Structural analysis revealed that, in the transformed cells described above, ceramide backbones containing phytosphingosine and a VLCFA molecule were also detected.
Structural analysis and modeling in bridge engineering and design are the themes of this chapter. The first section is dedicated to structural analysis, including equilibrium, compatibility, and constitutive laws equations, with a computational mechanics and theoretical approach. Furthermore, the structural behavior of materials, including nonlinearity, is discussed. The second section is dedicated to structural modeling, including finite element method (FEM) basic principles, modeling elements, modeling methods, material and cross-section details, boundaries, modeling strategies, modeling approaches, and modeling tips subdivided by bridge type.
Structural Analysis for FDI exists for decades, and a large number of studies in this field have contributed to reach a certain maturity regarding theoretical issues (Cocquempot et al. (1998); Staroswiecki et al. (2000); Krysander and Nyberg (2002); Blanke et al. (2003)). Recently, algorithmic aspects of structural analysis have been investigated (Dustegor et al. (2004c,a,b); Krysander and Nyberg (2005); Dustegor (2005)) but many implementation issues are still to be addressed.
Systems’ structure changes can be caused by the modification of operating modes or production objectives, the technological evolution of some equipments or the failure of any component that makes some subsystems temporarily unavailable. The current approach re-iterates the whole structural analysis from the beginning. This can be a real drawback, when very large scale applications are considered. The major aim of this paper is to adapt the existing structural analysis methodology to structure modifications, that is to say, re-use some of the structural results.
The benefit of such an adaptive algorithm is twofold. First, it enables determining structural properties and performing structural analysis efficiently when system structure changes. Especially when very large scale system are considered, the efficiency due to re-use of already obtained results is valuable. Secondly, such an algorithm is an important tool for safe system design. Indeed, such adaptive algorithms enable the rapid test of different configurations. The designer can efficiently and easily add sensors, try different fault scenarii, change the system’s component architecture.
Section 2 recalls the main steps of structural analysis for FDI. Section 3 analyzes the different kinds of structure modifications that can occur. Then, section 4 treats the constraint removal case whereas 5 proposes a solution to the constraint addition case. Finally, section 6 summarizes the whole analysis.
Structural analysis comprises the set of mechanics theories that obey physical laws required to study and predict the behavior of structures. The subjects of structural analysis are engineering artifacts whose integrity is judged largely on their ability to withstand loads. Structural analysis incorporates the fields of mechanics and dynamics as well as the many failure theories. From a theoretical perspective, the primary goal of structural analysis is the computation of deformations, internal forces, and stresses. In practice, structural analysis reveals the structural performance of the engineering design and ensures the soundness of structural integrity in design without dependence on direct testing.
In the mechanical and aerospace industries, engineers often confront the challenge of designing mechanical systems and components that can sustain operating loads, meet functional requirements, and last longer. It is imperative that these structures contain a minimum of material to reduce cost and increase efficiency of the mechanical system, such as in terms of fuel consumption. The geometry of these load-bearing structural components is usually complicated because of strength and efficiency requirements. Three of such structural components are shown in Figure 7.1.
Figure 7.1. Structural components of highly complex geometry: (a) automotive suspension component and engine block and (b) airplane landing gear strut.
A number of approaches have been developed to support the design of structural components and systems, such as shape optimization (Chang and Edke, 2010), topology optimization (Bendsoe and Sigmund, 2003), and reliability-based design (Choi et al., 2007). Many have been employed to create designs for challenging applications, such as those shown in Figure 7.1. The success of these design methods is largely attributed to accurate underlying analysis methods that are built on fundamental mechanics theory and physics laws.
To perform an accurate analysis a structural engineer must determine such information as structural loads, geometry, support conditions, and materials properties. The results of his or her analysis typically include support reactions, stresses, and displacements. This information is then compared to criteria that indicate the conditions of failure. Advanced structural analysis may examine dynamic response, stability, and nonlinear behavior.
Analytical methods make use of analytical formulations that apply mostly to simple linear elastic models, lead to closed-form solutions, and can often be solved by hand. Such methods include strength of materials, energy methods, and linear elasticity. Numerical approaches, such as FEM, are more applicable to structures of arbitrary size and complexity; they employ numerical algorithms for solving differential equations built upon theories of mechanics.
