Modeling of Composite Box Girder with Concrete—Corrugated Steel Webs of Base Plate

CBGCSW is composed of a top concrete slab, corrugated steel webs, and a bottom plate. It is known for its ability to resist shear, flexural, and torsional stress while having fast construction and low cost compared to typical composite girders [1]. Chen et al. [2, 3] created two identical models, one with concrete-filled steel tubes and the other with hollow steel tubes, both of which exhibited high ductility and failed in a ductile manner. Concrete-filled steel tubes were found to enhance yield load and minimize deflection. The composite action between concrete and steel provides increased section modulus, resulting in higher resistance to bending and improved yield load capacity. Additionally, the concrete core contributes to reduced deflection by enhancing overall stiffness. Huang et al. [4] compared the two models to composite girders with truss chords and found that concrete-filling the chords reduced chord radial deformation and relieved hot-spot stress in composite girders by 18.5%-60.1%. It also decreased the rate of crack development during fracture propagation and failure and increased fatigue life by 61.5%. Ghanim et al. [1] explained that corrugated steel plate girders are widely used as a structural element in many sectors due to their beneficial qualities. They have a greater maximum moment carrying capacity than almost any hot-rolled section and transverse shear forces are transmitted only through the corrugated steel web. Webs with a greater depth-to-thickness ratio are typically used, which can lead to slender sections that are vulnerable to buckling on the flat web. However, advancements in the automated production process for corrugated steel webs and a reduction in weight have led to an increase in the use of corrugated web girders, particularly for wide-top flanged concrete box girders, so the using of corrugated webs prevent buckling occur when the section is slenderness. Tu et al. [5] presented a full-scale fatigue test and a numerical study of a new composite girder that was bent in four places. The test results showed that even at a relatively low level of stress, the composite girder still suffered fatigue damage at a very high number of cycles (9.84 million), causing it to fail as multiple cracks started at the top and bottom of the steel tube near the middle of the span and spread outward, here explain failure mode and crack propagation. He et al. [6] found that Live loads were effectively distributed using diaphragms, particularly under eccentric load conditions, because the diaphragms enhanced the lateral stiffness of two box girders joined together, so by connecting the girders, the diaphragms provided increased rigidity, ensuring that live loads were evenly spread across the structure. Zhou et al. [7] compared the original box girder design and proposed two improved CSW forms to increase transverse bending stiffness. The top flange is stiffened with transverse ribs, and lateral bracings are adjusted. These modifications aim to reduce the accumulated deformation differences caused by self-weight during segmental precasting using the short-line method. Numerical analysis further demonstrated that the improved structural form with lateral bracings reduced the maximum tensile transverse stress in the top concrete flange by 33% compared to the original box girder with CSWs. Ding et al. [8] found that the connection between the ultimate torsional strength and either the shear modulus or web thickness is almost linear. Under the same external torque, corrugated steel webs with a thick web can withstand higher torque than those with a thin web, it is clear from the above that the web thickness has an effective effect on the resistance to torsional torque. Majeed [9] investigated the behavior of simply supported beams with lightweight concrete (LC) and normal concrete (NC) slabs. Shear interaction was considered at various levels (100% to 40%). It was discovered that the measured end slip for beams with LC had larger values for various degrees of shear connection than values obtained from testing on beams with NC. Al-Zaidee and Saadi [10] found a replace of concrete type for composite beam with a lightweight concrete deck slab, the strength and stiffness of the system are slightly impacted. The strength is only increased by 3.5% when normal weight concrete. Niu and Guo [11] found that many Multiple factors influenced the shear bearing capacity of girder oblique sections, including temperature, prestressed, material properties, and corrugated steel web thickness.

Finally, the above studies show the general behavior of composite girder with corrugated steel webs -concrete under different loads and finding weak points in the section for the possibility of improvement by adding strengthen to the weak sections.

