### 2.1 Field testing

Information on field testing is excerpted from a previously conducted experimental program and further details are available elsewhere (Rutz 2004). A steel truss bridge, the Four Mile Bridge in Steamboat Springs, Colorado, USA, was instrumented and its responses were recorded under wind load (Fig. 1(a)). The 102-year-old bridge system, 36 m in length, 5 m in width, and 6 m in height, was composed of steel channels, eye bars, and hot-rolled cables for the chords and lateral bracings, as depicted in Fig. 1(b). Each chord was constituted with two eye bars possessing an elastic modulus of 200 GPa. The elastic modulus, yield strength, and ultimate strength of the cables were 159 GPa, 248 MPa, and 400 MPa, respectively. To properly measure wind loading, a plastic sail (26 m long by 1.6 m high) was placed on a windward side (Fig. 1(a)). Anemometers were positioned at five locations to log variable wind speeds (Fig. 2(a)): the individual locations were designated as WS1 to WS5. In addition, eight strain transducers were installed to the truss members for the quantification of wind-induced responses (Fig. 2(b)), which were recorded at every 0.1 seconds.

### 2.2 Wind-induced force

The dynamic pressure of wind (*p*) is expressed as.

$$p=\frac12{\rho v}^2$$

(1)

where *ρ* is the fluid mass density (*ρ* = 1.225 kg/m^{3} for sea-level air at 15 °C, Carta and Mentado 2007) and *ν* is the wind velocity in m/s. As far as a truss system is concerned, the pressure in Pascals may be attained from (Fouad and Calvert 2003).

$$p=0.613{C}_d{v}^2$$

(2)

where *C*_{d} is the shape-dependent drag coefficient (*C*_{d} = 2 and 1.7 for the truss members and the sail, respectively, Hoerner 1958). As mentioned earlier, multiple strain transducers were employed to examine the response of the truss eye bars (Fig. 2(c)). Two bottom chords were selected at midspan and two eye bars A and B (Fig. 2(c)) were paired to form one chord (Fig. 2(b), where C1 and C2 are visible on the leeward and windward sides, respectively). Using fundamental mechanics, the force of C1 (*F*_{t1}) was calculated by.

$${F}_{t1}={F}_A+{F}_B= EA\left({\varepsilon}_A+{\varepsilon}_B\right)$$

(3)

where *F*_{A} and *F*_{B} are the forces of the eye bars A and B, respectively; *E* and *A* are the elastic modulus and the cross-sectional area of the bars, respectively (*E* = 200 GPa and *A* = 1129 mm^{2}); and *ε*_{A} and *ε*_{B} are the axial strains of the A and B bars, respectively. Considering the strain reading scheme (*ε*_{1} through *ε*_{4}) given in Fig. 2(c),

$${\varepsilon}_A=\frac{\left({\varepsilon}_1+{\varepsilon}_2\right)}{2}$$

(4)

$${\varepsilon}_B=\frac{\left({\varepsilon}_3+{\varepsilon}_4\right)}{2}$$

(5)

Substituting Eqs. 4 and 5 into Eq. 3 yields.

$$F_{t1}=EA\frac{\left(\varepsilon_1+\varepsilon_2+\varepsilon_3+\varepsilon_4\right)}2$$

(6)

Similarly, the force of C2 (*F*_{t2}) can be determined. Shown in Figs.3 (a) and (b) are the measured wind speeds and the member strains, respectively.

### 2.3 Characterized wind speed

Because the magnitude of wind speed is not deterministic, a two-parameter Weibull distribution was adopted to characterize the speed. The probability density function (f(*v*)) and the cumulative distribution function (F(*v*)) of the Weibull distribution are written as (Bhattacharya and Bhattacharjee 2010; Ozay and Celiktas 2016).

$$f(v)=\frac{k}{c}{\left(\frac{v}{c}\right)}^{k-1}{e}^{-{\left(\frac{v}{c}\right)}^k}$$

(7)

$$F(v)=1-e^{-\left(\frac vc\right)^k}$$

(8)

where *k* and *c* are the shape and scale parameters, respectively. For the determination of these parameters, an open-source Python library called SciPy was used (Van Rossum and Drake 1995). The library is considered a comprehensive Python package specialized in solving multiple functions (Virtanen et al. 2020), which calculated the maximum likelihood of the wind speeds at a minimum difference between the recorded and calibrated values.