Keywords: reinforced concrete, corbel, strut-and-tie model, structural design, lightweight concrete, stress trajectories, load path.

In this paper, normal and lightweight reinforced concrete corbels first were designed to TS500(Turkish Standards)[1], and then, a strut-and-tie model was designed with SAP90 program. Strut-and-tie model is attended to analyse all parts of a structure and to consider load path in a structural element. To demonstrate the theoretical results, reinforced concrete corbels having various shear span-depth ratios were produced and tested. Obtained behaviour of tested corbels are concluded with tables and graphics.

When bracket's length is equal or small to his depth, this member shows different behaviour than flexure. Thus, these members are called corbels. Corbels are used in precast RC members as supports of crane beams on the columns[2]. In order to solve a corbel, strut-and-tie model may be used. Because of this model considers the loadpath in a structure, each load position will arise a different strut-and-tie model. Standard truss models, today, are used to design for cracked reinforced concrete beams under flexure, shear and torsion[3]. However a design based on a standard truss model, is only rational some parts of a structure. Therefore, to design of reinforced concrete structures, strut-and-tie method that is called generalised truss analogy and may be used to all parts of a structure easily, are proposed. This model is especially valid in disturbed stress distribution. In this paper, an application of strut-and-tie model to reinforced concrete corbels that are especially in practice are not designed with certain methods, is explained. First, an initial design was made by using results obtained from normal and lightweight reinforced concrete corbels test specimens and from SAP90 computer program and then, results obtained from tests were compared with results of initial design. For this purpose, total 8 test specimens that have 4 normal and 4 lightweight concrete specimens were made for examine of behaviour and ultimate load of normal and lightweight reinforced concrete corbels that were made with normal and lightweight concrete to develop a strut-and-tie model. Technical properties of test specimens, test arrangement and expanded knowledge about measurements are presented in this paper [4].

Strut-and-tie model is a method that is using in a wide range to design and dimension of RC structures. Strut-and-tie model is an effective method especially to solve statically or geometrical discontinuous regions (i.e., concentrated load or corner of frames, corbels, deep beams, holes and other openings). Because of disturbance in flow of interior load near discontinuous regions that was mentioned above, these regions are called to D regions. Areas except D regions in a structure have regular stress distribution and Bernoulli hypothesis is valid. This regions are called to B regions(Beam region). One of basic steps to this model, is determined to B and D regions of examining structures and thus is determined to model geometry. D regions of a structure are determined by Saint Vénant principle[3,5]. D regions of test specimen corbels is given in this paper[4].

In tests that were made until reaching failure load in corbels, LVDT's were used to measure the horizontal and vertical displacements at the determined points that have current spacing, at each load level[4]. At the end of the tests made about corbels, estimations that were made comparisonaly about measured deflections at the same loading type, it was shown that, lightweight reinforced concrete corbels crushed or failured with more little deflection than normal concrete. Furthermore, generally, more deflection occurred in continuous loading than stepped loading. Normal and lightweight concrete specimens showed more ductile behaviour under continuous loading than stepped loading. It can be observed from the comparison of graphics. In corbels, before failure arise, a few initial cracks was observed and then failure occurred abrupt and catastrophically. This situation is determined from load- displacement curves. Initial cracks, first observed at interior end of the support plate. The loadpath in the normal concrete has higher slope than lightweight concrete and in lightweight concrete, cracks distributed in a very wide area. At the end of these tests, members of strut-and-tie model were determined with SAP90 program by using cracks that were observed with tests. Therefore, determined loadpath degree's truth was proved. At the end of the controls with this model geometry, it was hoped for not arise crushing in nodal zones. Therefore, in tests, parallel to this conclusion, failure occurred only in strut members abrupt and catastrophically. It was obtained based on test results that SAP90 program is a rational approach to develop the strut-and-tie modelling. Finally, it was shown that, strut-and-tie model is a suitable and rational method to design of normal and lightweight concrete corbels according to real behaviour.

1

TS500, "Building Requirements for Reinforced Concrete", TSE, Ankara, Turkey, 1984.

2

U. Ersoy, "Reinforced Concrete", METU, Ankara, Turkey, 1991.

3

J. Schlaich, K. Schafer, M. Jennewein, "Toward a Consistent Design of Structural Concrete". PCI Journal, 32(3), 74-150, 1987.

4

Yavuz, G. "The Analysis of RC Corbel's Behaviours Subjected to Load Experimentaly and using Strut-and-Tie Model", Master thesis, Selçuk University Institute of Natural and Applied Sciences, Konya, Turkey, 1999.

5

J. Schlaich, K. Schafer, "Design and Detailing of Structural Concrete using Strut-and-Tie Models". Structural Engineer, 69(6), 113-125, 1991.

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