Three CBGCSW specimens were modeled with simply supported clear span 2.5m (the dimensions were chosen to be suitable for the available testing device in anticipation of developing the work and conducting experimental modeling in the future). One of the specimens was modeled without additional vertical stiffeners (G0) as shown in the Figure 1, while the other two were with additional external stiffener plates (G30 and G50) to study the improvement in the behavior of the box girder with vertical stiffeners compared to one without it. Additionally, the effect of the width of the web stiffeners on the girder behavior was investigated by changing the stiffener width for specimens G30 and G50 with 30mm and 50mm respectively. Figure 1 shows the nominal geometry and details of a typical specimen and Table 1 shows the vertical stiffener details for the specimens. Studs were used as shear connections to tie the concrete slab to the top steel flanges.

Table 1. Detail of models

1.png

Figure 1. Nominal geometry of cross - section (all dimensions are in mm)

5.1 Concrete

To simulate concrete part used solid element providing detailed stress distribution throughout the entire volume. Concrete behaves differently in compression and tension than steel reinforcement. According to the basic assumptions of CDP, there are two failure modes of the concrete material: tensile cracking and compressive crushing. The average compressive strength of concrete (f'_c) was 27.5 N/mm². Relations between f_c and f_cu are presented by Chen et al. [12], and the stress-strain curve of concrete shown in Figure 4. Table 2 shows the concrete properties for all models in this study.

$f_c^{\prime}= \begin{cases}0.8 f_{c u}, & f_{c u} \leq 50\, {Mpa} \\ f_{c u}-10, & f_{c u}>50 \,{Mpa}\end{cases}$

4.png

Figure 4. Stress-strain (compressive) curve of concrete

Table 2. Concrete properties

Mass Density Kg/mm3	Young’s Modulus MPa	Compressive Strength f’c MPa	$\varepsilon_o$
2.4E_ 09	24647	27.5	0.002

Concrete damaged plasticity: The concrete damaged plasticity (CDP) model employs the Drucker-Prager plastic flow functional and Lubliner yield function to simulate the behavior of concrete under stress. This model is defined by five key parameters: the shape factor, eccentricity, the ratio of biaxial compressive stress to uniaxial compressive stress, dilation angle, and viscosity. These parameters are typically established through experimental measurements or by analyzing existing data.

Lubliner et al. [13] recommended a value of 2/3 for the shape factor and an eccentricity of 0.1, which approximates the ratio of uniaxial concrete compressive strength to tensile strength. As reported by Kupfer et al. [14], the ratio of biaxial compressive stress to uniaxial compressive stress for normal strength reinforced concrete is 1.16. The dilation angle, which indicates the internal friction angle of concrete, generally ranges from 31° to 42°. Demir et al. [15] suggested a viscosity parameter of 0.0005 to optimize numerical accuracy. Table 3 presents the data considered in this study.

Table 3. Factor of concrete properties

Dilation Angle	Eccentricity	fb0/fc0	K	Viscosity Parameter
31	0.1	1.16	0.667	0.0005

For compression behavior, the following data (Table 4) and Figure 5 are used.

Table 4. Stress-strain of compression behavior (concrete)

Stress (MPa) σc	Inelastic Strain εcin
10	0
15.71685398	6.49839E-05
20.17747027	0.000145025
23.56721138	0.000266961
25.84087501	0.000431072
27.11891988	0.00064024
27.5	0.000884246
26.46090824	0.001421405
24.09757395	0.002021292
21.3448636	0.002633977
18.69744865	0.003236391
16.27352668	0.003838736
14.187811	0.00442436
7.700114836	0.007162584
4.675426178	0.009805305
3.123716348	0.012373262
2.236655657	0.014884252
1.670260181	0.017427233
1.295837673	0.019947424

5.png

Figure 5. Compressive stress-strain curve (concrete)

For the tensile behavior, bilinear stiffening response is used, Gerwick Jr. [16] recommended the value to be the uniaxial cracking strength: f,cr=0.33√fc'. this is the value used to calibrate the tension stiffening curve by Hsu and Mo [17] as discussed earlier and the value used by Lee et al. [18] for peak tensile strength.

The fracture energy G_fis the fracture energy of concrete that represents the area under the tensile stress-crack displacement curve. The fracture energy G_f is related to the concrete’s strength and aggregated size and can be calculated using Eq. (1) [19].

