Comparison Between Pedestrian and Road Bridges Designed with GFRP Pultruded Trusses

Abstract

The overall purpose of the article entitled “Comparison Between Pedestrian and Road Bridges Designed with GFRP Pultruded Trusses” was the comparison between the structural behavior of a pedestrian and road bridge composed by GFRP trusses beams and GFRP decks. A simple design procedure considers limit state with long time effects (ten years for temporary bridge) and shear deformation contribution is developed focusing on the choice of the best shape of truss structures and geometry of cross-section of constituent elements taking into account of buckling effects. Verification of connections, bridge deck and its connections with trusses are not considered at this stage of research. Major findings of the research were that the design of GFRP bridges with tubular elements, having diameter to thickness ratio lover than 20 and geometrical slenderness lower than 30, is not affected by local and global buckling but is governed by deflection and by the limitation of first period. The limits of 5 for road bridge and 15 for pedestrian bridge are suggested with a span 35 m, while for a bridge of 10 m of span values suggested are 10 and 30 for road and pedestrian bridges.

Introduction

The need for a lightweight and highly durable structure, especially in particularly aggressive environments such as the marine ones, has led bridge designers to consider the use of pultruded glass fiber reinforced polymer (GFRP) material. This material is produced with continuous glass fibers and resin through an industrial process to obtain one-dimensional elements with geometric shapes very similar to those of traditional carpentry, characterized by a much lower specific weight than that of steel and less susceptibility to atmospheric and corrosive agents. The significant reduction in fixed loads on the foundation abutments compared to the use of a metal carpentry structures, and above all the handling and installation of the structure using low-capacity lifting machines, and, consequently, small dimensions with extremely limited operating spaces on the construction site, show the indisputable advantages of using pultruded materials for constructing composite bridges. Alongside these indisputable advantages, there are several disadvantages, such as sensitivity to viscous effects; the dynamic behavior of a structure with low self-weight and low elastic modulus, making it susceptible to vibrations induced by traffic and pedestrians; fragile behavior at failure; and second-order effects that affect its design.

Today there are many examples of pedestrian bridges designed with variable loads between 3 and 5 kN/m² and built with structures formed by full-wall or lattice beams with spans between 10 and 20 m and a height of a couple of meters. In contrast, there are few constructions for road bridges, where much higher variable loads between 15 and 30 kN/m² and maximum deflection values between 1/300 and 1/600 of the span lead to heavy sizing that justify their construction only in particular conditions where the use of steel is not recommended. Fig. 1 shows an example of a pedestrian bridge built with lattice beams made from pultruded GFRP elements. The bridge is in Rotterdam and it is of the maritime type. The truss is formed with elements having double T sections assembled with bolted joints. It should be noted that most FRP pultruded bridges are pedestrian bridges, while in the field of road bridges, among the few achievements, we can mention the Marshal Jozef Pilsudski bridge in Poland, whose width has been expanded in the lateral cycle walkways from 2 to 4.5 m with triple cavity pultruded profiles with a 500 × 150 mm section, and the bridge in Rotterdam in Holland, where the deck is made of a pultruded GFRP grating (see Fig. 2).

Figure 1. Example of GFRP pedestrian bridge. GFRP, glass fiber reinforced polymer

Figure 2. Road bridge in Rotterdam in GFRP. GFRP, glass fiber reinforced polymer

In the United States, a pultruded GFRP bridge has been designed and built that supports 4.5-ton vehicles. The bridge is eco-sustainable, resistant to corrosion, and boasts the lowest cost of ownership for its entire life cycle.

Several past studies on truss bridge behavior are available in the literature.^1–7 However, even today, the use of pultruded GFRP for structural elements in infrastructures and bridges is limited, also because very few documents and pre-codes^8–10 provide details for their design at the ultimate and serviceability limit states, and none of them refer explicitly to bridge truss structures.

