I-beam Crack Identification Based on Study of Local Flexibility due to Crack

Local flexibility of crack plays an important role in crack identification of structures.Analytical methods on local flexibility in a cracked beam with simple geometric crossing sections,such as rectangle,circle,have been made,but there are some difficulties in calculating local flexibility in a cracked beam with complex crossing section,such as pipe and I-beam.In this paper,an analytical method to calculate the local flexibility and rotational spring stiffness due to crack in I-beam is proposed.The local flexibility with respect to various crack depths can be calculated by dividing a cracked I-beam into a series of thin rectangles.The forward and inverse problems in crack detection of I-beam are studied.The forward problem comprises the construction of crack model exclusively for crack section and the construction of a numerically I-beam model to gain crack detection database.The inverse problem consists of the measurement of modal parameters and the detection of crack parameters.Two experiments including measurement of rotational spring stiffness and prediction of cracks in I-beam are conducted.Experimental results based on the current methods indicate that relative error of crack location is less than 3%,while the error of crack depth identification is less than 6%.Crack identification of I-beam is expected to contribute to the development of automated crack detection techniques for railway lines and building skeletons.

Bending of Timoshenko beam with effect of crack gap based on equivalent spring model

Considering the effect of crack gap, the bending deformation of the Timoshenko beam with switching cracks is studied. To represent a crack with gap as a nonlinear unidirectional rotational spring, the equivalent flexural rigidity of the cracked beam is derived with the generalized Dirac delta function. A closed-form general solution is obtained for bending of a Timoshenko beam with an arbitrary number of switching cracks. Three examples of bending of the Timoshenko beam are presented. The influence of the beam＇s slenderness ratio, the crack＇s depth, and the external load on the crack state and bending performances of the cracked beam is analyzed. It is revealed that a cusp exists on the deflection curve, and a jump on the rotation angle curve occurs at a crack location. The relation between the beam＇s deflection and load is bilinear, each part corresponding to an open or closed state of crack, respectively. When the crack is open, flexibility of the cracked beam decreases with the increase of the beam＇s slenderness ratio and the decrease of the crack depth. The results are useful in identifying non-destructive cracks on a beam.

Four-Beam Model for Vibration Analysis of a Cantilever Beam with an Embedded Horizontal Crack

As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton＇s principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.

Modal and Fatigue Life Analysis on Beam with Multiple Cracks Subjected to Axial Force

Based on the transfer matrix method and Forman equation,a new method is proposed to conduct the modal and fatigue life analysis of a beam with multiple transverse cracks.In the modal analysis,the damping loss factor is introduced by the complex elastic modulus,bending springs without mass are used to replace the transverse cracks,and the characteristic transfer matrix of the whole cracked beam can be derived.In the fatigue life analysis,considering the interaction of the beam vibration and fatigue cracks growth,the fatigue life of the cracked beam is predicted by the timing analysis method.Numerical calculation shows that cracks have a significant influence on the modal and fatigue life of the beam.

Tensile Strength Characteristics of GFRP Bars in Concrete Beams with Work Cracks under Sustained Loading and Severe Environments

To investigate the effect of different environmental conditions of GFRP bars in concrete beams with work cracks subjected to sustained loads, the beams were exposed in indoor, freeze/thaw cycles and immersed in alkaline solution at elevated temperature. The bars were carefully extracted from the beams and tested in order to evaluate residual tensile properties. The results show that the tensile strength decreased significantly in the highly aggressive conditions but not in the natural conditions. The effect of GFRP bars casting in concrete beams demonstrated approximately 2.5% decrease of tensile strength caused by pore water environment in concrete beams on basis of those of the original bars. The effect of sustained loading plus work cracks demonstrated about 10.5% tensile strength decrease on basis of those of the bars only casted in concrete beams. The effect of environments under sustained loading plus work cracks demonstrated about 17% tensile strength decrease caused by a saturated solution of Ca（OH）2 and 60-2 ℃ tap water （pH=12-13） and about 8% tensile strength decrease caused by freezing and thawing cycle （F/T）, both on basis of those of the bars of the indoor beams only under sustained loading plus work cracks. The results demonstrate the effects of the tensile strengths under different environmental conditions of GFRP bars in concrete beams with work cracks subjected to sustained loads.

