By R. Walls and A. Elvin,
University of the Witwatersrand,
School of Civil & Environmental
This article presents a method for automating the structural design process and optimising structures. If the geometry, loading and design requirements of a building are provided a newly developed computer program can choose member sections to satisfy design criteria.
When project schedules are tight, or design budgets are limited, engineers cannot easily produce cost-effective designs because they do not have the time, or sometimes the experience, to optimise structures. Yet, the cost of a building is governed far more by material and labour costs than design costs, which makes good designs essential.
When designing a structure the main requirements that have to be satisfied are deflection limits and strength criteria. It is relatively easy to satisfy strength requirements using design codes, but the process of satisfying deflections is based on an engineer’s intuition while using time-consuming, iterative methods. For instance, if the deflection of the structure shown in figure 1 was to be reduced it would be difficult to identify which members to stiffen and at least several changes would be required before each deflection limit is satisfied. Material and time can be wasted if the wrong members are strengthened.
HOW TO AUTOMATE THE DESIGN PROCESS
The new method developed uses mathematical techniques based on the principle of virtual work to determine which sections should be used in a structure to efficiently satisfy deflection limits, whilst also meeting strength requirements. Most design systems are generally limited in that they cannot consider deflection code requirements.
The automated design program will be described considering the warehouse in figure 2 as an example.
1. Input your structure, its loading, its design specifications (such as effective lengths) and the deflection limits that must be met. In this example two deflection limits are considered: (a) horizontal deflection of the latticed column on the left, and (b) the vertical deflection of the apex of the roof. The loadings are shown in figures 3 and 4 respectively.
2. Members are initially chosen by the program to satisfy only strength criteria for all load cases. Once member strength requirements have been satisfied deflection limits have to be met.
3. Deflection contributions of each member in the structure to the deflection of the critical nodes are calculated using the principle of virtual work. This is represented in Figures 3 and 4 where the thicknesses of the lines are proportional to the deflection contributions of the members. In figure 3 crane loads are applied and the critical node is where the maximum horizontal sway occurs in the latticed column on the left. In figure 4 dead, imposed and wind loads are applied and the critical node is at the roof apex.
4. Standard section databases (e.g. SAISC ‘Red Book’) are searched to find which groups of members should be changed to give the highest deflection decrease per mass increase. These changes are then made and the structure is retested and adjusted in an iterative manner.
5. The program continues to make changes to reduce deflections until all limits and strength requirements are satisfied.
6. The program is fully automated requiring no experience or engineering intuition to produce a final structure of minimal weight and cost.
FEATURES OF THE OPTIMISATION PROCESS
In this method members can be adjusted as entire groups and not only as individual members. This ensures that practical construction considerations can be taken into account by limiting the number of different section sizes in a structure. The member selection process can be linked to standard pricing databases such that cost estimates can be quickly obtained during the design process. This is particularly useful in the tendering process where cost estimates are required before full designs are done. If a variety of structures need to be investigated to determine which option will be cheapest this method can be used to design all the various alternatives, and the designer can then choose the best one. When optimising a structure relative deflections can be taken into account. Figure 5 shows the member deflection contributions to the relative horizontal sway between the 15th and 16th floors in a 24 storey building when wind loads were applied. The program was used on this structure until the relative sway between each floor was limited to L/300. Deflections drop as members are stiffened and at the same time the total mass of the structure increases. The irregularities in the graph are due to the fact that 30 different deflection criteria are being met simultaneously. Also, strength dependent members are continuously being adjusted, as forces redistribute, to be the lightest possible sections satisfying strength requirements.
The method and program discussed here are currently being developed to optimise structures efficiently with multiple deflection criteria and load cases. The aim is to produce an integrated optimisation and design software system. This software will help engineers design structures in less time while saving clients money.