From the hundreds of **shear** tests that have been performed in previous studies, few are tests that have been performed on **lightweight** **concrete**. For this **analysis** two different compiled databases were actually investigated. An older **database** of **concrete** girder tests which used many of the papers mentioned previous were of normal weight **concrete**. However these older papers did also have tests on **lightweight** girders that weren’t recorded in the **database**. These values were looked at and chosen based on the accuracy of the tests and failure mode. Another current large **database** compiled by Reineck, Bentz, Kuchma, and Bayrak is also available to the research committee. This **database** was a joint effort between European and American researchers. After looking at the ACI published **database** titled “ACI-DAfStb” most if not all tests were also **shear** tests on normal weight **concrete**. This cannot be confirmed because the authors would not respond to communications. Due to these setbacks a **database** of 95 **lightweight** **concrete** bridge girder tests were compiled separately. Table 2 shows all compiled test data for

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Four **lightweight** **reinforced** **concrete** **shear** wall specimens were constructed and tested to investigate the influence of diagonal web reinforcement on the hysteretic response of structural **lightweight** **concrete** **shear** walls. All walls had a barbell-shaped cross section with a web thickness of 100 mm and 250x250 mm boundary elements. The overall length of the cross section was 1500 mm. Vertical and diagonal reinforcement was anchored in a 600 mm thick base girder that was bolted to the laboratory floor. A 250 mm wide by 500 mm deep **beam** was cast on top of the wall panel, and a hydraulic actuator was attached to the specimen at mid depth of the top **beam**. Lateral loads were applied 2150 mm above the base of the wall.

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ACI 318-11 7 recommends a modification factor to account for the reduced **shear** transfer contribution of LWC owing to the softened aggregate interlock at inclined crack interfaces. This modification factor was introduced by Ivey and Buth 8 based on a regression **analysis** of limited 26 LWC **beam** specimens. However, the accuracy and **reliability** of this modification factor remain controversial, and their application can be problematic because of a lack of mathematical consensus on **shear** transfer mechanism along crack interfaces in LWC elements. Yang et al. 5, 6 showed that the modification factor specified in ACI 318-11 is unconservative for the LWC continuous beams tested and the lack of conservatism increases as the maximum aggregate size increases. Therefore, a more rational analytical model for the modification factor would be welcomed to reasonably explain the reduced friction properties along crack interfaces of LWC beams.

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kip. Figure 4-26 indicates that, **beam** G1-C60 and G1-M100 has a higher V c , compared with G1-M0 due to the higher **concrete** compressive strength used for these beams. It is observed that the beams **reinforced** with MMFX stirrups, G1-M80 and G1-M100 display a linear slope up to strain of 0.01 and then follow the non-linear behavior of MMFX steel as shown in Figure 4-3 and Figure 4-4. It can be seen that at any given load, the strains in all the beams are almost the same i.e. even though beams **reinforced** with MMFX stirrups have lesser transverse reinforcement ratio compared with beams **reinforced** with Grade 60 steel, they have approximately similar stains at a given load. This is due to constant elastic modulus of MMFX bars. Within the elastic range, the value is same as conventional steel.

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Twelve low aspect ratio, rectangular **reinforced** **concrete** (RC) walls were constructed and tested at the University at Buffalo to characterize their inelastic behaviour under reversed cyclic loading. One of the objectives of the research project was to develop equations for peak **shear** strength suitable for inclusion in seismic codes and standards. New equations for peak **shear** strength of rectangular walls, without and with boundary elements, are presented in this paper, based on internal force-resisting mechanisms measured during the experiments.

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Discrepancies exist between UK design codes for the prediction of pile cap **shear** strength. A series of reduced scale pile cap experiments to investigate **shear** strength have been performed. Results from seven samples are presented. Details of test methodology and procedure are shown. Final crack distributions show that pile caps under wall load behave close to simply supported two- dimensional deep beams, except for hogging cracks over the pile head indicating the existence of moment restraint at the piles. Results for failure load indicate that pile cap **shear** strength is at least two to three times higher than current code predictions from semi-empirical formulae. The truss method is shown to be more reliable to predict pile cap **shear** strength than bending theory. Keywords: pile cap; **shear**; truss method; **shear** enhancement factor.

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shear links. Further details about the accelerated corrosion process are given below. The number refers to the actual shear link corrosion level in a given beam.. The beams were designed[r]

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TITLES OF FIGURES 3 1•1 5 1.2 Interaction between ultimate moment and shear span Failure Mechanism I 5 7 1.3 1.4 Failure Mechanism II Failure Mechanism III 9 1.5 Crack pattern of a beam [r]

