Experimental study of the strength and behaviour of reinforced coped beams

A total of 10 full-scale tests were conducted to investigate the strength and behaviour of reinforced coped steel I-beams. The test parameters included the length of longitudinal stiffeners, length of transverse stiffeners, combined longitudinal and transverse stiffeners, double transverse stiffeners, cope depth and cope length. For the coped beam specimens without stiffeners, local web buckling failure occurred in the cope. For the specimens with longitudinal stiffeners only, the general failure mode was flexural yielding of the full beam section at the location of maximum bending moment followed by web crippling at the end of the cope between the longitudinal stiffeners and the top flange of the full beam section. In contrast, the general failure mode for the specimens with combined longitudinal and transverse stiffeners consisted of flexural yielding of the full beam section at the location of maximum bending moment followed by flange local buckling near the loading position.The test results show that the reinforcements were able to increase the capacity of the coped beam specimens significantly and the results also illustrate that in addition to cope depth, cope length also affects the behaviour and strength of the reinforced coped beam specimens. Based on the limited test data, a modification to the current reinforcement details for coped beams was proposed. The proposed reinforcement details accounted for the effects of various cope details. To increase the range of applicability of the proposed reinforcement details, a numerical study is currently underway to consider a wider range of cope details.     

Block shear strength of coped beams with single-sided bolted connection

Block shear is one of the major failure modes for coped steel I-beams. While focus of previous studies on the block shear capacity of coped steel I-beam was mainly given to the connections with double clip angles, single-sided connections, which induce out-of-plane loading eccentricity, have not been adequately considered. Ten full-scale coped steel I-beam tests were conducted to examine the effects of two main test parameters, namely, out-of-plane loading eccentricity and web block aspect ratio (ratio of shear area to tension area). It was found that nine test specimens failed with tension fracture along the bottom bolt row of the web, and the remaining one failed in a whole block tear-out manner. Twisting of the web near the cope was observed for specimens with single-sided connection. More importantly, the test results showed that the out-of-plane loading eccentricity due to the single-sided connection did not have a detrimental effect on the block shear capacity of the specimens. Moreover, increasing the connection rotational stiffness could increase the block shear capacity. These effects are further discussed via a finite element analysis and a preliminary parametric study. Finally, the test results are compared with four major design standards. It is found that the Canadian Standards CAN/CSA-S16-09, which gives a test-to-predicted ratio ranged from 0.93 to 1.17, provided relatively good predictions for the specimens with single bolt line layout, while the predictions by other codes are too conservative. For those specimens with double bolt line layout, the capacities are underestimated by all the considered standards.     

Development and validation of a numerical model for buckling of coped beams

The lateral torsional buckling resistance of a beam depends on the support conditions. In structures for buildings, coped beams are often used. A numerical model is developed to investigate the influence of copes on the lateral buckling resistance. The model was verified with laboratory tests. This paper describes the background of the numerical model, the test program and the results of the validation. In a companion paper [Maljaars J, Stark JWB, Steenbergen HMGM, Abspoel R. Lateral-torsional buckling resistance of coped beams. Journal of Constructional Steel Research 2005;61(11):1559-75], the results of a parameter study are presented.     

A numerical study of the behaviour of restrained RC beams at elevated temperatures

By using the virtual work principle, a beam-element model for reinforced concrete at elevated temperature is established. Based on the beam-element model, an analytical programme for reinforced concrete structures subjected to high temperature is proposed. After validating the feasibility of the programme against available experimental results of fire tests for RC frame structures, a RC beam with elastic axial and rotational restraints at beam ends was selected for numerical parametric study. The parameters investigated include different beam spans, different levels of applied load, different load types and different levels of axial and rotational stiffness at beam ends. Through the parametric analysis, the following conclusions can be drawn: (1) axial restraint may induce axially compressive force and increase the mid-span deflection when temperature is rising; the higher the axial restraint stiffness, the larger the compressive force generated and also the larger the beam deflection. (2) The effect of the rotational restraint on the generated axial force is very limited, if the same value of axial restrained stiffness is added at the beam ends, the generated axial forces are almost the same, irrespective of the levels of rotational restrained stiffness and the load types. (3) If the same value of axial restrained stiffness is added at beam ends with an increase in the rotational restraint, there will be a reduction in the mid-span deflection. (4) When the rotations of beam ends are restrained, the rising temperature will induce an increase in hogging moment at the beam ends.     