$G_f=G_{f 0}\left(f_{c m} / f_{c m 0}\right)^{0.7}({N} / {mm})$            (1)

Gerwick Jr. [16] recommended the value to be the uniaxial.

Cracking strength: f,cr=0.33√fc', this is the value used to calibrate the tension stiffening curve by Hsu and Mo [17] as discussed earlier and the value used by Lee et al. [18] for peak tensile strength. Table 5 and Figure 6 are used in models.

The Hordijk 's model with two parameters, f_t and G_f:

$\frac{\sigma(w)}{f_t}=\left[1+\left(c_1 \frac{w}{w_{u l t}}\right)^3\right] e^{\left(-\frac{c_2 w}{w_{u l t}}\right)}-\frac{w}{w_{u l t}}\left(1+c_1^3\right) e^{-c_2}$             (2)

where, c₁=3; c₂=6.93; and w_ult=5.136×G_f /f_t.

Table 5. Stress-displacement of tensile behaviors (concrete)

Stress (MPa)	Displacement (mm)
3.042903097	0
1.649021782	0.066
0.779215604	0.173
0.629143257	0.22
0.458746567	0.308
0.395143878	0.35
0.338344875	0.39
0.284313161	0.43
0.22100944	0.48

6.png

Figure 6. Tensile stress-displacement curve (concrete)

Compression damage: The compressive damage in concrete materials is quantified by the parameter d_c. A value of 0 for this parameter indicates that the concrete is undamaged, whereas a value of 1 signifies that the concrete is fully damaged. The damage parameter can be defined using a tabular format as shown in the following equation. If this parameter is not specified, the model defaults to functioning purely as a plasticity model.

$\begin{aligned} b_c & =0.7 \\ \varepsilon_c^{p l} & =b_c \varepsilon_c^{i n} \\ d_c & =1-\frac{\sigma_c E_c^{-1}}{\varepsilon_c^{p l}\left(\frac{1}{b_c}-1\right)+\sigma_c E_c^{-1}}\end{aligned}$             (3)

where, d_c is the compression damage parameter, σ_c is the compression stress, and f_c′ is the compressive strength of concrete. The compression damage used is shown in Table 6.

Table 6. Compression damage

dc	Inelastic Strain
0	0
0.029665195	6.49839E-05
0.050463112	0.000145025
0.077284654	0.000266961
0.109803092	0.000431072
0.148620561	0.00064024
0.192084301	0.000884246
0.284277822	0.001421405
0.382797393	0.002021292
0.477107675	0.002633977
0.561377479	0.003236391
0.635592816	0.003838736
0.697500807	0.00442436
0.873063164	0.007162584
0.93941932	0.009805305
0.966984238	0.012373262
0.980081851	0.014884252
0.987203915	0.017427233
0.991290778	0.019947424

5.2 Steel reinforcement

The reinforcement in uniaxial tensile tests is characterized as a steel material based on experimental stress-strain results. The behavior of the steel is described using an elastic linear strain hardening bilinear curve. The elastic properties are defined by a longitudinal modulus of elasticity of 200 GPa and a Poisson's ratio of 0.3. According to the British Standards Institution, the plastic behavior is characterized by the actual stress, σs, and the true plastic strain, $\sigma S$. Table 7 presents the data used in determining the properties of the reinforcing bars.

Table 7. Reinforcement stress

Ultimate Stress MPa	Plastic Pl Strain
560	0

5.3 Steel plate

The S4R element is chosen for its ability to model thin-shell plates, with high accuracy and computational efficiency.

The bi-linear plus nonlinear hardening model described by Eq. (4) below represents the rounded strain hardening response of hot-rolled steel and will therefore be suited for advanced numerical simulations of scenarios requiring tracking the progressive loss of stiffness. The nonlinear expression has a similar shape to that provided by Mander [20], and it has four model coefficients (K1, K2, K3, and K4) that are calibrated using least squares regression using tensile coupon test data. The authors believe that the quad-linear model is adequate and sufficiently accurate for the vast majority of engineering applications. Figure 7 shows stress-strain for steel plates in models.