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Genikomsou and Polak [56] presented a finite element model for the slab specimen SB1 with the damaged plasticity model parameters of: dilation angle of 38 o , shape factor of 0.67, stress ratio of 1.16, and eccentricity of 0.1. A stress vs crack opening displacement approach was used to simulate the tensile response of the **concrete**. The fracture energy was calculated as 0.9 N/mm according to the CEB-FIB Model Code 1990 [60]. This model only specified tensile damage parameters. A static **analysis** approach was used in ABAQUS/Standard with a viscosity, μ taken as 0.000085 and then compared to a quasi-static **analysis** with the dynamic procedure of ABAQUS/Explicit at a very slow rate of velocity. As shown in Figure 2-18, both **analysis** procedures compare well with the experimental results. The quasi-static **analysis** shows a noticeable downward trend which was interpreted by the authors as the point of punching **shear** failure. The static **analysis** does not show this same downward trend and thus it is not clear how the authors determined that punching **shear** had occurred and why the curve was cut-off at a deflection of 15 mm. The authors conducted a parametric study on the sensitivity of the viscosity parameter. Figure 2-19 shows the influence of the viscosity parameter on the load-deflection response. The graph shows that the higher the viscosity parameter the stiffer the load-deflection response. The authors also used the FEA model to show the influence that the flexural

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performance of these high-strength lightweight coarse aggregate – normal weight fine aggregate concrete beams without transverse reinforcement against design equations[r]

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EC 2 also specifies **shear** provisions for slender and deep beams **using** empirical equations and strut-and-tie models, respectively. The equations for slender beams without web reinforcement con- sider the influence of **concrete** strength, dowel action of longitu- dinal reinforcement and size effect, whereas neglect the effect of **shear** span-to-depth ratio as given by Eq. (10). Unlike Eq. 3 (see Table 3) used by KBCS and ACI318-05, EC2 requires that the **shear** capacity of slender beams requiring web reinforcement is determined from the **shear** transfer capacity of only web rein- forcement ignoring the contribution of **concrete**. The **shear** trans- fer capacity of vertical web reinforcement is obtained from variable- angle truss model; however, the slope of diagonal cracking planes is limited between 21 o (cot θ = 2.5) and 45 o (cot θ = 1.0).

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practical **bridges**, previous studies have focused on the resistance capacity of the structural elements in **shear** and bending moments for straight **bridges**. In particular conditions, the eccentric loading can generate torsional moment, which is sometimes disregarded by engineers. However, for curved **bridges**, apart from **shear** and bending moments, the torsional moment should be taken as well in view of its importance in design.

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Since the problem is dominated by material properties, most studies related to **shear** are experimental. However, experimental work is expensive and usually limited by the size of the facilities, the type of member or design parameters investigated in a particular set of experiment. Results from **shear** tests are notoriously variable and often contradictory; furthermore, most published data do not provide sufficient detail for the in-depth investigation of the **shear** mechanism. Despite this, all current **shear** design procedures, such as Eurocode (EC2) [3] and ACI 318-14 [4] code, are based on statistical best fits of experimental data. The inadequacy of these empirical **shear** design procedures is more pronounce in non-flexural and **shear** critical members such as deep beams. Numerous theoretical approaches have been proposed to explain the **shear** mechanism such as the truss analogy theory [5, 6], the variable angle truss model [7], the theory of **shear** resistance of RC beams by Kupfer et al. [8] the modified compression field theory [9] and strut-and-tie model [10, 11]. The **shear** strength predicted according to these theories is in general more reliable than that of empirical procedures but there are still parameters that need to be further investigated such as effectiveness factor of **concrete** used in strut- and tie model.

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Abstract: In this study, we propose a new equation that evaluates the **shear** strength of **beam**–column connections in **reinforced** **concrete** and steel **beam** (RCS) composite materials. This equation encompasses the effect of **shear** keys, extended face bearing plates (E-FBP), and transverse beams on connection **shear** strength, as well as the contribution of cover plates. Mobilization coefﬁcients for **beam**–column connections in the RCS composite system are suggested. The proposed model, validated by statistical **analysis**, provided the strongest correlation with test results for connections containing both E-FBP and transverse beams. Additionally, our results indicated that Architectural Institute of Japan (AIJ) and Modiﬁed AIJ (M-AIJ) equations should be used carefully to evaluate the **shear** strength for connections that do not have E-FBP or transverse beams.

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3. 1. General As mentioned in Sec. 1, a macro model of a **shear** wall contains a wall being linear throughout and a nonlinear rotational spring being concentrated at the base of wall to represent the moment-rotation behavior. Such a model is a simple and fast computational tool for calculation of the general lateral behavior of such a wall with much less effort compared to the micro and meso models discussed. Of course, such a tool cannot be used for calculation of local behavior. In this section, first the macro model of this study, is developed for nonlinear static **analysis**. Since good accuracy and computation speed of the fiber **analysis** were established in the previous section, and regarding the large number of **shear** walls, accuracy of the developed macro model will be shown in comparison with the meso model.