Lateral-torsional buckling resistance of coped beams

The lateral-torsional buckling resistance of beams depends on the support conditions. In floor structures for buildings coped beams are often used. A numerical model was developed to investigate the influence of copes on the lateral buckling resistance. This model is described in a companion paper [Maljaars J, Stark JWB, Steenbergen HMGM, Abspoel R. Development and validation of a numerical model for buckling of coped beams. Journal of Constructional Steel Research 2005;61(11):1576-93]. In this paper results of a parameter study carried out with the numerical model are presented. Based on these results recommendations for design rules are given. The study is restricted to (coped) beams with end plates.     

高强钢筋活性粉末混凝土梁变形性能试验研究

在研究剪跨比、配箍率、纵筋配筋率对试验梁抗剪性能影响规律的基础上,对8根高强钢筋活性粉末混凝土简支梁的变形性能进行了研究。结果表明:无腹筋活性粉末混凝土梁具有一定的变形性能,混凝土构件变形随剪跨比、纵筋配筋率的增大而增大;而对于有腹筋梁,高强钢筋活性粉末混凝土梁变形发展曲线基本相同。     

Creep behaviour of CFRP-strengthened reinforced concrete beams

The strengthening of reinforced concrete structures with externally bonded fibre reinforced polymer (FRP) laminates has shown excellent performance and, as a result, this technology is rapidly replacing steel plate bonding techniques. The numerous studies that have been carried out to date on FRP-strengthened concrete elements have mainly focussed on the static and short-term responses; very little work has been done regarding the long-term performance. This paper addresses this issue, and presents results from a series of experiments on the time-dependent behaviour of carbon FRP-strengthened concrete beams. Twenty-six reinforced concrete beams with dimensions 100 × 150 × 1800 mm, with and without bonded CFRP laminates, were investigated for their creep behaviour. Different reinforcement ratios were used to evaluate the contribution of the external reinforcement on the creep resistance of the beams. High levels of sustained load were used in order to determine the maximum sustained load that can be applied without any risk of creep failure. The applied sustained loads varied from 59% to 78% of the ultimate static capacities of the un-strengthened beams. For most of the long-term tests, the applied sustained loads were higher than the service loads. This was done to account for the fact that strengthening is typically required when a structure is expected to carry increased service loads. The main parameters of this study were (i) the level of sustained load and (ii) the strengthening scheme. The results confirm that FRP strengthening is effective for increasing the ultimate capacities of the beams; however, there is virtually no improvement in performance with regard to the long-term deflections.     

Structural behaviour of babadua reinforced concrete beams

The strength and deformation characteristics of concrete beams reinforced with babadua bars ranging from 2.87 to 12.13% were examined from tests performed on the beams. The beams were tested to failure mostly under third-point loading. Collapse of the beams occurred mostly through either flexural failure of concrete in compression or diagonal tension failure. The experimental failure loads averaged, respectively, 6.40 and 2.62 times the theoretical flexural strength and theoretical shear strength of the unreinforced concrete section. Also, the experimental failure loads were only approximately 1.18 times the theoretical flexural strength of the reinforced concrete and 1.05 times the theoretical shear strength of the concrete sections taking into consideration the resistance of the tension reinforcement.     

Shear strength of reinforced concrete deep beams

An hypothesis is made for the shear mechanism of concrete deep beams based on the failure mode observed during testing. Using the hypothesis an equation is developed for predicting the ultimate strength of the beam. The equation is found to give reasonable values for the ultimate loads for beams with depth to span ratio as low as .     

锈蚀钢筋混凝土梁的抗剪承载力分析模型

锈蚀钢筋混凝土梁的传统抗剪承载力模型大多属于经验模型,考虑的影响因素不全面且缺乏严密的理论推导,导致计算精度有限。基于修正压力场理论,建立了可以综合考虑钢筋锈蚀对临界斜裂缝倾角、梁有效抗剪截面积、配筋率、配箍率等关键因素影响的锈蚀钢筋混凝土梁的抗剪承载力模型,通过与85组试验数据和现有模型的对比分析,验证了模型的适用性和计算精度。结果表明,该模型具有严密的理论基础,考虑的影响因素全面,计算精度较高、离散性较小。     

