Advanced Modelling Techniques in Structural Design

Chapter 1

Introduction

1.1 Aims and scope

With the fast development of modern construction technology, major international city skylines are changing dramatically. More and more complex buildings, such as Burj Khalifa in Dubai, the Birds Nest Stadium in Beijing and the London Aquatic Centre, have been built over the past decade. As a Chartered Structural Engineer, the author has worked for several leading international consultancy companies and has worked on several prestigious projects around the world. The experience of the author demonstrates that in current design practice most of these buildings could not have been designed without the use of advanced modelling techniques. Fierce competition in the current design market also requires structural engineers to handle the increasing difficulty in designing the more complicated projects required by both clients and architects. This challenge can only be tackled by using modern computer technology. It also imposes a big change in the role of the structural engineer: in addition to knowledge of basic design principles and structural analysis methods, an engineer should also have a full understanding of the latest modelling techniques. This is also the reason that advanced computer modelling skills have recently become essential for an engineer's recruitment by increasing numbers of design consultancies.

However, in the construction industry, most structural engineers find themselves lacking modelling knowledge, as few textbooks have been provided in this area. For students, although some elementary modelling techniques are taught in most Civil Engineering courses, no systematic introduction is made, let alone how to model a real construction project in practice. Therefore, a book in this area is imperative.

The main purpose of this book is to introduce and provide detailed knowledge of advanced numerical analysis methods and important design principles for both students and design practitioners. It addresses effective modelling techniques in solving real design problems and covers a broad range of design issues – such as lateral stability of tall buildings, buckling analysis of long-span structures and earthquake design – and some special issues such as progressive collapse, blast, structural fire analysis, foot-induced vibrations and so on.

It also introduces a variety of major modelling programs (such as SAP2000, ETABS, Abaqus®¹, ANSYS) and preprocessing software (Rhino, Revit, AutoCAD) used in current structural design practice. A number of modelling examples using this software are provided in the book. Most of the model examples are based on a worldwide selection of real design projects, such as the Millennium Bridge and Burj Kalifa, helping readers to find an effective way to model these types of structures.

In addition, the algorithms and theories that underpin the analysis, such as the finite element method (FEM) and smoothed particle hydrodynamics (SPH) method, are also introduced. Along with the introduction of modelling techniques, relevant design principles and design guidance are also covered. Thus this book can also serve as a handbook for structural engineers. A feature of this work is that it introduces advanced and complicated theory in a more understandable and practical way.

In real design practice, we analyse the structure with an advanced program to gain a level of confidence, such as a ball-park figure for the size of the structural members, but when we start the design we will still follow a code of practice, even though some are quite conservative. Advanced modelling is particularly complementary to current design guidance in those areas where it is still not clear. Therefore, this book will help readers understand the balance between analysis and design.

1.2 Main structural design problems

As a structural engineer, one is required to design different type of buildings such as tall buildings, bridges and space structures. Each type of structure features different structural design problems that a structural engineer needs to pay special attention to during their design. This book covers almost all the important design issues in modern construction projects. In this section, a brief introduction to these different structural problems will be given.

In tall building design, the main issue is the design of the lateral stability systems. In Chapter 3, a detailed introduction to the different lateral stability systems – such as out-triggers, tubular systems and bracing systems – will be given in addition to information on how to model them effectively.

Earthquake design is important for buildings being built in high seismic activity areas. This is covered in Chapter 4. The major earthquake analysis methods – such as response spectrum analysis, time history analysis and push-over analysis – are introduced and modelling examples in SAP2000 are also provided.

Progressive collapse has become another important issue since 911: Chapter 5 covers this topic. The design methods provided by the design guidance are introduced. Different analysis procedures, such as linear static, nonlinear static, linear dynamic and nonlinear dynamic analysis, are explained. A modelling example of nonlinear dynamic progressive collapse analysis is demonstrated using SAP2000.

Aside from conventional loading, blast and fire are other possible threats to the building and its occupants, and Chapters 6 and 7 cover these issues. How to represent these types of special loading and the corresponding design guidance are introduced. In Chapter 6 a new technique in modelling blast or impact effect, the SPH method, is introduced and a modelling example of SPH analysis using Abaqus® is demonstrated. In Chapter 7, a modelling example of heat transfer analysis of a structure is demonstrated.

