Comparative Analysis of Three Typical Cantilever Scaffold Supporting Systems


 In order to effectively guide the selection of scaffold in designing the cantilever scaffold, comprehensive analyses of three typical scaffold supporting systems (including fully cantilever, bottom-supporting cantilever and pull-up cantilever) are carried out. The calculation formulas of the internal force for the three scaffold supporting systems are proposed based on the theoretical analysis, which are effectively verified by the finite element method (FEM). In addition, the force mechanism and benefits of the three scaffold supporting systems are compared and analyzed combined with actual engineering. The results indicate that there is high calculating accuracy for the proposed internal force and deflection calculation formulas about the scaffold supporting systems. According to the distribution uniformity of the internal force and controlling of the deformation of the main girder, the bottom-supporting cantilever system is undoubtedly the best choice. While the pull-up cantilever supporting system is the best choice when considering the aspects of cost, construction period and social benefits, which ought to be popularized in engineering practice.


Introduction
Scaffold plays an important role in the building construction, based on the principles of action, scaffold currently includes attached lifting frames, climbing frames and cantilever frames [1][2][3].
According to the classification of the force systems, the scaffold includes fully cantilever, bottomsupporting cantilever, pull-up cantilever and bottom-supporting pull-up cantilever systems [4][5][6].
Even though the fully cantilever scaffold is widely used in actual engineering [7], this type of scaffold requiring holes left ahead of time in the walls and floors, which do harm to the building structure and may lead to later leakage. In order to solve these problems when using fully cantilever scaffold, the bottom-supporting cantilever scaffold [4,5,8] and pull-up cantilever scaffold [9][10][11][12] were effectively put forward. So far, much work has been done on the designing, installation, using and monitoring of the fully cantilever scaffold [13][14][15][16][17][18][19][20], and rich experience has also been accumulated on the actual engineering application. However, even though the bottom-supporting cantilever scaffold and pull-up cantilever scaffold are widely used, as well as current research focuses on the engineering construction, the designing method of these two types of scaffolds remain referring to the designing of fully cantilever scaffold. Because the supporting systems of fully cantilever scaffold, bottom-supporting cantilever scaffold and pull-up cantilever scaffold are different, it is obviously unreasonable to design these two scaffolds according to the method of fully cantilever scaffold.
In addition, cutting cost is hoped when erecting and dismantling scaffolds. Therefore, this research try to evaluate the differences of three typical cantilever scaffold supporting systems on the structures, forces and benefits, which provide a valuable reference for the engineering designing and choosing of scaffold supporting systems.

Comparative analysis of the structures of three supporting system
The structures of the three scaffolds (cantilever scaffold, bottom-supporting cantilever scaffold, and pull-up cantilever scaffold) are shown in Fig. 1(a), Figs. 1(b) and 1(c), respectively. According to Fig.1, the force transmission systems of the three scaffolds are similar, in which the force is transmitted from scaffold plate → horizontal rod → longitudinal horizontal rod → vertical rod → load-bearing beam. And the major difference of the scaffolds is the way the force transmitting from the load-bearing beam to the structure. The load on the bearing beam in Fig. 1(a) is directly transmitted to the structure floor and wall, and the load-bearing beam and structure floor are generally fixed by 3 U-shape bolts. While the load on the cantilever bearing beam of bottom-supporting cantilever scaffold (see in Fig. 1(b)) is partially transmitted to the bottom-supporting beam, which is eventually transmitted to the building structure by the bottom-supporting beam and cantilever beam. The fixing bolts are used between bottomsupporting beams and building structure walls, between cantilever beams and building structure walls, between bottom-supporting beams and cantilever beams, respectively. As to the pull-up cantilever scaffold in Fig. 1(c), the load on the cantilever bearing beam is partially transmitted to the upper tie rod and then transmitted to the structure through upper tie rod and cantilever beam. It is notable that the cantilever beams and building structure walls are fixed by bolts, and the upper tie rods and structure walls are articulated, the articulated connection is also used for the upper tie rods and cantilever beams.
Therefore, the most obvious differences among the three scaffold systems are the supporting systems, and the difference in supporting system will inevitably lead to different force transmission paths and force on the scaffold, different installation and disassembly construction procedures, as well as different construction periods, economic benefits and social benefits.
3 The overall force analysis of three supporting systems 3.1 Force analysis and verification of the fully cantilever supporting system

Force analysis
As Figure 1(a) shows, the supporting system of fully cantilever scaffold can be simplified to The free end deflection is Where, x represents the distance between the section of cantilever main beam and the anchor point center. E means the elastic modulus of the cantilever main beam, and I represents the inertia moment of the cantilever main beam.

FEM verification
FEM is an effective way for the modern numerical calculation, which has been widely used in engineering practice [21,22]. Hence, the FEM was used in this research to verify the accuracy and precision of the force of fully cantilever supporting system before calculating it by eqs. (1) to (3).
As table 1 shows the geometric parameters, the cantilever main beam is an articulated unit with a cantilever on one side, which was set as I16 steel. A 2-node linear beam element and ideal elastoplastic constitutive model were used in the simulation, with the elastic modulus 206 GPa, Poisson's ratio 0.30, and the yield stress 235 MPa. The value of concentrated load n =20.00kN F , and the self-weight load =0.246kN / m q . Table 1 Calculation parameters of fully cantilever supporting system  Considering the relationships of angle coordination, displacement coordination in two directions and force-balance between the connection of the bottom-supporting beam and cantilever main beam, the axial force on the bottom-supporting beam is 10 And the shear force is 10 The bending moment is 10 The process variables 11 Where,  represents the angle between the axial direction and vertical direction of the bottom-supporting beam, which satisfies When obtaining the force of the node, the bending moment of the cantilever main beam can be obtained by eq. (18).
And the shear force is The axial force is The free end deflection is Where, x represents the horizontal distance between the internal force section point and the fixed end of the cantilever main beam.
The bending moment of the bottom-supporting beam is And the shear force is The axial force is Where, x is the horizontal distance between the internal force section point and the fixed end of the bottom-supporting beam.