大尺寸钢筋混凝土无腹筋梁受剪试验研究

进行集中荷载作用下7根大尺寸钢筋混凝土无腹筋简支梁的受剪试验,分析截面高度和纵筋配筋率对钢筋混凝土梁受剪承载力的影响,研究无腹筋梁斜裂缝产生和发展的过程及开裂模式。对试验梁的破坏形式、开裂荷载、受剪承载力、荷载-位移曲线、混凝土受压区应变、最大裂缝宽度和平均裂缝间距受截面有效高度的影响进行讨论。结合试验数据及国内外已有受剪试验成果的基础上对我国《混凝土结构设计规范》(GB 50010—2002)受剪承载力公式的准确性与适用性进行了探讨。     

An investigation of the block shear strength of coped beams with a welded clip angle connection — Part I: Experimental study

The ends of a coped beam are commonly connected to the web of a girder by double clip angles. The clip angles may either be bolted or welded to the web of the beam. One of the potential modes for the failure of the clip angle connection is the block shear of the beam web material. To investigate the strength and the behavior of the block shear of coped beams with welded end connections, ten full-scale coped beam tests were conducted. The test parameters included the aspect ratio of the clip angles, the web shear and tension area around the clip angles, the web thickness, beam section depth, cope length, and connection position. The test results indicated that the specimens failed, developing either tension fractures of the web near the bottom of the clip angles or local web buckling near the end of the cope. Although the final failure mode of the six specimens was local web buckling, it was observed during the tests that these specimens exhibited a significant deformation of the block shear type prior to reaching their final failure mode. No shear fracture was observed in all of the tests. A comparison between the ultimate loads in the test and the predictions using the current design equations indicates that the current design standards such as the AISC-LRFD, CSA-S16-01, Eurocode 3, BS5950-1:2000, AIJ and GB50017, are inconsistent in predicting the block shear strength of coped beams with welded end connections. The analytical study of the strength of the test specimens using the finite element method, a parametric study, and a proposed design model for designing block shears for coped beams with welded clip angles are included in a companion paper.     

An investigation of the block shear strength of coped beams with a welded clip angle connection — Part II: Numerical study

An experimental study of the block shear capacity of ten full-scale coped beams with a welded clip angle connection was presented in Part I. The test results were compared with predictions using block shear design equations in several current design standards. In general, the results showed that the existing design standards did not provide consistent predictions of the block shear capacity of coped beams with welded clip angles. In addition, the equations provided by the standards cannot accurately reflect the failure mode of the specimens observed in the tests. In order to gain a better understanding of the connection behavior, such as the stress distribution in the web near the periphery of the clip angles and the failure mechanism of the connection, an analytical study of the block shear capacity of coped beams with welded clip angles was carried out using the finite element method. Based on the limited test data and the results of the finite element analysis (FEA), a strength model was established and a design equation was proposed to evaluate the block shear strength of coped beams with welded clip angles. It was shown that the proposed design equation gave better predictions of the block shear capacity of the specimens.     

Shear behaviour of reinforced palm kernel shell concrete beams

The shear behaviour of palm kernel shell concrete (PKSC) beams prepared using palm kernel shell (PKS) as lightweight aggregate (LWA) is reported here. The shear strength of grade 30 PKSC with a density of 1850 kg/m³ was found 24% higher than the corresponding normal weight concrete (NWC). Good aggregate interlock in PKSC was evident as it produced shorter jagged cracks compared to longer plain cracks of NWC. Further, PKSC was able to produce twice as many flexural and shear cracks compared to NWC. Tension stiffening between the tensile cracks of PKSC enhanced flexural rigidity and dowel action. The non-linear numerical analysis predicted the shear strength within an average 20% of the experimental results.     

A numerical approach for modeling the fire induced restraint effects in reinforced concrete beams

In this paper, a model to predict the influence of fire induced restraints on the fire resistance of reinforced concrete (RC) beams is presented. The three stages, associated with the fire growth, thermal and structural analysis, for the calculation of fire resistance of the RC beams are explained. A simplified approach to account for spalling under fire conditions is incorporated into the model. The validity of the numerical model is established by comparing the predictions from the computer program with results from full-scale fire resistance tests. The program is used to conduct two case studies to investigate the influence of both the rotational and the axial restraint on the fire response of the RC beams. Through these case studies, it is shown that the restraint, both rotational and axial, has significant influence on the fire resistance of the RC beams.     