7.png

Figure 7. Stress -strain curve for steel plate

$f(\varepsilon)=\left\{\begin{array}{c}E_{\varepsilon} \quad \text { for } \varepsilon \leq \varepsilon_y \\ f_y \quad\text { for } \varepsilon_{s h}<\varepsilon \leq \varepsilon_u \\ f_y+\left(f_u-f_y\right)\left\{K_1\left(\frac{\varepsilon-\varepsilon_{s h}}{\varepsilon_u-\varepsilon_{s h}}\right)+\frac{K_2\left(\frac{\varepsilon-\varepsilon_{s h}}{\varepsilon_u-\varepsilon_{s h}}\right)}{\left[1+K_3\left(\frac{\varepsilon-\varepsilon_{s h}}{\varepsilon_u-\varepsilon_{s h}}\right)^{K_4}\right]^{\frac{1}{K_4}}}\right\} \text { for } \varepsilon_{s h}<\varepsilon \leq \varepsilon_u\end{array}\right.$

$\varepsilon_{s h}=0.1 \frac{f_y}{f_u}-0.055$ but $0.015 \leq \varepsilon_{s h} \leq 0.03$

$A=\pi r^2$ .

Finally, we summary the properties values used in models in Table 8.

Table 8. Properties of materials

Hassanein et al. [20] offered experimental work as shown in Figure 9 investigations to evaluate the shear and bending moment behavior of a composite box girder with steel corrugated webs. We study the experimental work by finite element analytical in ABAQUS 2020 by using the same data in his work and compared the results. Figure 10 views the FEM for box girder.

The load-mid span deflection and failure mechanisms based on experimental testing were compared to finite element findings. As demonstrated in Figure 11, the finite element findings accord well with the experimental data. The finite element analysis predicted the maximum load for the specimen, which was 1090 kN, while the highest experimental load for the verification specimen was 1055 kN.

According to Hassanein, the effective width for shear resistance of a concrete slab is roughly equal to the width of the upper steel flange. Figure 12 depicts the von Mises stress levels at failure of specimen. The stresses can be seen to be focused in the upper and lower flanges, at the plastic hinge locations, and in the web yielded zone. Figure 13 also depicts the normal stress contours at failure of specimen. Normal stresses are similarly focused with high values at the plastic hinge sites in the upper and lower flanges.

As shown in Figure 14, the cracks are localized at shear stud positions and are restricted by the upper steel flange band width, after which the cracks progress throughout the whole width of the slab.

9.png

Figure 9. Specimen fabrication from the study conducted by Hassanein et al. [20]

10.png

Figure 10. Detail of FEM box girder

11.png

Figure 11. Load-deflection curve for exp. (Hassanein) and FEA

12.png

Figure 12. The von Mises stress

13.png

Figure 13. Normal stresses at failure

14.png

Figure 14. Failure mechanisms, both experimental (Hassanein) and FEA

In this work, composite box girders with corrugated steel web underwent finite element analysis to examine their bending and shear behaviour with strengthening. From this research, the following findings are drawn:

-The steel corrugated webs on the composite box girders with strengthens have a sufficiently ductile behaviour.

-By preventing the predicted rapid collapse of the corrugated web, the concrete slab helps to improve the shear behaviour of steel box girders with corrugated web.

-Because steel is supposed to transmit shear and concrete is expected to withstand bending most of the time, the materials are used more effectively.

-The ductility of model G50 resulted in a notable increase in buckling wave compared to model G0, owing to its wider plasticity range before failure

-The employ the strengthen decrease the shear stress in web.

-The model gave a very good representation of the behavior of the actual model with a percentage of approximately 95%.

Future studies could build upon the findings of this research in several ways to address remaining questions and explore related issues:

Experimental validation: Performing experimental validation of the findings using physical testing of box girder prototypes. This can verify the accuracy and applicability of the theoretical models developed in this study

Cyclic loads: Cyclic loads can be applied, which represent, for example, the movement of vehicles over the bridge to understand the behavior of the box girder more realistically.