For space structures, the main design issue is member buckling and overall buckling of the structure; the analysis theories underpinning buckling analysis are introduced in detail in Chapter 8 and corresponding modelling examples are also given. This chapter also covers a special topic on Tensegrity domes, which have a different structural form to conventional long-span space structures.

Regarding bridge structures, different structure types – such as the beam bridge, cantilever bridge, suspension bridge and cable-stayed bridge – are introduced in Chapter 9. One of the main design issues for bridges is designing the structure under moving load from vehicles, and the corresponding design guidance is introduced. Modelling examples of two famous bridges, Millau Viaduct and the Forth Bridge, are also given.

Foot-induced vibration is a critical issue for the design of foot bridges and hospitals. This is because foot bridges are prone to vibration problems, and hospital buildings have strict requirements for vibration prevention. The vibration problem and corresponding modelling examples are covered in Chapter 10.

1.3 Introduction of finite element method

Numerical methods are fundamental to most analysis software. There are extensive numerical methods that have been developed so far, which include the finite element method, boundary element method, finite difference method, finite volume method and the meshless method (such as the SPH method).

In structural analysis, the finite element method (FEM) is one widely used numerical method. Therefore, it is important for a structural engineer to have some basic knowledge of FEM. In this section, the basic principles of the finite element method will be introduced. Another numerical method, the SPH method, which is used for the analysis of blast or impact loading, will be introduced in Chapter 6.

1.3.1 Finite element methods

The development of the finite element method can be traced back to Courant (1943) in his investigation of the torsion problem. The term ‘finite element’ was first coined by Clough (1960) and research on this topic has also been conducted by other researchers such as Turner (1956). This numerical method was first used in structural analysis problems in civil and aeronautical engineering. Following that, FEM was applied to a wide range of engineering problems, and most commercial FEM software packages – such as Abaqus®, ADINA and ANSYS – were developed in the 1970s.

FEM is one of the numerical techniques for finding approximate solutions for differential equations with different boundary conditions. It divides a structure into several small elements, named finite elements, then reconnects these elements at their nodes through the compatibility relationships between each element, as the adjacent elements share the same degree of freedom (DOF) at connecting nodes (as is shown in Figure 1.1). The methods for connecting these simple element equations are provided to approximate a more complex equation over a larger domain. The displacement of each node can be determined by a set of simultaneous algebraic equations. Through the compatibility relationship, the displacement can be interpolated over the entire structure.

Fig. 1.1 Finite element mesh in Abaqus®.

Abaqus® screenshot reprinted with permission from Dassault Systèmes. Abaqus® is a registered trademark of Dassault Systèmes and/or its subsidiaries.

The major steps of a finite element model can be identified as follows:

Select element types.

Discretise the structure into pieces (elements with nodes).

Assemble the elements at the nodes to form a set of simultaneous equations.

Solve the equations, obtaining unknown variables (such as displacement) at the nodes.

Calculate the desired quantities at elements (strains, stresses etc.).

1.3.2 Finite element types

Based on actual engineering problems, there are different types of finite elements available that can be used in the analysis. The key difference between these different types of elements is in their degrees of freedom, and hence a suitable choice requires a reasonable assumption of structural behaviour by the engineer.

a. The truss element, as shown in Figure 1.2, is assumed to only resist axial force, not bending load and shear load; it is also called a two-force member, as it only has two internal forces at each end. It is usually used for modelling trusses (either bridge trusses or roof trusses) and space structures (domes, vaults etc.). Figure 1.3 illustrates an example of a roof truss model.

b. The frame element is shown in Figure 1.4; it can model axial, bending and torsional behaviour and is usually used to model beams and columns in a multi-storey building. In most finite elements programs there is also a beam element available, and the axial force is ignored in this type of element. In most structures, such as multi-storey buildings, the axial force in the structural beams can be ignored; therefore the beam element is accurate enough to model this type of structural element. For columns, as they withstand high axial loads and are also subject to bending and shear, frame elements are ideal for the simulation of this type of structural element.

c. The plate element is used to model flat structures whose deformation can be assumed to be predominantly flexural. Plate elements only consider out-of-plane forces; this means in-plane stress, such as the membrane effect, is not considered. Typical plate elements are shown in Figure 1.5.

d. The shell element is used to model both in-plane and out-of-plane forces. It consists of two types of conventional shell elements: 2D shell elements and 3D continuum shell elements.

The nodes of a conventional 2D shell element, however, do not define the shell thickness; the thickness is defined through section properties.