Regardless of approach, the formulation is based on the same three fundamental relations: equilibrium, constitutive, and compatibility. The solutions are approximate when any of these relations is only approximately satisfied or is only an approximation of reality. There always exist uncertainties in modeling and analysis of structural components. It is imperative to account for these uncertainties in order to design more reliable mechanical systems.
In this chapter, we start by briefly reviewing analytical methods and then discuss finite element methods. Essential ingredients in using FEM for modeling and analysis of structural problems, such as mesh generation and boundary conditions, are discussed in detail. We also discuss commercial FEA software, both general-purpose and specialized. Example problems modeled and solved using commercial codes are presented. In this chapter, we also include advanced FEA methods that might be of interest in solving more complex and specialized problems.
The structural analysis of offshore structures should be carried out using a commercial software, as it is will be difficult to analyze it manually due to the complicate loading scenarios and their complex structural system. There are several analysis packages available for offshore such as Staad_Pro, SAP2000 and Bentley. Staad_Pro can perform nonlinear structural analysis. Dynamic response analysis due to environmental loads, impact effects analysis and severe accidental loadings analysis.
Program SAP2000 is another option. In this section, we are going to describe how to set up a Jacket Platform model and analyze using SAP2000, the global buckling analysis will also be covered.
Structural analysis is a science that ensures that the structures are safe and fulfill the functions for which they were built. Safety requirements must be met so that a structure is able to serve its purpose with the minimum of costs. Structural concepts arise from the work of engineers from different fields with a common aim that the structure is functional, aesthetic, and economic. Detailed planning of the structure usually comes from several studies made by town planners, investors, users, architects, and other engineers. In general, an architect is responsible to the investor and a structural engineer works in collaboration with the architect as an equal partner in a project. In some structures, such as industrial halls, bridges, and sports halls, a structural engineer has the main influence on the overall structural design and an architect is involved in aesthetic details. The process of analysis has to be repeated until the structure as a whole is optimal from all points of view, followed by final analysis and dimensioning.
Structural analysis of an average size offshore structure with many hundreds of members and as many as thirty to fifty load combinations result in the output of tens of thousands of quantities of deflections, stresses, interaction ratios and reaction forces. Review and sorting of these quantities by visual inspection may get quite involved, time consuming and error prone. To overcome this difficulty, most computer programs contain special post-processing sub-routines where the information is summarised and output in conveniently formatted tables. Some common output summary tables are:
Member Lowest and Highest Stress and Interaction Ratio Tables:
Members with stresses or interaction ratios above a specified maximum or below a specified minimum are flagged out. Using this table, over or undersigned members can be identified and resized.
Maximum Support Reaction Tables:
Load conditions that cause maximum axial load, bending moment or shear for a given support is tabulated. These tables can be used for the design of the piled supports.
Member Maximum Stress or Interaction Tables:
These types of tables identify the load condition for which the stress, interaction ratio or any other stress related quantity of a given parameter is a maximum. Figure 6.41 shows a graphic output of maximum interaction ratios from an offshore platform analysis software program.
Figure 6.41. Maximum interaction/utilization ratios of a jacket structure from a typical offshore platform analysis software program
Member Group Maximum Stress or Interaction Ratio Tables:
These tables identify the load conditions for which the stress or interaction ratio of a given member group is maximum. Such information enables sizing of a group as a whole and is useful in the design of symmetric or functionally similar members without the need for running many load directions.
Structural analysis of an ultra-deepwater riser will show larger axial (vertical) dynamic response than a shallower water riser due to the influence of the riser's additional mass and increased axial flexibility. Several computer programs are available within the industry for the 3-D time-domain riser analysis required for the combination of axial and lateral dynamic riser analysis.
Brekke, et al (1999) shows that 3-D random wave riser analysis is needed to determine accurate riser response estimates. This analysis discussed the fundamental contributors to tension variation, including (1) mass of the riser string times the vessel's vertical acceleration, (2) resonance at the axial natural period, and (3) lateral motions of the riser leading to additional tension variation. Random analysis is more accurate than regular wave analysis because it models the full spectrum of the seastate and thus avoids artificial response peaks near natural periods.
In random analysis, a realistic random seastate is generated in preparation for the riser analysis. The typical riser simulation is run for 1000 wave cycles, representing about a 3 h storm. In order to determine the results from this analysis, the peak and trough response of each parameter are determined as the maximum and minimum values that occurred during the simulation. If need be, this random analysis approach could be made more accurate by running multiple simulations and averaging the results or using statistical methods to obtain the extreme values.