FEM Verification
Similarly, the I16 I-beam and I10 I-beam are used for the cantilever main beam and bottomsupporting beams, respectively, with the 2-node linear beam elements adopted in the simulation. In addition, the boundary conditions of fixed connection were used among the cantilever main beams,   The supporting system of the pull-up cantilever scaffold in Fig. 1(c) can be simplified to Fig.   6. h represents the vertical distance of the articulated point between tie rod and building structure to the fixed point between the cantilever main beam and building structure, and ppo l is the horizontal distance of connecting point between tie rod and building structure to the fixed point between the cantilever main beam and building structure. In addition, pro l denotes the length of the tie rod.
The axial force of the cantilever main beam is And the maximum deflection of the cantilever main beam at the free end of the beam is

FEM Verification
In this section, the I16 I-beam and 2-node linear beam elements are used for the cantilever main beams. In addition, the fixed connections are also adapted for the cantilever main beams and building structure, while the connections between the pull-up tie rods and cantilever main beams and between the pull-up tie rods and building structure are the articulated way. Moreover, the ideal elasto-plastic model is selected for the cantilever main beams and pull-up tie rods, with the value of elastic modulus 206 GPa, Poisson's ratio 0.30, yield stress 235 MPa, concentrated load n =20.00kN F and self-weight load =0.246kN / m q . The rest parameters can be seen in Table 3.  Because the main cantilever beam is a common component of the three supporting systems, which is often used for bearing bending moment. As Fig. 8 shows, comparing with the fully cantilever main beam, the bending moments of the bottom-supporting cantilever main beam and pull-up cantilever main beam along the axial direction of the beam are more reasonable, whose bearing capacities are well balanced along the axial direction. Besides, the bearing capacity of the bottom-supporting cantilever main beam plays more rational than that in the pull-up cantilever main beam. As a result, the existence of the bottom-supporting beam and pull-up tie rod effectively improve the utilization rate of the material strength of the cantilever main beam. While this effect is more obvious for the bottom-supporting beam since its stiffness is larger than the pull-up tie rod, which means the restraining effect on the cantilever main beam is more obvious for the bottomsupporting beam other than the pull-up tie rod.

Comparison of the benefits of the three supporting systems
Because the scaffold is mainly used for a platform for on-site construction, which does not directly generate economic benefits. However, as the profit margin of the construction industry continues to decline, it is hoped to end a project without prolonging the construction period and complete building and disassembling the scaffold at the lowest cost.
Hence, in order to guide actual engineering practice, the designing of the cantilever scaffold at economic benefits, social benefits and construction period are compared based on a real estate project in Beijing, the corresponding cost is shown in table 4. In order to compare the economic benefits of the three supporting systems, the main beams of the fully cantilever supporting system, the main beams and bottom-supporting beams of the bottomsupporting cantilever supporting system are selected to ensure the maximum principal stress and deflection of the two systems are close.
The cost of the three systems is shown in Table 4, when the deflections and stress controlling levels of the main beam are the same, the cost ranking from high to low is fully, bottom-supporting and pull-up cantilever system. And the cost of the pull-up cantilever system only accounts for 51.07% of the fully cantilever system, which is due to the main beam of the fully cantilever system partially inserts to the building and the insert part is hard to bear load. As a result, the difference of the utilization rate of the three systems along the length of the main beam are huge.

Comparison of the construction period
As shown in table 5, the construction period of the pull-up and bottom-supporting cantilever systems account for 37.5% of the fully cantilever supporting systems, since both the connections of pull-up and bottom-supporting systems mainly by bolts, and easy to be installed and removed. In addition, the existence of the small holes in the building left by the two systems can be quickly blocked through grouting. However, when dismantling the main beam of a fully cantilever supporting system, it is inevitable to cut the U-shaped ring, which eventually leading to a large hole, which requires a long time to be blocked by concrete or block plugging.

Comparison of the social benefits
Compared with the fully cantilever supporting system, the main beams of the pull-up cantilever supporting system and bottom-supporting cantilever supporting system have the advantages in short length, small cross-sectional area and light weight, which are beneficial for the construction workers and the construction efficiency can be effectively enhanced.
In addition, the structural holes left by the fully cantilever supporting system are larger than the holes due to the pull-up and bottom-supporting cantilever supporting system, which is difficult to be blocked and easy to cause external wall leakage. As a result, the owners' living experience are greatly affected and the maintenance cost is also increased.

Conclusion
The theoretical analysis and FEM are used to compare the structure, force mechanism and benefits of the three cantilever scaffolds, the conclusions are as follows: (1) The formulas of the internal force and deflection about the three proposed scaffold supporting systems have high accuracy, which can be used as a reference for specific designing work.
(2) The bottom-supporting cantilever supporting system has the best uniformity of the internal force distribution and deformation controlling of the main girder, followed by the pull-up cantilever supporting system, and the fully cantilever supporting system lies worst.
(3) Compared with the fully cantilever supporting system, the pull-up cantilever supporting system can effectively save 48.93% cost and 62.5% construction period, as well as has good social benefits, which is recommended in engineering practice.

Data availability
All data generated or analyzed during this study are included in figures of the current manuscript.