## MUHAMMAD AJMAL KAREEMI

PhD Graduate**PhD program:**: XXXIV

**supervisor**: Prof. Giorgio Monti

**Thesis title:**The Shear Capacity of Truss-Type Prefabricated Beams: Tests, Mechanical Model, Design Calibration, and Optimization

Abstract
Truss-Type Prefabricated beams (TTP beams) are composed by prefabricated steel trusses, embedded in cast-in-place structural concrete, also called hybrid truss beams, which were invented in Italy in the 60ies and are currently known under the name of REP® beams. Their use in the construction industry has constantly increased, since they allow to considerably speed up the construction process, to reduce the on-site labor, while providing economic suitability. Nowadays, they are a well-established construction typology not only in Italy, but also in some other European countries, where their use is gaining popularity.
When mounted on-site, TTP beams carry their own weight and the weight of the slabs without any provisional support during floor construction (Phase I), thanks to a steel truss which is connected to the bottom chord. After casting of concrete on top of the floor and on the TTP beams themselves, they effectively collaborate with the hardened concrete topping (Phase II). Apart from optional longitudinal bar placed at the beam’s ends to resist the negative moments in multi-span beams, the TTP beam does not require any additional longitudinal or transverse reinforcement, because the internal steel truss becomes effective in resisting shear.
Though extensive work has been done in the past, there are still some aspects that deserve to be studied in more depth, which result in the lack of recommendations and proper guidelines in both the Italian code and the Eurocode to address such typology of beams. In order to pursue this goal, a set of experimental tests on TTP beams subjected to distributed loading has been carried out. Based on the experimental results, it emerged that the shear capacity of these beams is different from what predicted with the usual formulations.
In particular, it was observed and proven through the strain gauges measurements, that an inclined strut develops naturally across the web bars, thus allowing yielding to progress from the first web bars toward the adjacent ones with the consequence of increasing the shear capacity.
As a matter of fact, there exist some additional resisting mechanisms that emerged from the analysis of the results, which are not correctly predicted and modelled by the current theories.
This is exactly the objective of this thesis: to develop an alternative theory that accounts for such additional shear resisting mechanism. The theoretical framework is that of the variable-angle strut theory, largely adopted in many Codes, including NTC-2018 and EN 1992. This theory has been preferred to others, possibly even more accurate, because of its mechanics-based approach, which facilitate the extension to a different beam configuration, such as that of TTP beams. This allows to consistently introduce the observed yield progression in subsequent diagonal elements of the steel truss.
Having developed the new equation for the shear capacity, the following important step was to include the effects of construction phases in the formulation of the shear capacity. These significantly affect the distribution of forces among the resisting parts of the truss mechanism, because when concrete is cast, the steel truss is already under stress. Thus, the initial stress in the web bars due to the loads applied in Phase I is evaluated and accounted for in the capacity equation.
The following task has been that of developing a usable design equation. This has been done by calibrating a suitable value for the model uncertainty γ_Rd factor in the code-formatted equation, by adopting the Design-by-Testing approach of EN 1990, Annex D, whereby the predictions offered by the code-calibrated equation have been compared with the experimental results available in the literature and those carried out by the candidate.
In this process, the EN 1990 calibration approach has been reviewed and modified to simplify its application, while retaining its reliability features. The simplified procedure has been then applied to the calibration of the model partial factor for both the Eurocode shear equation, adapted to the case of TTP beams, and the proposed equation.
The study is finally concluded by an application of the newly developed code-calibrated shear capacity equation. Such application refers to the optimized design of TTP beams, considering different spans and different phase II / phase I loads ratios. The developed equations allow obtaining optimized TTP beams where both Phase I and Phase II safety requirements are effectively fulfilled. It is shown that, for shorter values of the span, the load ratio is less affecting the outcome of design, which can be explained by the fulfilment of minimum requirements on the sizes, while for intermediate and longer values of the span, the load ratio significantly affects the resulting design and is therefore more sensitive to the building use.
In summary, the main outcomes research of this thesis work regarding TTP beams have been:
new experimental tests conducted under distributed loads,
new interpretation of the shear resisting mechanism,
new predictive equation of shear capacity, accounting for distributed yield of web bars and for construction sequence,
new design equation, with calibrated model uncertainty factor,
procedure for obtaining optimized elements, accounting for safety requirements pertaining to torsional-bending instability, moment capacity, and shear capacity.

**Research products**

11573/1348761 - 2016 -

**Experimental tests on composite steel-concrete truss beams**Kareemi, Muhammad Ajmal; Petrone, Floriana; Monti, Giorgio - 01a Articolo in rivista

**paper:**APPLIED MECHANICS AND MATERIALS ([Stäfa] : Trans Tech Publications) pp. 68-75 - issn: 1662-7482 - wos: (0) - scopus: (0)