100 66.41

Column 24.00 0.5000 Steel 36 29,000 360.00

The truss connects to the column at the top and bottom chords of the truss by 1-in.

aluminum plates slotted through the center and welded to the chords. The bottom plate has a hole to accommodate the column and sits atop four welded vertical ribs as well as being bolted with 1¼-in. diameter bolts. The cap plate sits over the top of the column and is bolted to the column via an aluminum collar that is welded to the plate and fit over the top of the column (see Figures 2.2-2 and 2.2-3). This connection is a very rigid one, with the ability to transfer the moments from the truss to the column resulting from wind force normal to the sign and from gravity loads. For this reason, the connection was simplified in the model by using rigid links to connect each of the four chords to the column.

The fixity at the base of the column was modeled by a reinforced concrete pile, representative of the drilled shaft used for the structure. The actual shaft has a total length of 17.75 ft, with about 2.5 to 3 ft exposed above ground and the remainder below ground. This was approximately represented in the model by having the pile fixed at a distance of 6 ft below the bottom of the column. The overall analytical model for the cantilever sign structure is shown in Figure 4.1-2.

Figure 4.2-1 Finite element model of cantilever structure

Besides the dead loads of the sign structure (principally the self-weight of the truss, sign, and walkways), the other significant loading case is the wind load. The wind loads were defined and applied to the model in the same manner as in IDOT’s original design of the structure. This resulted in a pressure of 30 psf acting normal to the sign panel. In order to obtain results that will be comparable to the data acquired in the field, the wind pressure was applied to a sign panel with dimensions equal to the actual sign installed on the structure, plus 1 ft of additional height to account for wind loads on brackets, grating edges, handrails, U-bolts, and luminaries. The truss currently has a sign with an approximate area of 152 ft², which is less than 50 percent of the allowed total sign area of 340 ft². For the open truss, it was determined that the design wind load on each member is equivalent to a uniform pressure of 9 psf on a closed surface at the face of the truss. Finally, the wind load on the column was resolved into a uniform load of 0.021 k/ft. This is all illustrated in Figure 4.2-2.

Figure 4.2-2 Design wind loading of the cantilever structure (IDOT, 2001)

In order to determine the effect of the loading simplification, the loading in the model was applied in the above manner and also by using loads calculated directly from the drag coefficients for the sign and the truss members. To calculate the load acting on the tube members, a drag coefficient was first determined from Table 4.2-2, as designated in the AASHTO specifications. The pressure was calculated starting from a basic wind speed for Illinois of 90 mph and then converted into a distributed load by multiplying the pressure by the diameter of the member. The results are shown below, without the gust factor. (Comparisons of these loads to actual field measurements will be covered later on in Chapter 6.)

Table 4.2-2 Cantilever drag coefficients and resulting member loads

Member Drag Coefficient Load

Chord 0.82 9.26 plf

Diagonals 1.10 6.18 plf

Sign 1.20 24.88 psf

It was determined that the simplified IDOT approach for applying the equivalent static wind loads is reasonable and somewhat more conservative than using the drag coefficients based on individual member sizes. In order to have the most accurate comparison with the measured experimental values, the latter approach will be used and discussed from here forward.

Once the model was completed, two types of elastic analysis were performed: 1) linear static analysis for the wind load and gravity load, and 2) modal analysis. The wind load results were examined to determine the maximum stresses in the truss members and which members are the most critical. As expected for a cantilever truss, the maximum stresses occurred in the main chords near the truss to column connection. The highest

stress was found in the bottom chord member closest to the column. This stress was calculated as the sum of the bending stress and axial stress in the member as follows:

bending

y = distance from the neutral axis to the extreme fiber I = moment of inertia about axis of bending

P = axial force

A = cross-sectional area

Table 4.2-3 provides the stresses in each member that resulted from the application of the design wind loading. The stresses shown in Table 4.2-4 are the result of the design wind load and the dead load applied together. As expected, the axial forces dominate due to truss action. The chord members see the highest stresses; however, they are much smaller than the yield stress of 35 ksi (as well as below the allowable stresses).

Table 4.2-3 Cantilever member stresses from model with applied design wind loading (excluding the gust factor, G)

Member Axial Stress (ksi)

Table 4.2-4 Cantilever member stresses from model with dead load and applied design wind loading (excluding G)

Member Axial Stress (ksi)

The modal analysis was performed to determine the primary modes of vibration of the structure and the corresponding natural periods. As expected there were two predominant modes. The results are summarized in Table 4.2-5.

Table 4.2-5 Results of modal analysis for cantilever structure Mode Mode Description Period

(sec)

Frequency (Hz) 1 Horizontal, about the

column end 0.440 2.27

2 Vertical 0.405 2.46

3 Horizontal, about the horizontal midpoint

of the truss 0.190 5.26

4 Longitudinal 0.140 7.14

5 Torsional, about the longitudinal axis of

the truss 0.114 8.84

The transverse (or horizontal) motion of the truss rotating about the column was the predominant mode; however, the vertical rocking of the truss was also found to be significant. These mode shapes are illustrated below in Figures 4.2-3 and 4.2-4.

Figure 4.2-3 Cantilever mode shape 1, plan view – rotation of truss about the column

Figure 4.2-4 Cantilever mode shape 2, elevation view– vertical motion of truss