Fracture characteristics and ductility of cracked concrete beam post-strengthened with CFRP Sheet

The present paper concerns the fracture characteristics and ductility of cracked concrete beam externally bonded with carbon fiber-reinforced polymer (CFRP) sheet as well as the integration behaviors between CFRP/concrete interfacial debonding and concrete cracking.Three-point bending tests were carried out on the CFRP-strengthened cracked concrete beams with varying specimen depth and initial crack length.A straingauge method was developed to monitor the crack initiation and propagation in concrete,and the CFRP/concrete interfacial bonding behaviors,respectively.Clip gauges were used to measure crack mouth opening displacement (CMOD) and the deflection at midspan.Experimental results revealed that CFRP-strengthened specimen shows a higher load capacity under the same deformation level and a better inelastic deformation capacity compared with the unstrengthened one.For there are two manifest peak values in the obtained load versus displacement curve,the ductility of CFRP-strengthened concrete beams were investigated using index expressed as area ratio on the load versus displacement curve.The calculated results indicated that the contribution from CFRP sheet to the ductility improvement of specimen is notable when the deflection at midspan exceeded 10.5 times the first-crack deflection.

CRACK IDENTIFICATION IN STEPPED CANTILEVER BEAM COMBINING WAVELET ANALYSIS WITH TRANSFORM MATRIX

This paper illustrates the crack identification method combining wavelet analysis with transform matrix. Firstly, the fundamental vibration mode was applied to wavelet analysis. The crack location was found by the peaks of the wavelet coefficients. Secondly, based on the identified crack locations, a simple transform matrix method requiring only the first two tested natural frequencies was used to further identify the crack depth. The present method can be used for crack identification in a complex structure. Numerical results of crack identification of a stepped cantilever beam show that the suggested method is feasible.

AN APPROXIMATE METHOD OF RESPONSE ANALYSIS OFVIBRATIONS FOR CRACKED BEAMS

In this paper a method based on a line-spring model was proposed to analyze approximately vibration responses of cracked beams. The method is conjunction with the Euler-Bernoulli beam theory, modal analysis and fracture mechanics principle was applied to derive a characteristic equation for the cracked beam vibration. As application examples, natural frequency responses for a cracked hinged-hinged beam and a cracked cantilever beam were examined. It was shown that the present solutions obtained are quite in agreement with the solutions or experimental results in available references.

AN APPROXIMATE ANALYSIS OF FREQUENCY RESPONSE OF A CRACKED HINGEDHINGED BEAM

A new method based on a modified line-spring model is developed for evaluating the natural frequencies of vibration of a cracked beam.This model in conjunction with the Euler-Bernoulli beam theory,modal analysis and linear elastic fracture mechanics is applied to obtain an approximate characteristic equation of a cracked hinged-hinged beam.By solving this equation the natural frequencies are determined for different crack lengths in different positions.The results show good agreement with the solutions through finite element analysis.The present method may be extended to analyze other cracked complicated structures with various boundary conditions.

Limit Load Solution for Electron Beam Welded Joints with Single Edge Weld Center Crack in Tension

Limit loads are widely studied and several limit load solutions are proposed to some typical geometry of weldments.However,there are no limit load solutions exist for the single edge crack weldments in tension（SEC（T））,which is also a typical geometry in fracture analysis.The mis-matching limit load for thick plate with SEC（T） are investigated and the special limit load solutions are proposed based on the available mis-matching limit load solutions and systematic finite element analyses.The real weld configurations are simplified as a strip,and different weld strength mis-matching ratio M,crack depth/width ratio a/W and weld width 2H are in consideration.As a result,it is found that there exists excellent agreement between the limit load solutions and the FE results for almost all the mis-matching ration M,a/W and ligament-to-weld width ratio（W-a）/H.Moreover,useful recommendations are given for evaluating the limit loads of the EBW structure with SEC（T）.For the EBW joints with SEC（T）,the mis-matching limit loads can be obtained assuming that the components are wholly made of base metal,when M changing from 1.6 to 0.6.When M decreasing to 0.4,the mis-matching limit loads can be obtained assuming that the components are wholly made of base metal only for large value of（W-a）/H.The recommendations may be useful for evaluating the limit loads of the EBW structures with SEC（T）.The engineering simplifications are given for assessing the limit loads of electron beam welded structure with SEC（T）.

Assessment of Existing Bridge’s Beam Bending Stiffness Using Crack Characteristics

At present, the bearing capacity evaluation is mainly based on load detection, which requires closed traffic and has certain risks. With the increase of service time, the cracks of reinforced concrete beam bridge will gradually develop and the stiffness will reduce, resulting in the decrease of bearing capacity. Therefore, in this paper, the calculation of stiffness reduction coefficient by using crack characteristic parameters, which provides basic data for bearing capacity evaluation, has been studied. In this paper, using regression analysis through fracture characteristics of four model beam observation and test load-displacement curve characteristic parameters, crack flexural rigidity of the beam bridge relationship has been set up. The qualitative assessment based appearance of cracks in the structure of checks has been converted to quantitative assessment. And compared with the test results of a real bridge, comparative results show that the assessment is objective and reliable. It makes the assessment more objective and scientific. A new way of Quantitative assessment of the structural performance has been provided for a large number of existing reinforced concrete beam bridge.

