WP3

1 - NTUA

Modelling, analysis and design of optimized structural systems: Steel - Concrete

13

36

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In this work package the collapse load of optimized steel and concrete structures, hence their strength, will be predicted by means of advanced nonlinear numerical analysis, in order to verify the ultimate limit state criteria. It is well known that collapse may be due to development at certain cross-sections of stresses exceeding the material capacity, a condition known as material nonlinearity, or due to buckling, associated with sudden increase of displacements for a small increase in applied load, a condition known also as geometric nonlinearity, or due to a combination of both types of nonlinearity. The prevailing approach proposed by modern codes for carrying out checks of steel members in the ultimate limit state consists of obtaining action effects by means of linear elastic analysis of the structure subjected to design loads, and comparing them for each member to resistances that account for both types of eventual nonlinearity. This is usually accomplished by multiplying the cross-section resistance, assuming full exploitation of the material capacity of the cross-section, by appropriate reduction factors, representing the influence of geometric nonlinearity, accounting also for the reduction of strength due to interaction between axial forces and bending moments. However, such reduction and interaction factors are available only for simple, common cases of geometry and loading. For the unconventional shapes of structural members resulting from the optimization process a different approach will be needed, as outlined in this work package.

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WP3 - Modelling, analysis and design of optimized structural systems: Steel - Concrete [Months: 13-36]

NTUA

In recent years structural design codes have adopted limit state design (LSD), replacing the older concept of allowable
stress design (ASD) [1-2]. Limit state design requires the structure to satisfy two principal criteria: the ultimate limit
state (ULS) and the serviceability limit state (SLS). A limit state is a set of performance criteria that must be met when
the structure is subject to loads. To satisfy the ultimate limit state, the structure must not collapse when subjected to
any of the pertinent combinations of its design loads. To satisfy the serviceability limit state criteria, a structure must
remain functional for its intended use subject to routine, everyday loading. In SLS the structure remains elastic, thus
modelling and analysis do not pose any substantial difficulties, taking also into account the powerful computational
tools that are available nowadays. For ULS checks, however, the issue described above is a significant obstacle for the
design of structures with unconventional geometry. In order to address this shortcoming, modern codes already allow
predicting collapse by means of more elaborate, nonlinear analysis with imperfections [1]. Recent technical literature
contributes in that direction [3-10]. The WP consists of the following Tasks:
Task 3.1: Methodology
Numerical tools for understanding the behaviour, predicting all possible failure mechanisms, and evaluating the ultimate
strength of steel structures by means of commercially available finite element software will be critically reviewed. Failure
dominated by either material yielding or instability will be addressed, as well as interaction of failure modes. Steps
will include setting up an appropriate finite element models, obtaining critical buckling modes from linearized buckling
analysis (LBA), and then using a linear combination of these modes as imperfection pattern for geometrically and
material nonlinear imperfection analyses (GMNIA). Equilibrium paths accompanied by snapshots of deformation and
stress distribution at characteristic points will be employed for evaluating the results of the GMNI analysis, identifying
the dominant failure modes and the corresponding weak areas, thus being able to propose appropriate strengthening
measures, if needed. Practical details of the implementation of the proposed strategy will be addressed.
Task 3.2: Case studies
The methodology of Task 4.1 will be applied for the structural design of a wide range of steel and concrete structures
resulting from the optimization process of WP1 and WP2. This will consists of (i) Transformation of the obtained
optimized shapes into structural members that can actually be manufactured, (ii) Dimensioning of these members by
means of the above mentioned advanced nonlinear finite element analysis methodology, (iii) Iterative interaction with the
“Optimization Group” in order to balance eventual conflicts between optimization, aesthetics, safety, constructability,
(iv) Design of connections between finalized structural members.
Task 3.3: Comparison between numerical and code-based design
For the case studies addressed in Task 4.2, it will be attempted to compare the more exact dimensioning based on
nonlinear analyses with approximate results obtained if trying to adapt the available code provisions to the unusual
geometries of the optimized structures, taking into account that the latter approach would be the one followed by practising structural engineers, if confronted with such a problem. Depending on the results of the comparison, it will
also be attempted to propose simple guidelines and corrective factors in order to better adapt code provisions to certain
types of optimized steel structures, for example trusses and arches.

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