International graduate ventures in Structural Engineering
Prof. Peter Mark
Institure of Concrete Structures
Prof. Rüdiger Höffer
Wind Engineering and Fluid Dynamics
International cooperation for graduation of doctoral researchers in sturctural engineering
The project aims to support and qualify young Macedonian researchers by means of a tightly guided and well-structured graduation program that, after three years of sound scientific investigations, leads to a German doctoral degree awarded by the faculty of Civil and Environmental Engineering of RUB. It is proposed as an extension of an already existent international cooperation named Dynamic Networking (DYNET) that constitutes an educational program within the framework of the stability pact for South Eastern Europe funded by DAAD and one of its spin-offs SEEFORM that denotes the South East European Graduate School for Master and PhD FORMation.
The latter one already comprises multi-lateral agreements between regional universities and offers a structured PhD program with courses taught by experts in Germany and abroad. Right this year in October the first 10 successful years of SEEFORM achievements – by the way an already existent excellent and international visible RUB beacon – will be celebrated in Skopje, Republic of Macedonia.
Further partner universities are located in Serbia (Belgrade and Nis) and Sarajevo (Bosnia and Herzegovina). Recently Pristina University in Kosovo joined the group. Its statutory targets are an inclusion of the South-Eastern European colleagues to the international scientific community, as well as to establish and to further develop joint research activities and cooperation. Thereby, a keystone is training and qualification of young researchers by means of mutual exchange of experience, knowledge transfer as well as open data access.
Especially this keystone is of great importance since the Macedonian government recently decided to generally dispose the so long mandatory position of assistants at research institutes. These institutes now face serious problems in finding and financing qualified personnel to keep things going. Especially due to large teaching obligations of the few affordable high-potentials left, their research work is in danger to suffer from these bad conditions.
Yet, the aim of the proposal is to live and to deepen the joint international cooperation with RUB’s institutional partner “University Ss. Cyril and Methodius” (USCM), in Skopje. Originally inspired and established by the pioneering commitments of em. Prof. G. Schmid (RUB) the two universities, mainly by means of their faculties of Civil Engineering and especially the chairs of concrete structures (Prof. Markovski, Prof. Mark), structural analysis (Prof. Dumova-Jovanovska) as well as wind engineering and fluid dynamics (Prof. Höffer) cooperate actively.
Of great value for the Macedonian partner are especially so called “sur-place” scholarships for PhD-candidates offered by the SEEFORM program. These allow the candidates to work and teach at their home institutes meanwhile research journeys to Germany are scheduled regularly. However, up to now no “sur-place” scholarship is available at USCM. Hence, the proposal aims at closing this gap by a co-financed and structured PhD-program for two candidates per phase of three years duration (Fig.1).
Due to the fast track their PhD-work is thoroughly scheduled right from the beginning by means of comprehensive work-plans comprising both experimental and numerical parts, definition of distinct steps to target mile-stones and regular assessments of intermediate achievements. In between active contribution to international conferences is mandatory. Supervisors will be in close contact to the candidates and offer seminar and workshops at the partner’s institution. This procedure grants a mutual and ongoing exchange of experience and facilitates to employ synergetic potentials of all parties involved.
Additionally, the candidates will obtain guest status within the RURS community and benefit from RURS training offers and officially signed agreements of supervision of the bilateral partners.
Finally, their written thesis shall be submitted in English and being defended, if once approved by the examiners, against an international graduation committee. The partners jointly agree to award a German doctoral degree instead of a national one. In the remainder the scientific background of the advised first project phase is laid out in greater detail
July 1st - September 30th, 2015
Time-dependent behavior of reinforced concrete structures under random variable loads
Here is a brief introduction of myself. I am Marija Docevska from Macedonia, Phd candidate and scholarship holder at the Institute of Concrete Structures at Ruhr-University of Bochum. Supervisor of my doctoral thesis is Prof. Peter Mark (Ruhr-University of Bochum, Germany) and co-supervisor is Prof. Goran Markovski (University SS. Cyril and Methodius, Skopje, R. Macedonia).
In my project focus is set on random variable loads and their influence on time-dependent behavior on reinforced concrete elements.There are many cases in which concrete structures undergo variable, but non-periodic loads with random load-time history. The most characteristic case is traffic loads on bridges, whose prediction at the designing stage is very difficult due to inherent complexity and randomness. Application of rainflow counting algorithms reduces these complex load data into series of nominal stresses characterized by a maximum stress regarding vehicle type (Fig.1).
However, theoretical knowledge of time-dependent behavior of reinforced concrete elements subjected to variable random loads is still limited. Most specific time-dependent parameters of concrete are: compressive and tensile strength, modulus of elasticity and bond between concrete and reinforcement bars. Today, current building codes do not provide much information how to include parameters variation in time, when elements are subjected to these types of loads. From that point of view, experimental and theoretical investigations in this field will be of prime importance.
