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Journal of Engineering Science and Technology Vol. 11, No. 4 (2016) 548 - 562 © School of Engineering, Taylor’s University
548
SHEAR STRENGTH OF REINFORCED CONCRETE T-BEAMS WITHOUT STIRRUPS
RENDY THAMRIN*, JAFRIL TANJUNG, RIZA ARYANTI, OSCAR FITRAH NUR, AZMU DEVINUS
Department of Civil Engineering, Faculty of Engineering, Andalas University, Padang, 25163, West Sumatera, Indonesia
*Corresponding Author: rendy@ft.unand.ac.id
Abstract
This paper presents the test results of experimental study on shear strength of reinforced concrete beams without stirrups. The test variables in this study were type of beam cross section and ratio of longitudinal reinforcement. Six simple supported beams, consisting of three beams with rectangular cross section and three beams with T section, subjected to two point load were tested until failure. During the test, the values of the diagonal crack load and the maximum load were observed as well as the deformation of the beams. Existing empirical equations for shear strength of concrete presented in the literature and design codes were used and then compared to that value obtained from the test. Comparison between test results and theoretical shear capacity show that all of equations conservatively estimate the occurrence of shear failure with the values of the test results 10 to 90% higher than the theoretical values. It was confirmed from the test that the shear capacity of T-beams were higher than for rectangular beams, with the values ranging from 5 to 25%, depending on the ratio of longitudinal reinforcement. Also, it was observed that ratio of longitudinal reinforcement influences the shear capacity of the beam as well as the angle of diagonal shear crack. In addition, based on the test results, a simple model for predicting the contribution of flange to shear capacity in T-beam was presented. Keywords: Reinforced concrete, T-beam, shear crack, Longitudinal reinforcements ratio, Angle of diagonal crack.
1.
Introduction
Study on shear performance of reinforced concrete structures has been carried out by other researchers over the last 60 years [1-6]. The test variables used to investigate shear behavior of reinforced concrete structures frequently found in literature refer
Shear Strength of Reinforced Concrete T-Beams without Stirrups . . . .
549
Journal of Engineering Science and Technology
April 2016, Vol. 11(4)
Nomenclatures
a
shear span length
b
f
width of flange
b
w
width of web
c
neutral axis depth
d
effective depth
f
c
'
concrete compressive strength
h
f
height of flange
k
0.2)200(0.1
≤+
d
V
c
shear capacity of concrete
Greek Symbols
α
parameter taking into account the effect of flange in T section
ρ
w
ratio of longitudinal reinforcement (%)
Abbreviations
ACI American Concrete Institute SNI Standar Nasional Indonesia LVDT Linear Variable Differential Transformer RCCSA Reinforced Concrete Cross Section Analysis to the main parameters affecting the occurrence of shear failure e.g. concrete compressive strength, longitudinal reinforcement ratio, shear span to effective depth ratio and effect of member size. Most studies in this area focused only on reinforced concrete beams with rectangular cross section. Bresler and McGregor [2] reported that shear failure is commonly initiated by the occurrence of diagonal cracks developing in the shear span. It is also stated in their paper that the flexural cracks always come before the occurrence of diagonal cracks in rectangular, I or T sections. Bresler and McGregor noted that the shape of the beam (I and T sections) influences the shear capacity and the behaviour of propagation of diagonal cracking due to the different magnitude of shearing stress developed in the web. However, not much attention has been given to the behavior of reinforced concrete beams with T sections. In another report, Swamy and Qureshi [5] proposed an analytical procedure to calculate the ultimate shear strength of the compression zone of T-beams with long shear span. The theory of this procedure was derived using the concept of biaxial stress criterion and was based on Mohr's theory of failure. In this method the variables affecting the ultimate shear strength of the compression zone of T-beams are concrete compression strength, longitudinal reinforcement ratio, shear span length and effective depth of the section. Even though Swamy and Qureshi stated that their theory showed good agreement with test results their computation procedure is not simple, it needs several steps of calculation and difficult to apply in practice. A series of tests designed to study shear failure in reinforced concrete beams without stirrups has been carried out previously [7]. In this earlier study, the type of cross section was rectangular and the test variables were ratio of longitudinal reinforcement and shear span to effective depth ratio. It is reported from this study that most of the beams tested collapsed suddenly after the formation of
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Journal of Engineering Science and Technology
April 2016, Vol. 11(4)
diagonal shear cracks. On the other hand, diagonal shear cracks were not noticeable if the flexural capacity of the beams was lower than the shear capacity of the concrete and in this case the beams failed in flexural mode. It is also reported that the ratio of longitudinal reinforcement influences not only the shear capacity but also the angle of diagonal shear cracks. So far, the codes have not covered the behavior of shear capacity of reinforced concrete beams with T sections. In addition, existing equations for shear capacity of concrete available in international design codes do not take into account the influence of the flange in T sections [8, 9]. Due to this fact, the main objective of this experimental work is to add to the data on this topic by focusing on the contribution of the flange to the shear capacity of reinforced concrete T-beams. In order to achieve the aim of this research, three beams with rectangular sections and three beams with T sections were tested. The effect of longitudinal reinforcement ratio to the shear capacity and the growth of diagonal shear cracks were examined during the test. In addition the angle of diagonal cracks was also measured in order to observe the influence of longitudinal reinforcement ratio on the distribution of stresses in the shear span zone. Empirical equations for shear capacity of concrete available in literature and design code were also used in this study and then compared with shear strength obtained from the test. Finally, available experimental data from literature was added to the data obtained from this study and by using a simple statistical procedure a model for predicting the contribution of flange to the shear capacity of concrete in reinforced concrete beams with T sections was proposed.