Experimental and numerical analysis on the structural behaviour of cold-formed steel beams

A research study on the structural behaviour of cold formed steel beams with C-, I-, R- and 2R-shaped cross-sections at ambient temperature is presented, based on the results of a large programme of experimental tests and numerical simulations. Firstly, several four-point bending tests were carried out in order to assess mainly the failure loads and failure modes of the beams. Secondly, a suitable finite element model was developed to compare with the experimental results, and finally, a parametric study was undertaken in order to investigate the influence of the thickness, height and length of the beams on its structural behaviour.     

Shear strength prediction for steel reinforced concrete deep beams

This study proposes an analytical method for determining the shear strengths of steel reinforced concrete deep beams under the failure mode of concrete crushing originally based on the softened strut-and-tie model. The proposed method is a good physical model that can correlate well with the observed failure phenomenon of steel reinforced concrete deep beams. By comparing the predictions of the proposed method with the available test results from the literature, it was found that the proposed method is capable of predicting the shear strengths for steel reinforced concrete deep beams with sufficient accuracy. The shear-carrying behavior of steel reinforced concrete deep beams is highly influenced by the ratios of flange width to gross width, the shear span-to-depth ratios, and the concrete strengths. When the ratio of flange width to gross width is low, the shear-carrying capacities of steel reinforced concrete deep beams increase with the increasing ratio. However, if the ratio of the flange width to gross width is higher than a critical value, then the failure mode of steel reinforced concrete deep beams will be converted from diagonal compression failure into bearing failure.     

Shear-flexural strength mechanical model for the design and assessment of reinforced concrete beams

A conceptual model for the prediction of the shear-flexural strength of slender reinforced concrete beams with and without transverse reinforcement is presented. The model incorporates the shear transferred by the un-cracked concrete chord, along the crack's length, by the stirrups, if they are, and, in that case by the longitudinal reinforcement. After the development of the first branch of the critical shear crack, failure is considered to occur when the stresses at any point of the concrete compression chord reach the assumed biaxial stress failure envelope. A physical explanation is provided for the evolution of the shear transfer mechanisms, and the contribution of each one at ultimate limit state is formulated accordingly. Simple equations are derived for shear strength verification and for designing transverse reinforcement. The method is validated by comparing its predictions with the results of 1131 shear tests, obtaining very good results in terms of mean value and coefficient of variation. Because of its accuracy, simplicity and theoretical consistency, the proposed method is considered to be very useful for the practical design and assessment of concrete structures subjected to combined shear and bending.     

Considerations on the numerical analysis of initial post-buckling behaviour in plates and beams

In this work, an exceedingly simple examination of the von Kármán theory for the buckling analysis of thin plates is carried out. It is shown that the von Kármán assumption, based on the interaction between axial and flexural deformation, is intrinsically less “robust” in capturing the target phenomenology than the usual treatment of Euler inextensible strut. Finally, the same observation is carried out in the case of a hinged cantilever, which constitutes the simplest structural example of a similar kind.     

Effects of stirrup corrosion on shear behaviour of reinforced concrete beams

Corrosion of stirrups is always more severe than longitudinal steel bars, leading to possible shear failure instead of bending failure. This paper covers the authors’ investigation on the effects of stirrup corrosion on shear behaviour of reinforced concrete beams. Based on modified compression field theory, a method of the whole process analysis was developed showing shear behaviour of reinforced concrete beams with corroded stirrups. Of particular interest was the cracking damage of concrete cross sections, the loss of cross-sectional area and deterioration of mechanical properties of corroded stirrups. After comparing analytical results with available shear test results, further analysis was carried out to investigate the deterioration of shear behaviour and the effects of corrosion degree, concrete strength, stirrup ratio and shear-span ratio. Stirrup corrosion was found to have little impact on cracking load, but shear strength and ductility decreased with the increase in corrosion degree, and shear failure was determined possible for beams originally designed for bending failure. With the decrease of concrete strength or the increase of stirrup ratio and shear-span ratio, the contribution of corroded stirrups to the shear strength of beams increased, and the shear strength and ductility caused by stirrup corrosion decreased as expected.