A structural typology that is very suitable for the construction of bridges is the truss structure, which, however, as observed in many experimental researches available in the literature^11,5–7 is very sensitive to compressive stresses with local and global buckling and, above all, shows vulnerability in bolted and glued connections.

CNR-DT 205,⁸ ASCE/SEI 74,¹⁰ and other pre-code documents provide details for the design of GFRP structures and the calculation of bolted and adhesive joints for connecting pultruded FRP elements. In this paper, a design methodology is proposed for medium-span road bridges and pedestrian bridges with a spatial truss beam structure, focusing on the choice of profile shapes, types of truss beams, and connection types, while stressing the main differences in the design of pedestrian and road GFRP bridges. This research aims to propose the use of GFRP truss structures to replace concrete decks and prestressed beams damaged by corrosion processes in single-span bridges while maintaining the piers and the foundation. The proposal utilizes the recent pre-code LRFD¹⁰ and CNR-DT 207⁸ to investigate the use of GFRP elements for the design of road and pedestrian bridges, with the limitations due to long-term effects, strength and deflection characteristics, and also connection design aspects.

Truss Shapes for Pultruded GFRP Bridges

Trusses are structural frames formed by one or more triangles with elements in compression or in tension connected at the joints, assumed to be frictionless hinges or pins that allow the ends of the members to rotate slightly, thus creating a stable shape or configuration.

In this section, an example of a road bridge (see Fig. 3) is presented, made of plane or spatial trusses of height h placed longitudinally with span L and transversally with depth B.

Figure 3. Proposal of pultruded GFRP bridges. GFRP, glass fiber reinforced polymer

The design load for road bridges at the operating limit state was estimated at 900 daN/m², with a concentrated load of 30 kN at the middle of the beam. For pedestrian bridges, a design load of 400 daN/m² was considered, with no concentrated load.

The deck is made of pultruded GFRP (see e.g., Li et al.¹²), with height h₁, with top and bottom flanges of thickness t₁, and webs placed at pitch s with thickness t₂.

Fig. 4 shows a drawing of a deck in GFRP also with GFRP H beams (see e.g., Li et al.¹²).

Figure 4. Proposal of GFRP deck. GFRP, glass fiber reinforced polymer

The joints between the truss elements are made as shown in Fig. 5 with steel plates connected by bolts.¹¹,¹³ GFRP elements are glued to stainless steel tubes placed inside the GFRP profile with a gluing length of 120 mm. The steel tubes are welded to steel plates and these are connected to the joints by high-strength bolts.

Figure 5. Proposal of joint connection for circular cross-sections. GFRP, glass fiber reinforced polymer

Table 1 gives some indicative ranges of mechanical characteristics of pultruded GFRP elements.

Table 1. Indicative mechanical properties for GFRP elements

Density	γ (daN/m3)	1600–2100
Tensile strength (coupons)	σt (MPa)	200–500
Elastic modulus in tension (coupons)	3E1 (GPa)	20–30
Shear modulus (profile)	G (GPa)	3–5
Longitudinal Poisson coefficient	v12	0.23
Transversal Poisson coefficient	v21	0.09

Referring to the single plane or spatial trusses with the collaboration of the GFRP deck of inertia J_d and area A_d, it is possible to derive the inertia and the modulus of strength of equivalent solid beams having the same inertia and strength modulus as the trusses. The geometrical properties of the equivalent beams can be found in Table 2. Cases of one or two upper elements or two lower elements are considered (cases a, b, c in Table 2).

For the preliminary design of a truss, we refer to the static scheme of a simply supported beam of length L at the ends, loaded with uniform loads q_sle and q_slu and a concentrated load P (in the case of a road bridge).

