Optimization of Quickly Assembled Steel-Concrete Composite Bridge Used in Temporary

The temporary bridge is used to cross river, canyon, ditches and other obstacles duo to its simplicity, convenience for operation and short construction time.How to design the temporary bridge economically and install it quickly are the primary considerations to meet the load requirements and traffic considerations. Based on the structural optimization design theory, the Small Arch Bridge, which is a steel-concrete composite girder bridge and locates in Fu ling district of Chongqing city, is optimized using the linear programming method. In this method, first assume the cross-section of I-girder and the dimensions of deck as the design variables, the mechanical behavior of the whole bridge and the deformation stiffness as the constraints, and then find the minimized cost using MATLAB optimization tools. On the basis of the optimization results, this paper presented the arguments of I-girder and deck panel which meet the mechanical and economical requirements and could provide some references for bridges of like.


Introduction
The temporarybridge isbuilt for constructionand transportation, for example, in thedisaster relief,the mountainsacrossthe valleygrooveorbridgelocateswhere the geological condition can'tmeet the constructionand transportationrequirements.Service time of the temporary bridge is short and it loses function as soon as the project completes, therefore, how to design the temporary bridge economically and install it quicklyarethe primaryconsiderations to meet theloadrequirements andtrafficconsiderations (Sun Z. & Hu W., 2010).
In recent years, the research about structural optimization theory and method are numerous at home and abroad, which have been exploring along different roads in engineering practice, and some have already achieved significant outcomes (André D. O. & Dan M. F., 2011).As a new field, it still has a lot of uncovered things worthy of further research and exploration.Based on modern technology and associated with the ideal design of structure, it has aroused great interest of many scientific and technical workers and attracted people for the further research on the theory and method, as well as made contribution to the application in the engineering design (Li Zh., 1982).
The designer is an optimizer (Richard B., 2006).Optimal design theory provides a shortcut to optimize the design of the temporary bridge, in this paper, the structural optimizationtheory is used to illustrate the optimization ofquicklyassembledsteel-concrete composite bridge availablefor emergency.(Jiang A., 1986) Structural optimization is using structural analysis theory to describe the problem in mathematical way, namely create a mathematical model, and then select a reasonable and effective calculation method to solve the problem by computer programming.On the basis of the structure parameters, the maximum or minimum solutions of the objective function that satisfy all the constraints can be found out.

The Structural Optimization Theory
The programming method is currently used in the structural optimization, which in fact is to seek the extreme point of the objective function.
When using the programming method, specify the design variable i x and the objective function Minimize W and make it satisfy the constraints.
Where n is the number of design variables, m is the number of constraints, w is the objective function of weight, g is the constraint function.
For simplicity, formula (a) can be abbreviated as: Where X is the vector comprising of 1 2 , ,

Project Introduction
The Small Arch Bridge locates in Fu ling District of Chongqing city, which is a 1-10 meter stone arch bridge built in 1958 and cross Yuelailong River.The design load is automotive-20 and trailer-100.After the water level of the Three Gorges Dam reservoir reaches 175 meter, the bridge site was flooded, so the original bridge was reconstructed as a 20 m steel-concrete composite simply supported beam bridge connected with PCCS shear connector.The vehicle load is highway -Ⅱ, the crowd load is 3.5kN/m 2 , and the bridge width is 2m (sidewalk) +2 × 3.5m (driveway) +2 m (sidewalk), the superelevation is 1.5%.C40 concrete is used for the deck and Q345 is used for the I-girder.To facilitate the fast construction and save material usage, the bridge was first built as temporary bridge, and then the deck and I-girder were connected by shear connector transforming the temporary bridge to long-term bridge.The general layout and cross-section of the Small Arch Bridge are shown in Figure 1 and Figure 2.

The Optimization Process
In the optimization of the Small Arch Bridge, the least cost is assumed as the objective function, the cross-section of I-girder and the dimensions of deck are assumed as the design variables, the mechanical behavior of the whole bridge was analyzed to identify the constraints, then to find the minimized solution of cost using MATLAB programming.

Calculation of the Temporary Bridge
The concrete deck of emergency bridge is directly placed on the I-girder and no connection measures such as shear key are implemented.The deformation of the I-girder under load is shown in Figures 3 and 4. As is shown in Figure 4, the I-girder of the emergency bridge is subjected to self-weight, lane load and concentrate load caused by the bridge deck, the concentrate load can be simplified as uniform load in the calculation.The deck panel itself can be simplified as a simply supported beam.

The Mechanical Analysis of I-girder
Figure 5 is the calculation diagram of the I-girder of the emergency bridge.The design load is highway -Ⅱ.

Figure 5. Calculation diagram of emergency bridge I-girder
The slandered lane uniform load and concentrate load of highway -Ⅱ is 0.75 times of the highway-Ⅰ.For highway-Ⅰ, 10.5 , k p is determined by linear interpolation.0.75 10.5 7.875 Where L is the bridge span (m), g is the self-weight of the bridge deck (KN), t is the thickness of the bridge deck (m), l is calculated span of deck panel (m).A is the cross-section area of I-girder (JTG D60-2004).
The moment of girder at the joint action of dead load and vehicle load is given by: Lower flange controlling stress of I-girder: 25 78.5 7.875 3 120 2 10 0 8 4 (5) Where: z c -centroid coordinate of I-girder cross section I -Moment of inertia of I-girder Figure 6 is the cross-section of I-girder.Assuming the thickness and the moment of inertia of the upper and lower flange is negligible.The cross-section area of I-girder is The selected a coordinate system oyz is shown in Figure 7, C is the centroid of cross-section.
Figure 7.The selected coordinate system The centroid coordinates of composite cross-section is given by: I-girder cross section can be regarded to consist of three rectangular cross sections when calculating the cross-section inertia moment, and then according to rectangular cross-section inertia moment formula (Where yi I is the inertia moment of each part of the composite cross-section in terms of y-axis, n is the number of rectangular cross-section), the moment of inertia of girder cross section is given by:  (8) 2) The lateral force analysis (Yao L., 2008) The lateral force analysis of the deck panel is in accordance with the internal forces analysis of carriageway board.The carriageway board is subjected to the wheel load directly, so 1 2 0.2 a a   , and the effective distribution width 2 3 a l 