The research work focuses on theoretical and experimental analysis and random processes of loading on reinforced concrete beams under bending. The analyzed elements are simple supported beams with a span of 300cm and a uniform cross-section of 15cm width by 28cm height made of ordinary strength concrete (C30/37). In a period of one year, time-dependent behavior of them subjected to various random histories of loads will be investigated. Strains in concrete and reinforcement, deflections and crack widths will be measured continuously with special experimental equipment. The loads will be applied in the third points of the beam’s length through gravity levers as depicted on Fig.2.
This is a collaborative project of the Institutes of Structural Engineering at the SS. Cyril and Methodius University of Skopje (Macedonia) and Ruhr-University of Bochum (Germany), financially supported by the Research School at the Ruhr-University of Bochum. The experimental part of this project will be executed in laboratories at the University in Skopje and the theoretical part at the University in Bochum.
Until this moment, analytical and numerical (FEM software DIANA) pre-calculations of short-term-instantaneous and long-term deflections subjected to constant sustained loads were done. They are found to be in a good agreement with the experimental results (Fig.3).
January - Feburary, 2016
Long-Term Deflections of Reinforced Concrete Beams
During my second stay in Bochum from January to February 2016, the main focus of research was set on computations of long-term deflections of reinforced concrete beams subjected to cyclic loading and partial unloading.
Therefore, a simply supported reference beam subjected to four point bending has been discretized with finite elements along its length and employing layers over the cross-sectional height to account for the very different constitutive behavior of concrete and reinforcement. Additionally, the time has been discretized in steps according to the cyclic load pattern displayed in Fig. 1.
Next, an attempt has been made to extend the application of the well-established layer section method for long-term deformation analyses including creep and shrinkage effects. Dealing with complex load histories as variable loads applied in load cycles generally are, an application of the Age-Adjusted Effective Modulus Method (AAEMM) is no longer appropriate and more refined time analysis techniques become necessary.
For that purpose, a step-by-step numerical method (SSM) was employed in which the state of stresses and strains in concrete in each time step depend on the previous ones. In these computations changes of the neutral axis position, the evolution of cracked portions of the cross-section, and the depth of the crack tip with time were taken into account owing to the layer section method.
Finally, the development of the beam’s mid-span deflections with time was obtained from moment-curvature integration employing Simpson’s rule.
Fig. 1: Schematic sketch of the applied methods
The right side of Fig. 2 shows experimental results taken from literature presenting the evolution of deflections under cycles of loading and partial unloading lasting 24 hours for each load cycle. The left part of the same figure presents a comparison between these results and own results obtained by the previously described calculation method. Here, the comparison was made only regarding two cycles of loading and two cycles of unloading, as marked on the figure. Comparison aims at a check of the reliability of the model.
From Fig. 2 it can be seen that the computational model to predict the deformation behaves less stiff than the reference beam. Actually and more precisely, the deflections are overestimated for the loading part and underestimated for the unloading one. The reason of these discrepancies is currently seen in a general exclusion of the cracked concrete’s contribution in tension to the global stiffness of the cracked beam element.
Fig. 2: Comparison between the deflections of RC cracked beam obtained analytically and experimentally
Therefore, the analytical approach is planned to be enhanced with non-linear material models such as constitutive relations that allow accounting for cracked concrete’s contribution in tension (“tension-softening”) under long-term loading and a reduced tensile concrete strength due to sustained loads in the future (Fig.3).
Fig. 3: Tension-softening diagrams for concrete subjected to short-term (a) and long-term (b) loading
Since concrete has a different creep behavior under loading and unloading, alternative compliance functions for the partial removal of loads should be employed in the calculations, too, taking into account the specific age of concrete at unloading.
Next is to implement the enhanced model in MATLAB for an automatic calculation of long-term deflections under different artificial random load histories. That way it can serve for pre-calculations and specimen design of the envisaged experimental tests.
June – September 2016
Long-Term Deflections of Reinforced Concrete Beams subjected to cyclic variable loads
The above described step-wise numerical procedure for prediction of time-dependent variable load-induced deflections has now been implemented in MATLAB software. Just for the sake of simplicity the single effects of creep and shrinkage under cyclic loads are treated separately. Computation is generally based on integration of the curvature. Both portions, induced by creep and shrinkage are simply superimposed to an instantaneous curvature. In order to obtain realistic long-term deflections, modified moment-curvature relations are separately used for short-term and long-term analysis accounting for an increasing curvature with time due to creep and shrinkage (Fig.1).
Fig.1: Modified moment-curvature relations for short-term (left) and long-term analysis (right) due to creep and shrinkage
Concrete’s phenomenological behavior to creep under variable repeated loads is nowadays well recognized in current design codes. For example, EN 1992-1-1 (Eurocode 2) considers creep in serviceability limit state load combinations assuming a quasi-permanent portion of the live loads ψ2Q, wherein ψ2 is the quasi-permanent coefficient which depends on the duration of the live load. Nevertheless, for more precise deformational analysis aside such rather coarse assumptions, the real loading history has to be considered carefully. This is reasoned by a distinct interaction between cracks and deflections in flexural members and especially holds true for cases in which the value of a quasi-permanent load is lower than the one inducing cracks but the actual load level (sum of permanent and live load) is higher. In the remainder results for deflections obtained from both approaches, considering a real load history and on the basis of quasi-permanent load combinations according to EC2 are presented and contrasted.
