Relación enseñanza- exigencias sociales

Dimensions and material properties for the model were taken directly from design calculations and drawings that were provided by IDOT (and these dimensions were later verified by field measurements). The member designations and properties are summarized in Table 4.3-1.

Table 4.3-1 Member properties for the Type I-A sign bridge

Member O.D.

(in.)

Wall

(in.) Material F_y (ksi)

E (ksi)

L_b (in.) TRUSS MEMBERS

Chord 5.00 0.3125 Aluminum 35 10,100 56

Vertical 2.50 0.3125 Aluminum 35 10,100 54 Horizontal 2.50 0.3125 Aluminum 35 10,100 48 Vertical Diagonal 2.50 0.3125 Aluminum 35 10,100 78

Horizontal

Diagonal 2.50 0.3125 Aluminum 35 10,100 74

Interior Diagonal 2.50 0.3125 Aluminum 35 10,100 72 SUPPORT STRUCTURE

Column 10.00 0.365 Steel >35 29,000 360

Diagonals 3.00 0.3125 Steel >35 29,000

126-I-Beam W8x28 Steel >35 29,000 143 62

The ends of the truss connect to the column support structure through the use of four U-bolts. I-beams of the support structure are utilized as seating for the truss chords, which bear directly on the top flange of the W8x28 members, as shown below.

Figure 4.3-1 Connection detail of truss to support frame

In describing the discretization of this connection detail in the model, much explanation is warranted because it has considerable influence on the response of the structure. Thus, the connections of the upper chords are represented as primarily pinned and the lower chords as primarily rigid.

Figure 4.3-2 Detail of truss/support column connection (left), upper chord/column connection (center), and lower chord/beam connection (right)

The following are images from the SAP2000 model depicting the end region of the sign. Figure 4.3-3 shows the rigid link connecting the top chord to the centerline of the column. The end of the link is released against torsion and moment about both the strong and weak axes. Hence, it models as a true pin, which is physically intuitive from inspection of the center photo of Figure 4.3-2.

Figure 4.3-3 End details of model: end release of rigid links connecting top chord/column

Figure 4.3-4 illustrates the use of rigid links to connect the chords with the beam centerline. From Figure 4.3-2 above, it is seen that two U-bolts are used to connect the chord member to the beam. Physically, this means the beam (see Figure 4.3-4) sees torsion (moment about z), and a point moment about its weak axis (about y). There is no moment transfer about the beam’s strong axis (about x) because the circular pipe of the chord can spin about its longitudinal axis. In terms of the rigid links, they carry torsion and moment about their strong axis. They are released from moment about their weak axis. (Variation from exactly these sets of fixity assumptions has little affect on most of the computed stresses, while modestly changing the computed frequencies.)

Figure 4.3-4 End details of model: end release of rigid links connecting bottom chords/beam (left/center), local axis of beam (right)

Each truss support structure rests on reinforced concrete piles at each end of the bridge. The following picture shows the view of the foundation at both sides of the sign structure. In the median, the slope is steep and the shafts are exposed. On the shoulder side, the slope is gradual and the grass covers the top of foundation. The top of

x y

z

Figure 4.3-5 Foundation detail of median end (left) and shoulder end (right)

Because the stiffness of the foundation is many times greater than the steel pipes, the model is fixed at the top of foundation on both ends. The complete model is shown in Figure 4.3-6.

Figure 4.3-6 SAP2000 finite element model of the Type I-A sign bridge

Member and sign self-weight were included in the model, and small masses representing the grating were applied at appropriate nodes throughout the structural model, which was an approximate method of representing this extra mass that is mostly important in the calculation of the twisting period of the structure.

IDOT design specifications prescribe that the wind loading be applied to the structure as shown in 4.3-7. This simplifies the way the load is applied to the truss

members by simply considering the exposed truss as a closed region with an applied pressure of 10 psf. A pressure of 30 psf is applied to the sign area.

Figure 4.3-7. Design wind loading (IDOT, 2001)

In order to determine the effect of this simplification, the loading in the model was applied in this 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 the AASHTO specifications as shown in Table 4.3-2. The pressure (from an assumed 90 mph design wind load) was then converted to a distributed load by multiplying the pressure by the diameter of the member. The results are shown below.

Table 4.3-2 Type I-A drag coefficients and resulting member loads

Member Drag Coefficient Load

Chord 1.10 9.50 plf

Diagonals 1.10 4.75 plf

Sign 1.20 24.88 psf

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

The signs that are currently mounted on this structure are approximately 13 ft × 18 ft and 13 ft × 10 ft, for a total area of about 352 ft². This is only 58 percent of the allowable sign area for this truss (of 610 ft²).

Table 4.3-3 provides the stresses in each member that resulted from the

(610 sq. ft)

90 ft

1.0). The stresses shown in Table 4.3-4 are the result of the design wind load and the dead load. 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 the allowable stresses).

Table 4.3-3 Type I-A member stresses from model with applied wind loading (excluding G) Table 4.3-4 Type I-A member stresses from model with dead load and applied

design wind loading (excluding G) Member

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. Field tests (see later chapters for further details) revealed the actual natural periods of the structure for its three primary and first twisting modes. The results are summarized below in Table 4.3-5.

Table 4.3-5 Type I-A Modal analysis results

Computer Model Actual Structure (Measured) Mode Mode

Description Period (sec)

Mode 1: Longitudinal motion is developed almost entirely through deformation of the support structures. This mode is not excited to any considerable extent by wind gusts due to the slim profile of the truss in this direction.

Mode 2: The most important mode for the sign structure is transverse horizontal motion, which is most easily excited by wind and truck gust loading on the face of the sign (it is easily seen in the plan view below).

Mode 3: Vertical motion is a combination of bending in the truss and the columns. Both wind and truck gusts can excite this mode.

Mode 4: There is considerable twisting of the structure under wind loading. This mode has a rather high frequency compared to the first three fundamental modes.

Differences between predicted and measured periods are due to the lack of model detail for the I-beams and grating in front of the sign (this adds mass at an eccentricity from the truss centerline, resulting in a longer period).

Figure 4.3-8 (a) First mode, elevation view of longitudinal motion, T = 0.66s;

(b) Second mode, plan view of horizontal motion, T = 0.37s; (c) Third mode, elevation view of vertical motion, T = 0.28s; (d) Fourth mode, profile view of twisting motion, T = 0.14s

(a)

(c)

(b)

(d)