The model in this paper is divided into two parts: the information model and the mathematical model. The information model includes establishing the BIM model of the construction site and the discretization of the construction site with () coordinates. A unit of 1 m is chosen as the reference of () coordinates in this paper, and the boundary of the edge of the building, which is less than 1 m, is not counted in the site. The information related to the crane location (Variable 1), trailer location (Variable 2), and component installation location (Variable 3) can be identified after the site location is turned into data by coordinates. The construction of the mathematical model is described in detail in Section 3.1
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The purpose of this paper is to give guidance in the selection and placement of tower cranes for a high-rise modular housing complex project during pre-construction. The objective is to determine the type of tower crane, its location, and the parking location of the trailer to transport each component so that the total cost of the tower crane is minimized.
Tower cranes can generally be divided by type into mobile and fixed tower cranes. Mobile tower cranes mainly rely on tracks or tires to move around the project cluster to achieve the work task, which is obviously unsuitable for crowded construction sites. Stationary tower cranes, on the other hand, do not move, use the rotation of the tower boom and trolley luffing to complete the work, and do not occupy a large area. Fixed tower cranes can be divided into two types: attached and internal climbing. The attached tower crane is mainly used in high-rise buildings because it can be raised according to the building and does not use too many tower standard joints and attachment rods as well as corresponding anchorages. The internal climbing tower crane is mostly used in super high-rise buildings, using the internal climbing device inside the core to raise the tower, which is not in line with the main body of this study. Therefore, this study selects the attached tower crane as the focus. The tower crane type refers to the different jib lengths and lifting capacities. A sketch of the attached tower crane structure is shown in Figure 1
To build the mathematical model, we used some information from the actual project, among which the available crane locations and crane configurations are limited and determined in advance; the height of the tower cranes is considered to meet the height requirements of the building as the number of tower sections increases; the trailer capacity is considered to meet the demand of the construction site because the trailers can continuously transport the components from the component factory to the construction site; the demand information of the components (location, component type, weight, and quantity), as well as the location of the demand points, are specific to the project itself. The operating cost of the tower crane is determined by the type of tower crane and the operating time of the tower crane. In addition to the above conditions, this paper also needs to set some assumptions:
For each lifting task, the tower crane operates at the same rate under full-load and no-load conditions;
The maximum lifting height of the tower crane meets the requirements of the building height;
There is no collision between tower cranes in operation;
The effect of component installation time on tower crane running time is excluded;
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Multiple components can be provided for a particular trailer dock.
One workflow of the tower crane is to start from the supply point, lift the components to the demand point, and then return from the demand point to the supply point to facilitate the next operation in this cycle. That is, the tower crane runs the same two distances in a lifting task, the difference is that during the first half, the tower crane is running with a heavy load and during the second half the crane is running with no load. However, the specific running rate is not only limited by the running rate of the tower crane itself but also related to the proficiency of the tower crane operator. In the model, the operator’s proficiency is adjusted by a factor, so the model defaults to the same operating rate for the tower at full and empty load, i.e., the tower spends twice as much time per hoisting task as it does one-way.
Because the model in this study is based on the jib length, lifting capacity, working rate, and the corresponding cost of the tower crane to make the selection, it does not take the height of the tower crane as the evaluation criterion, and because the selected tower crane is attached, as long as the maximum lifting height meets the requirements, the tower height can be increased by increasing the standard section of the tower. At this time, if the lifting boom length and lifting capacity also meet the requirements. the tower crane can meet the requirements. However, without Assumption 2, the maximum lifting height of some tower cranes will not meet the height requirements of the building, which may lead to the wrong answer for the model selection. Therefore Assumption 2 is necessary.
The constraint of minimum safe distance between tower cranes is set in this model, but it is not a conflict-free area between tower cranes, and there will be certain delays between tower cranes due to avoidance or coordination work, and these delays are affected by many factors and cannot be accurately evaluated in this study. So, this study assumes that there will be no collision between tower cranes; thus it is not affected by the delay time.
Unlike cast-in-place projects, tower cranes in modular projects also need to assist in the assembly of components. The difference in the difficulty of assembly between the components and the different proficiency of the staff in assembly will lead to different delay times for the tower crane to assist in assembly, which will only affect the progress of the project and will not affect the time for the tower crane to lift the components, so the impact of the assembly time of the components on the running time of the tower crane is not considered in the model.
Because the trailer consignment has the characteristic of walking and stopping, the components do not stay after lifting, and as long as the location is optimal, the next vehicle consigning the components can stop at the location where the previous vehicle stopped, which will not cause vehicle congestion, so the model considers that the trailer parking can be used many times, i.e., multiple components can be provided.
This document provides specifications for a European floor climbing crane model A-806. The crane has a maximum height of 120.75 meters and can operate at heights ranging from 40.52 to 150 meters over 7 levels. It has mechanisms for hoisting, trolley travel, slewing and traveling with specific speeds and horsepower ratings listed. Dimensions and weights are provided for the major crane components including the foundation mast, telescopic mast, slewing assembly, counterweight blocks and main jib assemblies.
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