3D continuum shell elements resemble 3D solid elements (this will be introduced later) in that they discretise an entire 3D body yet are formulated such that their kinematic and constitutive behaviour is similar to conventional shell elements.

Although 3D continuum shell elements are more accurate in terms of modelling, in most engineering problems conventional 2D shell elements provide sufficient accuracy. In structural analysis, in most cases, 2D shell is effective for analysing structural members such as floor slabs or concrete shell roofs.

Figure 1.6 illustrates some typical shell elements. Figure 1.7 shows an example of a typical floor modelled with 2D shell elements.

Fig. 1.2Truss element.

Drawn in AutoCAD®. Autodesk with the permission of Autodesk, Inc.

Fig. 1.3 A roof truss model in SAP2000.

SAP2000 screenshot reprinted with permission of CSI.

Fig. 1.4 Frame element.

Drawn in AutoCAD.

Fig. 1.5 Typical plate element.

Drawn in AutoCAD.

Fig. 1.6Typical shell elements.

Drawn in AutoCAD.

Fig. 1.7 A typical floor modelled with 2D shell elements in Abaqus®.

Abaqus® screenshot reprinted with permission from Dassault Systèmes. Abaqus® is a registered trademark of Dassault Systèmes and/or its subsidiaries.

e. The 3D continuum element (solid element), as shown in Figure 1.8, can be used to model fully 3D structures such as dams and steel connections. Solid elements are the most accurate way to represent a real structure, however their computational cost is very high. Depending on the dimension of the structure and the engineering problems you want investigate, solid elements are not suitable for modelling a space structure or multi-storey building due to the high computational cost, it is better to model the full behaviours of a structural element, such as a composite connection (as shown in Figure 1.9). There are some structures for which 3D stress analysis is critical, one example is dams. As thermal stress, shrinkage and creep are critical in the design of a dam, only 3D stress analysis can accurately represent its 3D behaviour.

Fig. 1.8 Typical 3D solid elements.

Drawn in AutoCAD.

Fig. 1.9 A composite connection modelled using 3D continuum elements in Abaqus®.

Abaqus® screenshot reprinted with permission from Dassault Systèmes.

There are enormous numbers of 3D solid element types in analysis packages, for example Abaqus® has over 100 types of 3D elements such as C3D10 and C3D20; one of the main differences among them are the integration node numbers for each element. An element with the same shape can have different integration nodes. Figure 1.8 shows some typical 3D solid elements.

1.4 Conclusion

In this chapter, we have discussed typical engineering design problems for different types of structures. We have also introduced the finite element method and its application in structural analysis.

References

Clough R.W, 1960. The finite element method in plane stress analysis, Proceedings of American Society of Civil Engineers, 2nd Conference on Electronic Computations, Vol. 23, American Society of Civil Engineers, pp. 345–378.

Courant R., 1943. Variational methods for the solution of the problems of equilibrium and vibrations, Bulletin of the American Mathematical Society, 49: 1–23.

Turner M.J., Clough R.W., Martin H.C., and Topp L.C. 1956. Stiffness and deflection analysis of complex structures, Journal of Aeronautical Science, 23: 805–823, 854.

¹ Abaqus® is a registered trademark of Dassault Systèmes and/or its subsidiaries.

Chapter 2

Major modelling programs and building information modelling (BIM)

2.1 Fundamentals of analysis programs

In this section, how to effectively select a suitable analysis package and basic analysis procedures will be introduced.

2.1.1 Selection of correct analysis packages

There are many modelling programs, such as ANSYS, Abaqus®, ETABS and SAP2000, available to the construction industry. The key to choosing a suitable analysis program in design practice is based on the feature of the specific engineering problems, whether it can provide a suitable model to replicate the structure and its ease of use. This is particularly important as the complexity of the analysis increases; certain software packages may be more suited to a particular application.

All analysis packages used in the design practice can be divided into two main categories: general purpose programs and design orientated programs.

General purpose program such as Abaqus® and ANSYS are suitable for more advanced analyses. For special engineering problems, such as blast and fire, general purpose programs are the right option as they have extensive material models, elements and different solvers (such as explicit or implicit solvers). This has resulted in many consultant companies starting to use these types of software in their design practice in recent years. The disadvantage of this type of package is that design checks against code are not always available.

For a conventional structure problem, design-orientated software packages such as SAP2000, Staad.Pro, Robot and ETABS will be the best option. However, they usually have limited capability to model