Fig.2: Time-dependent deflections under variable (cyclic) loading
Fig. 2 presents long term mid-span deflections of a simply supported beam calculated with the described method for the load pattern displayed on the same figure (solid black line) versus experimentally obtained deflections (grey line). The black solid lines present the deflections after removing (the lower one) and after applying the live load Q in a sustained manner for 24 hours (upper one). By contrast, the dashed line in Fig.1 presents the long-term deflection calculated on the basis of a quasi-permanent combination of loads. The value for the quasi-permanent coefficient ψ2 in these calculations was taken to 0.5, already established on the basis of available experimental results (quasi permanent load: F = FG + ψ2FQ = 4 + 0.5 * 7.6 = 7.8 kN). The results in both cases show a trend to underestimate deflections with time. However, in general they are in a good accordance with the experimental data.
Herein, the tension stiffening effect is considered interpolating between the curvature in non-cracked and cracked states through a distribution coefficient ζ (Eq. 1), as suggested in Eurocode 2, which results in an average curvature (Eq. 2).
Eq.1 & Eq.2
This procedure offers an opportunity to model tension-stiffening reduction due to sustained and repeated loads in a simple manner only. It employs an coefficient taken constant to a value of 0.50 right from the beginning of loading.
Doing so, tension-stiffening is underestimated during the first days of loading, which is the main reason for a larger overestimation of the calculated deflections at the beginning compared to the end of the considered time period (Fig.2). In future work an attempt will be made to propose a time-dependent reduction of tension-stiffening due to creep and shrinkage, or more precisely, a loss of tension-stiffening properties as a function of time.
Influence of load histories on the long-term behavior of RC structures
January-February 2017 (13.01.2017-01.03.2017)
Recently, the influence of expected but idealized load histories typical for structural service conditions during life-time is studied with special emphasis on long-term serviceability. For that purpose, a numerical step-by-step cross-sectional procedure has been developed and successfully verified applying it on simply supported RC beams and one-way slabs.
Load histories typical for construction phases commonly consist of an initial load during construction already applied at early concrete ages followed by a quasi-permanent load which covers self-weight (sw) and certain live load peaks. In general, the latter ones are specific for the service life of individual RC structures like parking garages, bridges, warehouses etc. and are characterized by individual load cycles with partial unloading of variable amplitude and duration. Of course, for numerical computation such specific patterns must be idealized to blocks of regular intensity and duration.
Within the load histories typical for construction phases (case 1 in Fig.1) the initial load peak during construction was varied in order to study its influence on the final long-term behavior. In those typical for structures service life (case 2 in Fig.1) a constant total load level was kept, while intensity and duration of the variable load as well as the portion of the permanent load regarding the cracking load (G/Fcr) were varied. Details on all characteristic variables for both types of load histories are contained in Fig. 1 below.
Fig. 1: Real vs. simplified load histories for RC structures during construction and service life
Some results by means of calculated local (curvature) and global (deflections) long-term deformations caused by the idealized load histories typical for construction and service lives are shown in Figs. 2 and 3 respectively. The results in Fig. 2 indicate that the initial load during construction affects the long-term final deformations due to collateral cracking. Even in short-term, these load peaks indirectly influence the long-term behavior of RC elements through an initial but permanent reduction of the member’s stiffness, especially when the load intensity exceeds the subsequent load level (in this case a quasi-permanent one).
Fig.2: Long-term curvature due to different load histories typical for construction phases of a structure
Fig. 3 shows that the permanent-to-cracking load ratio (G/Fcr), as well as the duration of the loading and unloading cycles (∆tU/∆tL=8h/16h and ∆tU/∆tL=24h/24h) influence the long-term final deflections also, but in different ways. Apparently, these characteristics of the load histories are of relevance when assessing long-term serviceability of creep sensitive structures, too.
Fig. 3: Long-term deflections caused by cyclic load histories with ∆tU/∆tL =8h/16h and ∆tU/∆tL =24h/24h along with the deflections caused by a permanent load only
The final long-term deflections caused by repeated loads highly depend on concrete creep and creep recovery and the way it is modeled in each cycle. Since a creep recovery law available from literature disables modelling of concrete behavior under cyclic load regimes, it was introduced herein with the same functions as those for creep. This way of modelling underestimates the final deflections and restricts the application of such calculations to cases when the time under load is less than the time in partial unloading. Thus, additional experimental and theoretical investigations for creep recovery functions after partial and full unloading are necessary in order to enhance the current numerical model.
Additionally, the challenge regarding an impact of cracking on the irreversible part of creep and the irreversible part of instantaneous deflections after unloading still remains. Experiments to solve these problems are scheduled for the next phase at Ruhr-University Bochum.