The strength and deformability checks are based on the use of the following expressions, which give the required strength modulus and inertia for a given design strength and deflection limit δ₀:

(1) $$W_e=(\frac{1}{2}\cdot q_{SLU}\cdot L+P_{SLU})\cdot \frac{L}{4\cdot f_{yd}}$$

(2) $$\begin{array}{rl}\delta & =\frac{L^3}{8\cdot E_1\cdot J}(5\cdot q_{SLE}\cdot L+P_{SLE})+\frac{L}{4\cdot k\cdot G\cdot A}\\ & (\frac{1}{2}\cdot q_{SLE}\cdot L+P_{SLE})\le {\delta }_{0}k=\frac{20\cdot (1+\upsilon )}{48+39\cdot \upsilon }\end{array}$$

For the deformability check, the elastic module E₁ was reduced by 0.66 and G by 0.448 to account for viscosity, as suggested by CNR-DT 207⁸ (assuming a useful life of 10 years as temporary structures), while the strength was reduced by the product of 1.35 × 1.15, as suggested in CNR-DT 207.⁸

Strength Verification of Strut and Tie Elements of Trusses

In this section, some expressions available in the literature for the strength verification of truss elements are presented, taking into account the local and global buckling of pultruded members.

CNR-DT 207⁸ and ASCE/SEI 74¹⁰ were utilized for the design of elements and connections using GFRP profiles.

The connection between the single elements in the joints is assumed to be made with steel bolted plates (see e.g., Hao et al.¹³), while the connection between the plates and GFRP elements is assumed to be glued (see e.g., Higgoda et al.⁷).

Elements in tension are verified referring to the gross area of the cross-section purged of the area of the bolts (if any) and to the tensile design strength of the material. The tensile strength of the material is obtained through direct tensile tests on coupons, while compression tests are performed on stub elements.

CNR-DT 207⁸ adopts a safety factor for the material depending on the uncertainties related to the determination of the material properties for a given coefficient of variation and an additional coefficient that accounts for the brittle behavior of the composite, leading to an overall coefficient that in the most severe case is 1.495. This coefficient, utilized to reduce the strength, is equal to 0.668, which is close to the coefficient of 0.7 assumed by ASCE/SEI 74.¹⁰

CNR-DT 207⁸ takes into account the viscoelastic effects of the composite, penalizing the elastic module with coefficients equal to 0.3 and 0.5 for quasi-permanent loads and fatigue, respectively.

In compression, in the absence of experimental values, it is possible to predict analytically the compressive strength, as done by Cardoso et al.,¹⁴ with a simple expression: where a, b, and $\mathrm{\chi }$_cr are the coefficients that are assumed in Eq. (1) as 0.21, −0.69, and 5.148, respectively, as suggested by Cardoso et al.,¹⁴ which give:

(3) $${\sigma }_m=G\cdot {(1+{\mathrm{\chi }}_{cr}/a)}^b$$

(4) $${\sigma }_m=0.107\cdot G$$

In this paper, the longitudinal elastic modulus of GFRP has been related to the compressive strength with a linear relationship of the following form:

(5) $$E_1=100\cdot {\sigma }_m\left(\text{MPa}\right)$$

By adopting Eqs. (4) and (5), it is possible to construct the diagram of Fig. 6, which provides the variation of the longitudinal and tangential elastic modulus (Eq. (3)) with the compressive strength. In the same graph, some experimental data available in the literature are reported (data of Pecce and Cosenza¹⁵).

Figure 6. Variation of longitudinal and shear modulus with compressive strength

It can be seen that the correlation proposed by Cardoso et al.¹⁴ gives an excellent interpolation of the experimental data when G = 1/9 E₁. Eq. (5) is safe with respect to the available experimental data and has the advantage over Eq. (4) that its use is related to the determination of E₁, which is easier to determine experimentally than G.

Table 3 gives expressions for critical stress for hollow square and circular cross-sections. CNR-DT 207⁸ does not give any analytical expression for the calculation of critical stress of circular cross-sections.

