HIGHER ORDER (HO4) FINITE STRIP ANALYSIS OF SIMPLY SUPPORTED THIN WALLED BOX GIRDER BRIDGE SUBJECTED TO VEHICULAR LOAD

A box girder bridge is a special case of folded plate with closed cross section. Box girder bridges have proved to be very efficient structural solution for medium and long span bridges. Thin-walled box girder bridges are most economical. There are three box girder configurations commonly used in practice. Box girders can be constructed as Single cell (one box), multi-spine cell (separate boxes) or multi-cell (contiguous boxes or cellular shape). Analytically, however, the box girder bridge is a complex indeterminate problem. Several researches have been carried out on advanced analytical methods of analyzing thin-walled box girder bridge for many years in order to better understand the behavior of all types of box-girder bridges, the results of these different research works are dispersed and undervalued. Therefore, existing methods for analyzing box girder bridges need to be improved; such improvements will either seek to simplify existing methods or attempt to improve results accuracy.

The present work introduced the structural analysis of box girder bridges using Higher Order (HO4) Finite Strip which is an improvement to the existing higher order HO3 type. On account of its complexity, a MATLAB Computer program for determining structural response of thin-walled box girder bridges was developed using Higher Order (HO4) Flat Shell Strip. A simply supported thin-walled multi-cell box girder bridge was be adopted as the analytical structure. Validation of the theoretical formulations, which is synthesized in the proposed higher order (H04) finite strip computer program, was carried out by comparing the results obtained using the developed program with beam theory solution and the theoretical analysis results in published literature. Using three prototype models of simply supported thin-walled multi-cell box girder bridge i.e. model 1 (two-cell), model 2 (three-cell) and model 3 (four-cell) a numerical study of displacement and stress distributions was carried out to demonstrate the application of the theoretical formulations and developed computer program to the analysis of a typical simply supported thin-walled multi-cell box girder bridge subjected to vehicular loads. The analysis results were compared to the beam theory solution which does not include the effects of shear deformation. Results of analysis showed, among other findings that the effect of shear deformation were more in deflection than in stresses. Based on the results of analysis, distribution of stresses were studied, it was observed that the bending moments are resisted mainly by flanges whereas the shear stresses are resisted mainly by the webs. Investigating the effect of number of cells in a reinforced concrete box girder bridge using the developed model, the analysis results as presented in Tables (4.4, 4.5, 4.6, 4.11 - 4.19) and Figs.(4.4 – 4.12) showed that the Model 3 (four-cell) is the most efficient of the three prototype model in terms of strength properties – deflection and stress distribution. However, it will be more costly in construction than the other two. Therefore, the principles and programs developed in this research could be used in practice for the analysis of simply supported thin-walled multi-cell box girder bridge, box beam and folded plate structures.

 

PRELIMINARIES

Front cover text

 

4.4:  Dead Load Deflection for various cells 79

4.5: Live Load Deflection for various cells 79

 

 

 

 

 

 

A box girder bridge is regarded as a special case of folded plate with closed cross section. Box girder bridges proved to be very efficient structural solution for bridges of medium and long span. The most economical are the thin-walled box girder bridges. There are three types of box girders that are widely used in practice. Box girders can be categorized as single cells (one box), multiple boxes (separate boxes) or multi-cells (contiguous boxes or cellular shape). It can be constructed together with the deck or afterwards, the deck can be constructed separately. The box girders are made up of pre-stressed concrete, reinforced concrete or structural steel. Box girders can be categorized as circular, trapezoidal and rectangular depending on its form (Savio and Reshma 2017).

Fig. 1.2: Typical multispine box girder bridge cross-section

Fig. 1.3: Typical multicell box girder bridge cross-section

However, analytically, the box girder bridge is an indeterminate structure. Vlasov (1961a, 1961b, and 1965) provided the fundamental solution for analyzing thin- walled box girder bridges using the theory of Thin-Walled Beam. Several researchers and scholars have since approached the analytical problem with different other methods [Wen (2011); Zhao et al., 2016; Ankush & Mamadapur, 2016; Kumar & Shilpa, 2016; Shuqin, 2016; Feng et al., 2017; Pragya & Bokare, 2017; Gajera et al., 2017; Najla & Priyanka, 2017; Bhagwat et al., 2017; Huili et al., 2017; Khadiranaikar and Venkateshwar, (2016); Wang et al. (2017); Feng et al., 2017; Zhao, 2017; Nalawade et al., 2018; Xue et al., 2018]. In the present research work, the finite strip approach of structural analysis will be used. It is one of the advanced approaches such as the system of finite elements. Cheung (1968A) first introduced the Lower Order Finite Strip Method (LO2) to analyze simply supported plates and extended it to rectangular slabs with general end boundary conditions (Cheung, 1968B). Independently, Power and Ogden (1969) develop the finite strip approach for the rectangular slab bridge analysis. Cheung (1969B) examined curved slab and box girder bridges, using the lower order finite strip.

In 1971, Loo and Cusens implemented a finite strip approach with one inner nodal line (higher order finite strip, HO3). In 1971, Cheung and Cheung used the approach to examine cut conical shaped structures. This method (HO3) has an advantage over the lower order (LO2) because it is more refined and as such converges faster with more accurate result than the lower order method.