Force Analysis of the Long-Term Bridge
The mechanism of the long-term bridge is significantly different from that of the emergency bridge.In the long-term bridge, the deck panel is connected to the I-girder through shear connector to form steel -concrete composite girder.Therefore, the external force is resisted by the joint work of steel girder and concrete panel, and the deformation of the deck panel is in accordance with the I-girder as is shown in Figure 10.The long-term bridge is a steel -concrete composite girder, in which the deck panels and the upper flange of girder are mainly in compression and the bottom flange in tension.This paper mainly calculated stress of I-girder.The main girder calculation diagram is shown in Figure 11.
The bending moment of girder under self-weight, secondary load and vehicle load is given by: ZC '-centroid coordinate of composite cross-section, I -Moment of inertia of composite cross-section Figure 12 is the cross-section of the steel-concrete composite girder.
Figure 12.Cross-section of composite girder Figure 13 shows the selected coordinate system oyz, C is centroid of composite cross-section.The centroid coordinates of composite cross-section is given by: When calculating the inertia moment of composite cross-section, the inertia moment should be first translated into a unified form.Here the inertia moment of deck panel is converted into the inertia moment that can be multiplied by steel elastic modulus, that is, 3 12 I lt  is converted to

.2 Force Analysis of the Deck Panel
For long-term bridge, the deck panels are covered with pavement comprising of 10cm anti-wear concrete and 8cm asphalt concrete.According to Internal force calculation method of the carriageway board, the calculation diagram of deck panel is shown in Figure 9.The minimum cost of the whole bridge is assumed as the objective function, due to that the price of steel is much higher than that of the concrete, calculation of the above formula will yield unexpected results of the deck thickness using the optimization toolbox in MATLAB directly, in some cases, the thickness is up to 1m or even more.Therefore, iterative method was used, first calculate the thickness and computing length of deck according to the stress controlling equation 6, and then assume that the deck thickness is 0.2m and the computing length of deck is 1.4m.The width of Small Arch Bridge is 9m, for the easy arrangement of girder, assume that the computing length of deck is 1.5m (the space of I-girder), then the deck thickness is 0.21m, and select a general thickness of 0.25m.Then the deck thickness of 0.25m, and calculating span of 1.5m were substituted into the equation 3.4 whose results proved its reasonability, thus the bridge deck thickness is 0.25m and the calculated span is 1.5m.
The fmincon function (constrained nonlinear programming) in MATLAB optimization toolbox was used.In the optimization process, if numerical level reaches10-4, the result is 0, therefore 0.001 is defined as the minimum value.The values of I-girder height h, I-beam web thickness TW are assumed as conventional integer and the calculation results are shown in Table 1.

Conclusions
In the design of a temporary bridge, except formeeting theloadrequirements andtrafficconsiderations, the cost economy should be taken into account.On the basis of the structural optimization design theory, the Small Arch Bridge, which is a steel-concrete composite girder bridge, is optimized by using the linear programming method and the basic theory of bridge engineering.Refereed to relevant specification,that is assuming the cross-section of I-girder and the dimensions of deck as the design variables, and the mechanical behavior of the whole bridge and the deformation stiffness as the constraints, the minimized solution of cost using optimization tool can be found out.To ensure the optimization toolbox in MATLAB yields the expected results, iterative method is proposed instead of using the toolbox directly.According to the optimization results, this paper presented the arguments of steel I-girder and deck panel that meet the mechanical and economical requirements for steel-concrete composite girder bridges within the span of 20m.The results of this paper could also provide some references for bridges of like.
This example also illustrates the structure optimal design theory in engineering application universality.The method is calculated by MATLAB software using the optimization theory of mathematics which is simple and intuitive but not so fast and convenient.It can be believed that with the development of mathematics, bridge engineering, new tools and methods can be found out to solve this kind of problems.

Figure 1 .
Figure 1.General layout of the Small Arch Bridge

Figure 2 .
Figure 2. Cross-section of the Small Arch Bridge

Figure 3 .
Figure 3. Deformation of I-girder 7) 4.1.2Force Analysis of the Deck Panel 1) The longitudinal force analysis According to Figures 1, 2, the deck along the longitudinal direction can be simplified as a simply supported beam shown in Figure 8.

Figure 8 .l
Figure 8.The longitudinal calculation diagram of deck panel

Figure 10 .
Figure 10.Deformation of the deck panel and I-girder

Figure
Figure 11.The calculation diagram of I-girder

Figure 13 .
Figure13.The selected coordinate system of composite cross-section

.I
Plus with the inertia moment of I-girder cross-section, the parallel shift formula of moment of is the inertia moment of each part of the composite cross-section in terms of y-axis, n is the number of rectangular cross-section), the inertia moment I z of composite girder cross section is given by (Chai H. Y., Kyungsik K., Kyoung C. Lee & Junsuk K., 2013):

Table 1 .
The results of optimization