Table 3. Expressions for critical stress available in the literature

Cross-section	References	Expression of critical stress σcr
Hollow square	MMFG (1990)	${\displaystyle \frac{E_1}{2\cdot {(2\cdot b/t)}^{1.5}}}$
Hollow square	Srongwell17	${\displaystyle \frac{E_1}{16}}\cdot {\left({\displaystyle \frac{t}{b}}\right)}^{0.85}$
Hollow circular	ASCE/SEI 7410	${\displaystyle \frac{2\cdot t}{D}}\cdot min(\sqrt{{\displaystyle \frac{E_1\cdot E_2}{3}}};\sqrt{{\displaystyle \frac{2}{3}}}\cdot G\cdot \sqrt{E_1\cdot E_2})$
Hollow circular	AASHTO18	$\begin{array}{l}{\displaystyle \frac{2\cdot t}{D}}\cdot {\displaystyle \frac{0.375\cdot E_1}{{(1-{{\upsilon }_{12}}^2\cdot E_2/E_1)}^{0.5}}}\\ \cdot 1.414\cdot {[(1+{\upsilon }_{12}\cdot {\left(E_2/E_1\right)}^{0.5})\cdot {\left(E_2/E_1\right)}^{0.5}\cdot \left(G/E_1\right)]}^{0.5}\end{array}$
Hollow circular	Campione19	$2\cdot {\displaystyle \frac{t}{D}}\cdot \sqrt{{\displaystyle \frac{E_1\cdot E_2}{3\cdot (1-{{\upsilon }_{12}}^2)}}}\cdot \sqrt{0.625\cdot {\left({\displaystyle \frac{E_2}{E_1}}\right)}^{0.85}}$

Most of these expressions for hollow circular cross-sections are derived from equations originally proposed by Timoshenko and Gere¹⁶ for homogeneous isotropic materials and corrected to account for the anisotropy of the material through the introduction of the longitudinal and transversal module of elasticity (E₁, E₂) and the Poisson coefficients v₁₂ and v₂₁. Adopting the equation given by ASCE/SEI 74¹⁰ with E2 = 1/3 E 1 and setting it equal to Eq. (5) gives the maximum D/t value of 54 to avoid strength reduction in compression due to buckling effects.

Fig. 8 shows a comparison between the critical stress determined with ASCE/SEI 74¹⁰ and the proposed model with variation in D/t. The comparison is made for material with E₁ = 23 GPa, E₂/E₁ = 1/3, G/E₁ = 1/9 (with E₁ > E₂). The same graph also shows the points related to the experimental investigations conducted by Yazhin and Ramesh,²³ Puente et al.,²¹ and Yousis et al.¹⁰ for hollow circular cross-sections. The case of square hollow cross-sections is not considered because it is not used here for members of bridge trusses. From the comparison in Fig. 7, the reduction of critical stress for local buckling is evident.

Figure 7. Variation of critical stress with D/t

Figure 8. Global critical buckling stress versus mechanical slenderness

For the calculus of critical load of slender columns ASCE/SEI 74¹⁰ adopts the expression of Eulero in the form where l₀ is the effective length of the element, and J the minimum moment of inertia. Using Eq. (6) and setting the critical stress equal to the compressive strength of the material (Eq. (5)) gives the limit slenderness of the elements equal to 17.

(6) $$P_e=\frac{{\pi }^2\cdot E\cdot J}{{l_0}^2}$$

It is widely shown in the literature that for high slenderness values, the critical load predicted with the Eulero formula must be corrected, as done by Engesser,²⁴ to account for the shear contribution, as follows:

(7) $$P_{Eg}=P_e\cdot \frac{1}{1+k\cdot P_e/(G\cdot A)}$$

The values of k adopted in Eq. (7) are those suggested by Timoshenko and Gere¹⁶ for isotropic materials, and for a thin-walled circular section and for a solid tube, they are equal to 0.5 and 0.75, respectively, and 5/6 for W shapes.

