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Evaluation of Shear Load Carrying Mechanism of RC Deep Beam by 3D-RBSM

JU Cheng, NAKAMURA Hikaru, Nagoya University

YAMAMOTO Yoshihito, National Defense Academy of JapanKUNIEDA Minoru, UEDA Naoshi, Nagoya University

FAX: 052-789-4635 E-mail: Kikusei.JP@Gmail.Com

In this study, RC deep beams were analyzed in order to investigate the shear load carrying mechanism by

3D-RBSM, which is one of the discrete models and can simulate the failure behavior of RC structure accurately.

The numerical results were investigated in detail by evaluation of load-displacement curves, crack patterns, 3-D

deformed shapes and stress and strain distributions. As a result, truss-mechanism, which was not been

considered in design of deep beams so far, was clearly observed by the stress distribution. It is confirmed that

3D-RBSM can strongly contribute to reveal the shear failure mechanism of RC deep beam.

1. Introduction

In ACI 318-05 Code (ACI 2005)1)

, the limit of shear span toheight ratio (a/h) is given as 2.0 to define deep beams, in which

the load carrying capacity could be calculated by using

Strut-Tied Model for assuming its stress distribution of concrete

struts in D-region as shown in Fig.1

Recently, an advanced numerical tool, 3D-RBSM2), is

developed based on Rigid Body Spring method (RBSM), which

can simulate the local behaviors of concrete structure such as

cracking, stress and strain distribution accurately as well as

global behavior such as load-displacement relationship. This

study investigates the shear load carrying mechanism of RC

deep beam by using 3D-RBSM based on the stress and strain

distribution.

Figure 1 Strut-Tie Model (STM)

2. Experimental evaluation of shear load carrying

mechanism

Two deep beams with a/d = 1.6 was tested as shown in Fig.2,in which the existence of stirrups is changed. The feature of

specimens is that the strain distribution of compressive concrete

along beam axial was measured by acrylic-bar with strain

gauges. The part of compressive concrete corresponds to

compression chord in the model of Truss-Analogy, which does

not appear in Strut-Tie Model in Fig.1. For this reason, the

failure mechanism would be clarified by measuring the

development of compressive chord in deep beam.

Fig.3 and Fig.4 show the load-displacement relationship of

specimens without and with stirrups, respectively. The strain

behavior at point A, B and C in Fig.2 are also shown in these

figures. The strain at point A which is between loading plates, isconcentrated and increasing in both specimens due to the effect

of bending moment. The strain behaviors at point B and C are

quite different in both specimens, where is the key functional

area of Truss-Analogy. In the case of specimen without stirrups,strain at B and C do not increase. On the other hand, the strain at

point B developed remarkably in the case of specimen with

stirrups. The different behaviors between these two implied that

the load carrying mechanism have essentially difference in the

specimens.

3. Numerical Evaluation

3.1. 3D-RBSM

3D-RBSM, which is developed by Yamamoto2), is used to

analyzed in this case. In the model, concrete is modeled as an

assemblage of rigid particles interconnected by springs along

their boundary surfaces. The crack pattern is strongly affected

by the initial mesh design as the cracks initiating and

propagating through the interface boundaries of particles.

Therefore, a random geometry of rigid particles is generated by

a Voronoi diagram, which reduces mesh bias on the initiation

and propagation of potential cracks.

Reinforcement is modeled as a series of regular beam

elements that can be freely located within the structure,

regardless of the concrete mesh design. The beam element is

attached to the concrete particles by means of zero-size link

elements that provide a load-transfer mechanism due to bond

effect between the beam node and the concrete particles. Fig.5

shows the element model around reinforcement.

3.2. Numerical Result

The load-displacement relationships obtained from RBSM are

shown in Fig.3 and Fig.4 as the black dashed lines. A good

agreement with test results can be seen both pre- and post-peak

behavior. RBSM can simulate global behavior such as load

displacement relationship with stirrups effect of RC deep beams

reasonably. Fig.6 shows the comparison about crack pattern of

the specimen without stirrups at different load levels. Flexural

and shear cracks initiation(a), development of shear cracks(b)

and crack at final stage(c) can be simulated similar with test

results. The strain values in compressive concrete along beam

axis show in Fig. 3 and Fig.4. The values of strain which is localinformation in beam are also similar with test results. The

different behaviors between with and without stirrups are

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Figure 2 Outlines of Specimens

Figure 3 Load-displacement and load-strain relationships of

specimen without stirrup

Figure 4 Load-displacement and load-strain relationships of

specimen with stirrups

reasonably. As mentioned above, shear load carrying capacity iscalculated based on assumed stress distribution of concrete

struts as shown in Fig.1. However, test and numerical results

show that stress distribution of specimen with stirrups is

different with assumption in design. That is, in specimen with

stirrups, the strain at compressive concrete in shear span

increased. In order to investigate the effect of stirrup on stress

distribution, the stress distribution difference between the

specimens with and without stirrups is shown in Fig.7.

Fig.7 is obtained by subtracting the principle stress distribution

of the specimen without stirrups at peak load from the one of the

specimen with stirrups at peak load. That is the figure

demonstrates the increase of principle stress caused by onlystirrups. As seen in figures, sub-strut are formed top for the

beam to longitudinal reinforcement level continuously and a

Figure 5 Elements Modeling of RBSM

Figure 6 Crack pattern of specimen without stirrup

(a):Diagonal Crack Point, (b):Peak Load, (c):Final Stage

Figure 7 Distribution of Stress increase due to stirrups

compression chord occurs on the top of the shear span that is

similar with the truss analogy. The result suggests that, truss

analogy is more dominant on the behavior rather than strut

action which is different from the assumption of ACI 318-05.

4. Conclusion

(1) 3D-RBSM has very excellent performance in predicating the

load carrying capacity and crack pattern of concrete structures.

(2) The results obtained from both analytical and experimental,

especially the stress distribution shows highly possibility of the

existence of Truss-Analogy in RC deep beam which a/d ratio isless than 2.0. 3D-RBSM contributes to reveal the shear failure

mechanism.

5. Reference

1) ACI Committee 318, (2005). Building code requirementfor structural concrete (ACI 318-05). Farmington Hills

(MI): American Concrete Institute

2) Yamamoto Y., Nakamura H., Kuroda I., Furuya N., 2008.Analysis of compression failure of concrete by

three-dimensional rigid body spring model. Doboku

Gakkai RonbunshuuE. 64(4):612630

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