The present work seeks an improvement over the Higher Order (HO3) finite strip method by introducing the Higher Order (HO4) finite strip method in which the strip has two internal nodal lines. The concept assumed a higher level of refinement over the HO3 type. Higher order (HO4) flat shell strips will be fully formulated in this work and then applied to the simply supported thin-walled box girder bridge analysis so as to examine the effect of number of cells on the static behaviour of simply supported thin-walled box girder bridges made of reinforced concrete. For example, the analytical rigors involved in higher order (HO4) finite strip method are supposed to be higher than those of the HO3 and lower order (LO2) forms.

MATLAB software will be used to formulate a computer program for the determination of structural behaviour. Shear deformation effects are included in the structural responses determined using Higher Order (HO4) finite strip model. Therefore, all parametric studies will be examined using this developed model. Finally, the results of the structural analysis obtained with the developed model will be compared with the beam theory solution which does not include the effect of shear deformation.

This work introduces the structural analysis of box girder bridges using Higher Order (HO4) Finite Strip Method, an improvement to the earlier established HO3 form of higher order. Although, several researches have been carried out on advanced analytical methods of analyzing thin-walled box girder bridge for many years in order to better understand the behavior of all types of box-girder bridges, the results of these different research works are dispersed and undervalued (Ezeokpube, 2015).

Therefore, existing methods for analyzing box girder bridges need to be improved; such improvements will either seek to simplify existing methods or attempt to improve results accuracy. The present work seek an improvement over the Higher Order (HO3) finite strip method by introducing the Higher order (HO4) finite strip method in which the strip has two internal nodal lines. The concept of higher order (HO4) assumed a higher level of refinement over the HO3 type, so it is expected that results will be improved in accuracy. Due to its complexity, the Higher Order (HO4) Flat Shell Strip Model will be used to develop a MATLAB Computer program to assess the structural response of thin-walled box girder. The analytical design shall be implemented as a simple supported thin-walled multi-cell box girder.

The Load considered includes Dead Load (Self-weight), Live Load (Vehicular Loading) and Combined Load Cases (Dead Load + Live Load). The bridge model is a thin-walled four-lane simply supported reinforced concrete box girder bridge. The dimensions of the bridge are chosen so as to fully obey the thin-walled cross-section theory [Kurian and Menon (2007)]. In this review, Higher Order (HO4) Flat Shell Strip will be fully developed and then applied to the Simply Supported Thin-Walled Box Girder Bridge analysis to investigate the effect of the number of cells on the static reaction of a reinforced concrete clearly supported thin walled box girder.

Box Girder Bridge will be categorized in three (3) models, i.e. two-cell, three-cell and four-cell box girders Fig. 4.3, 4.4 and 4.5. For all model the carriage width is kept unchanged as 14.64 m and on both sides the footpath is 1.83 m. The boundary condition is simply supported; span of 48 m with l/d ratio of 25, depth of the box girder is 1.92 m. The webs on the top and bottom flanges are normal; the top flanges are cantilevered due to economical and aesthetic reasons. At the middle span, each bridge lane is subjected to the model vehicle One Standard AASHTO HS-25. A total of four vehicles are centrally located at the four-lane bridge's mid-span. Just half of the bridge is tested for symmetry.

All parametric studies, however, must be evaluated using this computer program developed. Ultimately, compare the results of the analysis obtained using the developed program for 2-cell, 3-cell and 4-cell with the published literature and beam theory solution that totally omit influence of shear deformation.

The objective of this study is to formulate a higher-order (HO4) flat shell strip model and then apply it to the simply supported thin-walled box girder bridge assessment so as to examine the effect of number of cells on the static behavior of reinforced concrete simply supported thin-walled box girder bridges.

And, the specific objectives are to:

Because of its improved stability, serviceability, economy, artistic attractiveness and structural performance, the use of box girder is increasing in popularity in bridge engineering community (Bhivgade, 2016). Box girders are an efficient form of bridge construction because they have reduced weight with optimum flexural rigidity and strength. Box girders have high torsional rigidity and strength compared to an equivalent open cross section member (John & Prasad, 2017).

Significantly, box girder bridge could be a solution for potential problem of traffic growth in Nigeria due to its efficient dispersal of congested traffic, economic considerations and aesthetic beauty, as the hollow portion of such bridges could be used as subways for pedestrian traffic and to accommodate facilities such as public utilities and drainage systems.

Although, several researches have been carried out on advanced analytical methods of analyzing thin-walled box girder bridge for many years in order to better understand the behavior of all types of box-girder bridges, the results of these different research works are dispersed and undervalued (Ezeokpube, 2015). Therefore, existing methods for analyzing box girder bridges need to be improved; such improvements will either seek to simplify existing methods or attempt to improve results accuracy. The present work seek an improvement over the Higher Order (HO3) finite strip method by introducing the Higher order (HO4) finite strip method in which the strip has two internal nodal lines. The concept of higher order (HO4) assumed a higher level of refinement over the HO3 type, so it is expected that results will be improved in accuracy. Significantly, the developed method, higher order (HO4) finite strip model as presented will serve as a preliminary work and a leading research method in the field engineering analysis where very high level of accuracy is of outmost importance.

Using a high-order (HO4) finite strip method, elastic analysis of simply supported thin walled box girder bridge shall be performed to determine the static response that includes the effect of shear deformation. Study of dynamic and stability analysis are outside the scope of this work.

One of the limitations experienced during compilation of this research work is modeling the developed method {high order (HO4) finite strip model} in MatLab computer program. However, after further research and comprehensive training on MatLab computer program, I was able to overcome by applying the necessary methodologies and commands. Nevertheless, the major limitation of this work is that the fixed support and the continuous bridge structure were not addressed.