Analysis of Flexural Performance of Steel-timber Composite Cantilever Beam

Steel-timber composite member is a new kind of structural member composed of steel plates and planks which are connected by bolts. The finite element analysis results on the flexural behavior of steel-timber composite centilever beam show that the stress of steel plate exceeds the yield strength before the bearing capacity of the composite beam is lost. Under the premise of ensuring the yield of the steel plate, the increase in the thickness of plank has little effect on the in-plane bending stiffness of composite beam, and the lateral bending stiffness of the composite beam is obviously improved which means the plank can effectively restrain the lateral buckling of the core steel plate. Based on the deflection analysis of composite beams, the deflection coefficient of steel-timber composite is derived.


Introduction
Considering the national sustainable development strategy, it will be a general trend to select green building materials with less consumption of resources and energy, less impact on the ecological environment and higher recycling efficiency [1,2]. In the summary report on construction and climate change issued by the United Nations Environment Programme in 2012, it was pointed out that the annual greenhouse gas emissions of the construction industry accounted for 30% of the global annual greenhouse gas emissions, while consuming 40% of the global energy. If no rectification measures are taken, the greenhouse gas emissions of the construction industry in the next 20 years will be twice as much as the present. Steel has the advantages of light weight, high strength, recyclable, less environmental pollution and fast construction speed, but stability has always been a key concern in steel structure design [3].Timber is a kind of natural environmental protection and renewable material, but it has obvious anisotropic characteristics, and the design strength is relatively low, so it is limited in the application of large-span and high-rise buildings, and the failure is always brittle [4,5].The steel-timber composite member is a close and effective combination of steel plate and plank through bolts,which is showed in Fig. 1.Steel with high strength is used to bear external load directly, and wood is used as surface material to provide enough lateral and torsional stiffness for core steel plate, so that the core steel plate will not occur global instability and local buckling before yielding [6,7], so that the design strength can be fully utilized [8].

Finite Element Analysis of Steel Wood Composite Cantilever Beam
For comparing and analyzing the bending performance of steel cantilever beam and steel-timber composite cantilever beam, and considering the influence of timber thickness on the bending performance of composite beam [9,10], a set of finite element calculation models of cantilever steel beam and three groups of steel-timber composite cantilever beam are designed.

Component Design
For the steel-timber composite cantilever beam, both sides of the board provide enough lateral bending stiffness and torsional stiffness for the composite beam, which can effectively suppress the overall buckling instability of the core steel plate. In order to ensure that the local buckling of the steel plate will not occur before yielding, the bolt spacing is reasonably designed by using the thin plate theory. The specific design parameters are shown in Table 1. A transverse concentrated load of 4.5kN is applied on the upper surface of the cantilever end of the steel plate, which ensures that the maximum stress at the fixed end of the steel plate can reach the yield strength.

Mechanical Properties of Materials
The mechanical properties of steel and timber are tested respectively. The specific results are shown in Table 2.

Results of Finite Element Analysis
According to the shape of the first buckling mode, the initial defect is introduced into the model, and then the large deformation analysis is carried out on the model including the initial defect, and the 3 material nonlinearity is considered at the same time. When the program is calculated to 0.3397 times of the applied load, the calculation does not converge and the calculation is terminated. The vertical and lateral deformation of cantilever end of each load step are shown in Figure 2 and Figure 3.We can see that the steel plate is far from yielding.  After the static small deformation analysis of three kinds of steel-timber composite cantilever beam, the buckling analysis is carried out, and the buckling mode is obtained. After reading the first buckling mode, the model is loaded with initial defects, and the large deformation analysis is carried out with material nonlinearity considered. The vertical and lateral deformation of cantilever end and the lower surface point of fixed end of each load step are read as shown in Figure 4 and Figure 5.

Lateral Bending Stiffness of Steel-timber Composite Cantilever Beam
The results of finite element analysis show that the lateral deformation of steel-timber composite beam is small in elastic stage, and its bending stiffness can be calculated according to Eq. (1). When the thickness of the board is 30mm, the calculation results are shown in Table 3.

Conclusion
(1) Through the finite element analysis and calculation, the steel cantilever beam loses its bearing capacity due to the premature lateral buckling instability. Due to the sufficient lateral stiffness of the composite members provided by the boards on both sides, there is no obvious stiffness mutation of the composite members under the load. The stress of the core steel could reaches the yield strength, and the bearing capacity and ductility of the steel wood composite cantilever beam are significantly improved.
(2) After the steel reaches the yield, the increase of the thickness of the board has less effect on the transverse bending stiffness of the composite beam. Therefore, in the design of steel-timber composite components, the thickness of wood board should be controlled to reduce the weight of the structure and the cost.
(3) The deflection coefficient of steel-timber composite beam is deduced. It can be seen from the calculation results that the deflection coefficient of the composite beam has little difference under different loads, and the calculation result is reliable.