2.
Experimental Study
Six simply supported reinforced concrete beams without stirrups, consisting of three beams with rectangular cross sections and three beams with T cross sections, were tested in this study. The beams were monotonically loaded until failure with two point load using a 500 kN capacity hydraulic jack. Loading position and dimension of the beam are shown in Fig. 1. For all of the beams, the clear span was 2000 mm, the shear span length (
Ls
) was 800 mm and the end anchorage length beyond the support (
La
) was 150 mm. For all of the beams the shear span - effective depth ratio was about 3.7 (
a
/
d
> 2.5). Two types of cross section as shown in Fig. 1 were used. The rectangular section had dimensions of 125 mm width and 250 mm height, while T section had 250 mm flange width, 70 mm flange thickness, 125 web width and 250 height. Deformed steel bars with 13 mm diameter, 550 MPa yield strength, and 204 GPa modulus of elasticity were used as longitudinal reinforcement. Three ratios of longitudinal reinforcement (1, 1.5 and 2.5%) were used for both type of cross section as shown in Fig. 1. The bottom and side concrete covers were 30 mm and 20 mm, respectively. Two wooden plates placed at each end side of the beam's formwork and drilled at the position of longitudinal reinforcements were used to keep the bars in position during concrete casting. The longitudinal reinforcements were suspended using steel wire at the middle position of the beam. Fresh concrete was produced in the laboratory with a concrete mixer using maximum aggregate size of 20 mm and target compressive strength of 30 MPa. Afterwards, the average concrete cylinder strength obtained from compression
Shear Strength of Reinforced Concrete T-Beams without Stirrups . . . .
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Journal of Engineering Science and Technology
April 2016, Vol. 11(4)
tests was 32 MPa at age 28 days. For all beams the deflections at midspan and at one of the loading points were measured using two displacement transducers connected to a data acquisition system as illustrated in Fig. 1.
Fig. 1. Test setup and beam dimensions.
3.
Theoretical Concrete Shear Strength
Although many empirical equations for concrete shear strength have been suggested in the literature and design codes, only some of them are applied in this study. Four empirical equations listed in Table 1 were used to estimate shear capacity of the concrete. Equation (1) was selected from the literature because of its simplicity, ease of application, and because it takes into account the size effect and ratio of longitudinal reinforcement. This empirical equation is also well-known and frequently used by researchers. Zsutty's equation predicts the shear strength of reinforced concrete beams without stirrups with a high degree of accuracy.
Table 1. Empirical equations for shear capacity of concrete from literature.
Literature Empirical equations for shear capacity of concrete
Zsutty [3]
d wbad c f wcV
31'17.2
=
ρ
(1) Niwa [10]
( ) ( )
d bad d f V
wcwc
4.175.02.0
4131'
+=
−
ρ
(2) Eurocode 2 [11]
)
d b f k V
wcwc
)100(12.0
3/1
ρ
=
(3) SNI [12]
d bad f V
wwcc
12071
'
+=
ρ
(4) Equation (2) was selected as representative of empirical equations developed in response to the needs of a high seismic intensity environment. It also has good agreement with the experimental results [13]. Although apparently complex, parameters used in Niwa's equation are not so different to those used in Eq. (1).

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