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used to strengthen an existing structure. Twelve T-beams, two of which were maintained as a control, were tested. The beams had the following dimensions: 152 mm × 381 mm × 2743 mm. They were retrofitted with U-wrapped continuous FRP fabric in one or two layers with and without anchorage. Of the ten strengthened beams, eight were retrofitted with CFRP and the remainder with aramid composite. For the anchorage, the authors used the technique described by Khalifa et al. (2000). In addition, the small longitudinal steel reinforcement ratio led the authors to strengthen the beams in flexure in order to inhibit any premature failure in flexure. The flexural strengthening was applied to both critical positive and critical negative moment regions. The beams were tested under three-point loads with the load applied at distance 2.4 m from the support. In the beams with no anchorage, failure occurred by premature debonding of the FRP, accompanied by severe delamination. The gain in **shear** resistance was 11% to 16%, depending on the number of FRP layers. The beams with anchored FRP achieved higher gains, ranging from 35% to 27%, depending on the number of FRP layers. Failure in this case was caused by loss of anchorage. The addition of a second CFRP layer to the specimens with anchorage did not result in a capacity increase. The authors noted that the gains achieved are small compared to those predicted by theory. This behaviour was attributed to deep **beam** action by the authors, who strongly recommended further investigation into this phenomenon. It must be said that an a/d ratio of 2.4 is at the upper limit of what can be considered as a deep **beam**. It must also be noted that the resistance of **concrete** in compression was around 20 MPa. The quality of the **concrete** substrate could also explain the results obtained. In this context, it would have been interesting to know more details on the state of the **concrete** substrate and on the surface preparation prior to application of FRP.

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diagonal shear cracks were formed in the left shear span with maximum crack width of 0.76 mm.. The ultimate 4.[r]

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mm and a span length of 1770 mm, while the simply supported span was 1470 mm. A **shear** span to effective depth ratio of 3.5 was used. This study was found to be stimulating, as it fixated on something, which was quite different as compared to all other studies in the same scope. An assessment of the ability of crimped and hooked-end steel fibres to be used as minimum **shear** reinforcement in RC beams prepared with two different grades of **concrete** was completed. To accomplish this, the control samples were made from the beams, which were believed to be satisfactory. The fibre-**reinforced** beams also showed fluctuating degrees of multiple cracking at ultimate loads. The **shear** strength of the FRC beams was found to be more than a low value endorsed in the literature. The grade of **concrete** was found to be of little importance in this regard. A comparison of the strength of the two types of deformed fibres revealed that the beams **reinforced** with the hooked-end fibres were found to have up to 38% higher **shear** strength than the crimped fibres. A simple model for **shear** strength was also suggested for the calculation of the behaviour of fibre **reinforced** **concrete**. The proposed model was tested along with seven other **shear** strength models. The seven models were selected from the literature. The proposed model predicted fairly good values. However, a model proposed by other researchers from the selected literature was found to be projecting a better approximation. Imam et al. (1995) presented an analytical model for predicting the **shear** strength of **reinforced** high-strength **concrete** beams. The dimensions of all the specimens were constant and valued at 200 mm × 350 mm. All beams had span length of 3600 mm. All specimens were singly **reinforced** without stirrups. The author classified the beams into four groups based on three factors (a/d, V f , and ) in different levels. These beams

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19 aggregate interlock. The effect that course aggregate size has on the **shear** strength has also been explored in the work of Bazant and Kim (1984) in which fracture mechanics was used to develop a theoretical model that included this parameter. As previously stated, the **concrete** compressive strength has a significant effect on the mechanism of aggregate interlock, coining the more current term “interface **shear** transfer”. When high strength **concrete** is used in the construction of structural members, the strength of the cement matrix may exceed the strength of the course aggregate, resulting in **shear** cracks that pass through the aggregate. Consequently it is believed that increasing **concrete** strength causes a reduction in interface **shear** transfer due to a relatively smooth cracked plane (NCHRP, 2005). The research conducted by Angelakos et al. (2001) confirms this and also suggests that increasing **concrete** cylinder strength does not necessarily result in increased **shear** resistance. In fact, for members without transverse **shear** reinforcement, the margin of safety against **shear** failure decreases significantly with increased cylinder compressive strength. In addition, the margin will continue to become smaller as the longitudinal reinforcement ratio decreases and member size increases (Angelakos et al., 2001).

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A composite **beam** is composed of a steel **beam** and a **concrete** slab. These two members behave monolithically by means of **shear** connectors welded on the upper flange of the steel **beam**. Studs are widely used as **shear** connector. The structural behaviour of the composite **beam** depends on the degree of composite action developed by the **shear** connector at the steel-**concrete** interface. This composite action mainly governed by the type of **shear** connector and the degree of **shear** connection plays a decisive role as much as the material properties of the steel **beam** and **concrete** slab on the strength and stiffness of the composite **beam**. The horizontal **shear** behaviour at the steel-**concrete** interface of the composite **beam** that is, the **shear** strength and stiffness of the stud, is determined experimentally on a simplified push-out test specimen rather than on the composite **beam** itself (Fig. 1). A survey of previous research results on this topic reveals the difficulty to compare thoroughly the estimated **shear** behaviours among the push-out test specimens that have been fabricated in partially different shapes. However, the evaluation method is recently and gradually gaining popularity in USA and several European countries owing to the standard push-out test proposed by Eurocode 4[1].

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