Weldability and liquation cracking behavior of ZhS6U superalloy during electron-beam welding

The weldability of the ZhS6U nickel-based superalloy, which is prone to solidification cracking during electron-beam welding(EBW) repair processes, was investigated. The effects of two different pre-weld heat-treatment cycles on the final microstructure before and after welding were examined. Welds were made on flat coupons using an EBW machine, and the two heat-treatment cycles were designed to reduce γ′ liquation before welding. Microstructural features were also examined by optical and scanning electron microscopy. The results showed that the change in the morphology and size of the γ′ precipitates in the pre-weld heat-treatment cycles changed the ability of the superalloy to release the tensile stresses caused by the matrix phase cooling after EBW. The high hardness in the welded coupons subjected to the first heat-treatment cycle resulted in greater resistance to stress release by the base alloy, and the concentration of stress in the base metal caused liquation cracks in the heat-affected zone and solidification cracks in the weld area.

Crack elongation and its width of large depth reinforced concrete beams

In order to meet the requirement of structural inspection,the crack spacing and crack width at various heights in the tensile zone of six large depth reinforced concrete beams were measured under several loading levels of serviceability state.The effects of the depth of normal section beams on the crack spacing and crack width were analyzed,and the modified model is proposed for calculating the average crack spacing by thinking about the depth of normal section,the reinforcement arrangement and the effective reinforcement ratio.The relationships of crack widths at any position in the tensile zone and at the reinforcement level on the side surface of beam were studied.By theoretical and statistical analysis,a method is proposed to calculate the ratios of crack widths between any position and the reinforcement level on the side surface of large depth reinforced concrete beams.

Microstructure and crack sensitivity of electron beam welded titanium aluminide joints

Microstructural characterization and crack formed mechanism during electron beam welding of titanium aluminide Ti-45Al-1.7Cr-1.7Nb were investigated. The results show that the welded microstructure exhibits columnar and dendritic structure. Microstructural constituents in the fusion zone are a massive gamma structure and some lamellar structure consists of alternating platelets of α2 and γ. The major contributing factor of the susceptibility to solidstate cracking is thermally induced stress. The import role of the suppression of the α phase decomposition, the difference of α2/γ phases thermal expansion coefficient and the lamellar spacing changes of lamellar structure with cooling rate all play effect on the crack forming mechanism.

AN IMPEDANCE ANALYSIS FOR CRACK DETECTION IN THE TIMOSHENKO BEAM BASED ON THE ANTI-RESONANCE TECHNIQUE

An alternative technique for crack detection in a Timoshenko beam based on the first anti-resonant frequency is presented in this paper. Unlike the natural frequency, the anti-resonant frequency is a local parameter rather than a global parameter of structures, thus the proposed technique can be used to locate the structural defects. An impedance analysis of a cracked beam stimulated by a harmonic force based on the Timoshenko beam formulation is investigated. In order to characterize the local discontinuity due to cracks, a rotational spring model based on fracture mechanics is proposed to model the crack. Subsequently, the proposed method is verified by a numerical example of a simply-supported beam with a crack. The effect of the crack size on the anti-resonant frequency is investigated. The position of the crack of the simply-supported beam is also determined by the anti-resonance technique. The proposed technique is further applied to the ＂contaminated＂ anti-resonant frequency to detect crack damage, which is obtained by adding 1-3% noise to the calculated data. It is found that the proposed technique is effective and free from the environment noise. Finally, an experimental study is performed, which further verifies the validity of the proposed crack identification technique.

ON FATIGUE CRACK PATH DEVIATION AT ELEVATED TEMPERATURE IN ELECTRON BEAM REPAIRED WELDMENTS OF TURBINE DISK

Fatigue crack growth behaviors in electron beam weldments of a nickel-base superalloy are studied. The objective of this paper is to discuss effects of the inhomogeneity of mechanical performance on fatigue crack growth (FCG) rate and crack path deviation (CPD). The base metal served in a turbine disk of aerospace engine was selected to fabricate bead-on-plate weldments by using electron beam welding. Some wedge-type opening loading specimens, notched in three different zone of weld metal, HAZ and base metal, were employed and performed fatigue crack growth tests at 650℃. The results show that the fatigue crack growth of electron beam welded joints is instable due to the influence of mechanical heterogeneities. Owing to the crack deviation at the weld metal and heat-affected-zone (HAZ), the effective growth driving force at the tip of fatigue crack was reduced with the reduction of the effective stress intensity factor (SIF) which finally causes fatigue crack rate decrease. Fatigue crack was strongly affected by size and the symmetrical characteristics of the plastic zone at the crack tip, which means that the integrity of the welded structure containing the fatigue crack mainly depended on the toughness of the low strength zone.