In the next sections, the critical load will be represented in the graphs against the mechanical λ_c or geometrical slenderness λ defined as:

(8) $${\mathrm{\lambda }}_c=\sqrt{\frac{min({\sigma }_{cr},{\sigma }_m)\cdot A}{P_e}}\mathrm{\lambda }=\frac{l_0}{{\left(J/A\right)}^{0.5}}$$

In pultruded members, because of the initial imperfections of elements, local and global interaction plays an important role in the values of the critical load, and several authors propose analytical expressions for the calculation of the critical load taking into account the interaction between local and overall buckling, as shown in Table 4.

Table 4. Expressions for critical load

Author	Expression
Barbero and Tomblie20	$[{\displaystyle \frac{1+1/{\mathrm{\lambda }}_c^2}{1.30}}-\sqrt{{\left({\displaystyle \frac{1+1/{\mathrm{\lambda }}_c^2}{1.30}}\right)}^2-{\displaystyle \frac{1}{0.65\cdot {\mathrm{\lambda }}_c^2}}}]\cdot A\cdot F_{crl}$
Puente et al.21	${\displaystyle \frac{A\cdot F_{crl}}{0.5\cdot [1+0.12\cdot ({{\mathrm{\lambda }}_c}^2-0.25)+{{\mathrm{\lambda }}_c}^2]+\sqrt{{\{0.5\cdot [1+0.12\cdot ({{\mathrm{\lambda }}_c}^2-0.25)+{{\mathrm{\lambda }}_c}^2]\}}^2-{{\mathrm{\lambda }}^2}_c}}}$
Cardoso et al.14	$\left({\displaystyle \frac{1+\alpha +{\mathrm{\lambda }}_c^2\cdot {\rho }_p-\sqrt{{(1+\alpha +{\mathrm{\lambda }}_c^2\cdot {\rho }_p)}^2-4\cdot {\mathrm{\lambda }}_c^2\cdot {\rho }_p}}{2\cdot {\mathrm{\lambda }}_c^2}}\right)\cdot A\cdot F_{crl}$
Strongwell Corporation22	$1.3\cdot {\displaystyle \frac{E_1\cdot A}{{(2\cdot L/D)}^{0.33}}}$
ASCE10	$0.7\cdot A\cdot min({\displaystyle \frac{{\pi }^2\cdot E\cdot J}{L^2\cdot A}};{\sigma }_{cr};{\sigma }_m)$

ASCE/SEI 74¹⁰ considers the interaction between local and overall buckling and proposes calculating the critical load as

(9) $$P_{cr}={\sigma }_c\cdot A\cdot \frac{1+0.12\cdot ({\mathrm{\lambda }}^2-0.25)+{\mathrm{\lambda }}^2-\sqrt{1+0.12\cdot {[({\mathrm{\lambda }}^2-0.25)+{\mathrm{\lambda }}^2]}^2-4\cdot {\mathrm{\lambda }}^2}}{2\cdot {\mathrm{\lambda }}^2}$$

According to ASCE/SEI 74,¹⁰ P_u is the minimum among P₁ = σ_cr A (Table 4), P_e (Eq. 6), and P_cr (Eq. 9). In the equations shown in Table 4, F_crl is the minimum between the ultimate strength of the material in compression and the critical strength of the section.

Fig. 8 shows the variation of the ultimate stress (minimum between global buckling, local buckling, and compression material failure) as a function of the mechanical slenderness according to the different models considered. The theoretical values were calculated assuming E₁ = 23 GPa, E₂/1/3 E₁, G = 1/9 E₁, and v = 0.23. The same graph also reports the experimental data of Zhang et al.,²⁵ Zhang and Li²⁶. From the comparison, it is clear that most of the models predict the experimental values with good approximation.