2.3.3 Calculation of Quantity Reduction Effect by Application of High-Strength Concrete
Structural analysis was performed by replacing the four compressive strengths (24, 27, 30, and 35 MPa) with 40 MPa high-strength concrete. Based on this result, the quantity of concrete and reinforcing bars was computed and compared with existing designs. Reductions in cross-sections by the application of high-strength concrete were limited to vertical members (column, wall, core wall, and wall column). As a result, the reduction in concrete and reinforcing bars of vertical members was 8.8% and 30.3%, respectively, and such reduction is converted to a 5.7% and 19.7% reduction rate for the entire concrete and reinforcing bars on the entire building. Computed reduction rate was used to decrease the quantity of concrete and reinforcing bars. Such a decrease in quantity is caused by a reduction in the cross-section of vertical members from using high-strength concrete. Table 2.4 shows the reduction of the volume of concrete and reinforcing bars by applying high-strength concrete.
Table 2.4. The reduction of the volume of concrete and reinforcing bars by applying high-strength concrete (40 MPa)
Previous design
Design of high-strength concrete application
Reduction rate (%)
Vertical members
Concrete (m3)
11,377.30
10,374.10
8.8 ↓
Steel (ton)
545.33
379.94
30.3 ↓
Total members Horizontal + vertical
Concrete (m3)
17,596.06
16,589.57
5.7% ↓
Steel (t)
1667.94
1339.44
19.7% ↓
Relatively more CO2 is emitted when high-strength concrete is used because the amount of cement used is increased compared to normal-strength concrete. In order to solve this problem, methods such as substitution of a portion of cement with industrial wastes like blast furnace slag are being proposed [16–18]. This study assumed a mixture with 20% blast furnace slag in the cement. If a different mixture composition is used, an increase or decrease in concrete composition materials results, and such changes must be taken into consideration when calculating the amount of CO2. Fig. 2.2 shows the changes in the amount of cement, coarse aggregate, and fine aggregate with application of 40 MPa pressure. According to Fig. 2.2, the amount of cement increased by 1156 t, coarse aggregate increased by 490 t, and fine aggregate decreased by 1649 t when the high-strength concrete mixture composition was used. CO2 emission from the production of 1 kg of blast furnace slag is 0.0263 kg-CO2/kg, which is about 4% of the CO2 emission by 1 kg of cement at 0.7466 kg-CO2/kg. Table 2.5 shows the mixture compositions of concrete for each strength.
Figure 2.2. Change in quantity of materials upon application of high-strength concrete.
Table 2.5. Mixture compositions of concrete for each strength
Structural analysis is a powerful tool for early determination of detectability/isolability possibilities. This is important both to evaluate if the number and placement of sensors is adequate in order to meet diagnosis specifications.
Even though the structural information is very coarse, useful insights can be gained by analyzing the structure. This is also one of the strengths, since useful information can efficiently be obtained early in the development process before much work has been spent on obtaining detailed analytical models.
To evaluate possible isolability properties of the model, fault sensitivity of all possible parity relations need to be studied. Under some technical model assumptions [10], not included here, the isolability properties of a system can be determined by only considering the fault sensitivities of all MSO sets.
The fault isolability analysis, performed by the software, will be illustrated on the model in Figure 2. Assume that the actuator, the gain block, and the two sensors can fail. The corresponding fault modes are abbreviated A, G, S1, and S2 and the no-fault mode is denoted by NF. Multiple faults can be handled [11], but for brevity only single faults are considered. By including the behavioral mode information in the Simulink model the computed fault incidence matrix for the MSO sets is
In a noisy and uncertain environment we have to threshold the residuals such that the probability for false-alarm is low. Thus, conclusions about faults can only be drawn when a residual is larger than its associated threshold. When residuals are below thresholds, no conclusion can be drawn in a sound way. This means that for example S2 may invalidate the two last MSO sets. Thus, a large enough fault of the type S2 will be isolated as S2. However, no matter how large, a fault of the type A can not be separated from G. The output of the algorithm is a fault isolability matrix, which summarizes isolability properties of the model. The isolability matrix for the example is
where an X in position (i, j) means that behavioral mode i can be interpreted as behavioral mode j, i.e. behavioral mode i can not be isolated from behavioral mode j.