TRANSVERSELY ISOTROPIC DAMAGE AROUND CONDUCTING CRACK-TIP IN FOUR-POINT BENDING PIEZOELECTRIC BEAM

A static damage constitutive model was proposed on basis of the electrical enthalpy density, and then some characteristics of transversely isotropic damage were discussed. Finally, the effects of both crack depth and applied loads on damage distributions were investigated through numerically analyzing transversely isotropic damage in a four_point bending PZT_PIC151 beam with a central conducting crack. Some conclusions were given: 1) Crack depth and mechanical loading have great influence on both mechanical and electrical damages.With their increment,the damages at crack_tip obviously increase and their region sizes also expand. 2) Effects of electrical loading on the two kinds of damages are obviously different. Electrical loading monotonously changes magnitude but region size of mechanical damage, whose effect on electrical damage is very complex.

“贝壳板”加固直角突变式钢吊车梁疲劳性能研究

针对既有直角突变式钢吊车梁,提出一种“贝壳板”加固方法,即在吊车梁变截面处腹板两侧,焊接带圆弧的“类贝壳式”钢板对吊车梁进行疲劳加固的方法.该加固方法是通过增加变截面区域腹板的刚度来降低疲劳细节的应力水平,从而提高其疲劳强度.通过缩尺疲劳试验对使用“贝壳板”加固后的直角突变式钢吊车梁疲劳性能进行了研究,分析“贝壳板”加固后吊车梁的疲劳破坏规律,评估加固后吊车梁的疲劳性能.以加固后吊车梁最危险疲劳细节的主应力为基本参量,给出了加固后吊车梁的设计S_(r,p)-N疲劳曲线.并通过试验结果验证了加固后吊车梁裂纹扩展模拟和寿命计算的正确性,进一步分析“贝壳板”加固后吊车梁破坏细节的疲劳裂纹扩展特性,研究“贝壳板”高度和厚度变化对加固效果的影响,可为吊车梁的加固设计提供参考依据.

端钩型钢纤维混凝土简支梁受弯承载力试验

为改善普通钢筋混凝土梁自重大、易开裂、承载力低等缺点,在混凝土中常加入钢纤维,端钩型钢纤维,作为常见的一种高性能钢纤维得到广泛关注,中外学者针对端钩型钢纤维混凝土的基本力学性能开展了较多研究,而对端钩型钢纤维混凝土受弯构件的正截面受力性能有待深入研究。为研究端钩型钢纤维混凝土简支梁受弯性能,制作4根端钩型钢纤维混凝土梁及1根普通混凝土梁,对其进行受弯性能试验,根据试验得到的破坏形态、承载力、荷载-挠度曲线、荷载-应变曲线,分析端钩型钢纤维体积掺量对试件受弯承载力及破坏形态的影响。结果表明:端钩型钢纤维混凝土简支梁与一般混凝土简支梁受弯过程类似,均经历了弹性、开裂、带裂缝工作、破坏4个阶段;端钩型钢纤维混凝土简支梁与一般混凝土简支梁受弯过程均基本符合“平截面假定”;端钩型钢纤维限制了裂缝的产生和发展,使得纤维混凝土梁变形能力增强;与一般混凝土梁相比,端钩型钢纤维混凝土梁抗裂性及极限承载力得到提高,且构件承载力与钢纤维体积掺量基本呈现正相关;基于试验数据,对现行规范中开裂弯矩及极限承载力计算公式进行优化,开裂弯矩方面考虑对截面抵抗矩塑性影响系数进行修正,极限承载力方面引入纤维混凝土正截面承载力影响系数ζ,经修正计算值可较好吻合试验值。

Numerical stress analysis of crack at welded beam-to-column connection

In the past, brittle fracture of steel structure was reported rarely under earthquake. However, recent earthquakes, especially Northridge Earthquake (USA) and Hyogoken Nanbu earthquake (Japan), astonished engineers in the field of construction. The experience from recent earthquakes of USA and Japan shows that brittle fracture of welded steel structure always starts from high stress zone with welded crack [1～5] . As backing bar for grooved weld on beam flange exists, artificial crack is formed because of lack of fusion at the root of flange weld. In this paper stress distribution of connection is computed with FEM, and stress concentration at the root of flange weld is also analyzed. Stress intensity factors (SIFs), K I, at the root of flange weld are computed in the method of fracture mechanics. The computation shows that stress intensity factor on bottom flange weld is obviously higher than that on top flange weld. It is proved by the fact that brittle fracture is liable to start at the root of bottom flange weld on actual earthquake [1,4] . Finally measures are brought forward to avoid fracture of weld structure against earthquake.