Numerical Example

In this section, we refer to pedestrian and road bridges of different spans L having truss structures as in Fig. 4 with elements featuring circular cross-sections of diameter 210 mm and thickness 15 mm. The deck is made of pultruded GFRP of height 400 mm with a span between the load-bearing trusses of 1.5 m. The deck has top and bottom flanges of 6 mm and webs of 6 mm at a pitch of 75 mm. The example refers to E₁ = 30 GPa (E₂ = 1/3 E₁, G = 1/9 E₁). The useful life chosen was 10 years.

The design load of the road bridge at the operating limit state was estimated at 9 kN/m² with a concentrated load of 30 kN in the middle of the beam. For pedestrian bridges a design load of 4 kN/m² was considered (half of the road bridge load and no concentrated load). In both cases (pedestrian and road bridges), the load on each beam is increased by 1.5 at the ultimate limit state and by 1.35 × $\mathrm{\varphi },\mathrm{\varphi }$ being the dynamic coefficient assumed in the Italian code as $\varphi =1+0.01\cdot {\displaystyle \frac{{(100-L)}^2}{200-L}}$ according to CNR-DT 207.⁸

From a dynamic point of view, with reference to the scheme of a simply supported equivalent beam with mass M = P/g (where g is the gravitational acceleration) placed at the center of the beam, the vibration period of the first vibration mode is

(10) $$T=2\cdot \pi \cdot \sqrt{P/g(\frac{L^3}{48\cdot E_1\cdot J}+\frac{\mathrm{\chi }}{G\cdot A})}$$

In Eq. (10), the viscoelastic effect and duration of the loads are taken into account for a period of 10 years with a 30% reduction of E1 and 50% of G, as suggested by CNR-DT 207.⁸ According to the indications on the design of FRP Bridges,²⁷ the fundamental frequency must be less than 5 Hz (period 0.2 sec) for vertical vibrations and 2.5 Hz (period 0.1 sec) for flexural and torsional vibrations. If the fundamental frequency is less than 3 Hz (0.33 sec) for horizontal or torsional vibrations, the use of dampers is recommended. If with Eq. (10) the limit of the period of 0.2 sec is imposed, it is possible to obtain the inertia of the beam.

Fig. 9 shows for case b) in Table 4 the variation in the ratio L/h with variation in L, for road and pedestrian bridges.

Figure 9. Minimum ratios L/h with variation in L to respect limit states according to CNR-DT 207⁸

In the same graph, the minimum L/h ratios that satisfy the ultimate (strength) and serviceability limit states are shown. From the graph, it emerges that the design of GFRP bridges with D/t < 20 and λ < 28 is governed by deflection. By contrast, a check on the vibration period instead of the strength gives a limit of L/h = 15 for a pedestrian bridge and 5 for a road bridge. These are possible limits for a bridge of 35 m and 30 m and a footbridge of 10 m.

Conclusions

The specific application of GFRP truss structures could replace concrete deck and prestressed beams damaged by corrosion processes in single-span bridges while maintaining the piers and the foundation. This solution produces a significant reduction in seismic mass, with a consequent reduction of lateral forces on piers and foundation, and potentially cheaper strengthening of piers and foundation for seismic purposes. In this paper, a simple procedure for the design of temporary road bridges composed of GFRP truss beams and GFRP decks is shown. The model focuses on the choice of the best shape of truss structures and the geometry of the cross-section of the constituent elements, taking into account buckling effects and joint details to ensure the overstrength of the connections.

Major findings were that:

• Spatial truss structures having two upper chords or one chord having a circular cross-section with a diameter-to-thickness ratio lower than 54 is suggested, with a maximum geometrical slenderness of the upper chord of 17.
• The minimum height-to-span ratio of 1/5 and 1/15 of a span of 35 m are suggested to verify limit deflection of 1/500 of the span and a period lower than 0.2 sec for vertical vibration, also considering strength verification with long-term effects (10 years for a temporary bridge) and shear deformation contribution.
• Joints can be designed with bolted connections involving only steel plates at the joints and glued connections between steel elements and pultruded GFRP elements.