Intact Beam Research Articles

Numerical prediction of beam capacity using the new constitutive model based on concrete biaxial behavior

The biaxial strength of concrete exhibits intriguing nonlinearity and scattering, posing challenges to the assessment of building structural safety. Experiments have confirmed that biaxial strength envelopes can manifest concave, quasi-linear, and convex shapes. Despite various empirical formulas being proposed to describe this behavior, they cannot be applied to finite element simulations due to the absence of a constitutive perspective. To study the mechanisms forming the shape of strength envelopes, a novel three-invariant model constitutive model is proposed, which reveals the characteristics of the envelopes resulting from the coupling effect of hydrostatic pressure and Lode angle. By adjusting the model parameters, it effectively describes concave, quasi-linear, and convex envelopes. The model's accuracy and compatibility were validated against experimental data spanning various concrete types, with compression strengths ranging from 19.29 to 96.5 MPa and tension-compression ratios form 0.056 to 0.095. To investigate how biaxial strength impacts the capacity of beams, numerical experiments were conducted on notched and intact beams based on the proposed model. The results underscored that beams prepared using concrete with convex envelopes exhibited higher capacity compared to those with quasi-linear envelopes. Therefore, conducting biaxial tension-compression experiments is recommended to accurately evaluate beam bearing capacity. The proposed model is expected to have further applications in the safety evaluation of building structures.

Exact solution for mode shapes of cracked nonuniform axially functionally graded beams

This paper established the exact formulas for mode shapes of cracked nonuniform axially functionally graded (AFG) beams. The formula of the mode shape of cracked nonuniform AFG beam is derived in the form of a power presented as a recurrent relation. The power series solution of cracked beam is the same with the intact beam where the effect of cracks contributes to only the first four coefficients of the power series. The derivation of the formula of mode shapes is presented in details. Numerical simulations show that these effects on the natural frequency and mode shape are quite significant. The natural frequency and mode shape are more sensitive to cracks located at positions with low elastic modulus, small cross section and high mass density. For the case of tapered AFG cantilever beam, it is important to consider not only cracks located close to the fixed end but also cracks located close to the free end, especially when the free end has lower elastic modulus and higher mass density.

Experimental study of flexural behavior of glulam Douglas Fir beams spliced with engineered bamboo cover plates and inclined self-tapping screws

Due to the limitation of transportation and installation, long-span timber structural components need to be extended through multiple spliced joints. Among the common spliced joints, spliced beam joints with self-tapping screws have the advantages of low cross-section weakening, beautiful appearance, and convenient construction. However, the beam joints spliced by self-tapping screws have limitations in terms of bearing capacity and stiffness. To overcome these limitations, this paper proposes inclined self-tapping screw-engineered bamboo joints. In this novel joint, the high-strength engineered bamboo connection plates are used to improve the mechanical properties of spliced glulam beams. A total of thirteen glulam beams were designed. The effects of the layout and number of self-tapping screws, types of connection plates, and spliced gaps on the flexural performance of novel glulam beams were experimentally investigated through four-point bending tests. The results show that the mechanical properties of the spliced beam with parallel self-tapping screws are better than those with staggered self-tapping screws. The bending capacity of the glulam beams spliced with bamboo scrimber plates arranged in parallel increases with the increase of the number of self-tapping screws. The average bending capacity and stiffness can reach 97.3 % and 93.3 % of the intact beams, respectively. The bending capacity and stiffness of glulam beams with the same number of self-tapping screws arranged in parallel and spliced with plybamboo are lower than those of glulam beams spliced with bamboo scrimber. The gap between the spliced cross-sections of glulam beams significantly reduces the flexural mechanical properties of spliced beams, especially the stiffness.

An Efficient Approach for Damage Identification of Beams Using Mid-Span Static Deflection Changes

In structural health monitoring, determining the location and index of damage is a critical task in order to ensure the safe operation of the construction project and to enable the early recovery of losses. This paper presents a novel method for identifying damage location and damage index in simply supported (SS) beams by analyzing deflection changes at the mid-span point. Theoretical equations for mid-span deflection of simply supported beams with local damage are derived based on the principle of Virtual Work. Utilizing mid-span deflection, formulas for deflection change (DC) between two structural states, along with the first and second derivatives of DC at the mid-span point, are developed. The method of determining the location and damage index is then extended from intact beams to cases of beams with multiple damage zones and from damaged beams to beams with new failures. The graphical analysis of these quantities facilitates the determination of the number, location, and index of new damages. Various case studies on simply supported beams, involving one, two, and four damage zones at different positions and with varying damage indexes, are examined. The comparison of the theoretical method with the numerical simulations using Midas FEA NX 2020 (v1.1) software yields consistent results, affirming the accuracy and efficacy of the proposed approach in identifying and determining the damage locations as well as the damage indices.

Simulation of crack closure effect on cracked beam vibrations

Vibrations of beams containing cracks are usually investigated by using open or breathing crack models. Neither one of these approaches considers the plasticity induced crack closure (PICC) phenomena which occurs in fatigue crack growth. In this study, PICC is integrated into the vibration analysis of a cracked beam. First, fatigue crack growth at a notch is simulated with elastoplastic finite element analysis. Residual deformations, stresses and the contact pressures on crack faces are obtained. In the second phase, the model which includes these quantities is used for forced vibration analysis under harmonic loading by using implicit finite element method. For comparison, analyses are also running without PICC. Simulation results indicate that PICC has a significant effect on vibrations of cracked beams. For low load amplitude levels, cracked beam behaves like an intact beam. Nonlinear behavior appears only at rather high amplitude levels. It is concluded that PICC could suppress the crack breathing behavior and this could make it difficult to detect a fatigue crack in a beam from its nonlinear vibration response.

Comparative investigation on beam-to-beam connection with different types of connecting plates

The spliced glued laminated timber (glulam) beams have extensive applications in large-span timber structures since the length of the long solid wood beams is limited by transportation and construction. This paper investigated the flexural performance of glulam beam-to-beam connections with connecting plates and self-trapping screws. The influence of connecting plate types (steel plate, bamboo scrimber, and plybamboo plate) on the flexural performance of the spliced beams was studied. A total of 12 beams were designed, including the intact beam group (3 specimens) and the spliced beam group (9 specimens). The failure modes, ultimate bearing capacity, stiffness, moment-rotation curves, and carbon emissions of spliced beams with different connecting plates were studied. The test results showed that the failure mode of the spliced beams mainly included bending failure of glulam and fracture of the connecting plates. The average bearing capacity of the spliced beams with bamboo scrimber plates and those with steel plates could reach the intact beams. The average stiffness of the spliced beams with bamboo scrimber plates was higher than that of the splice beams with steel plates, reaching 97.6% of the intact beams. The average bearing capacity and stiffness of the splice beams with plybamboo plate reached 80.9% and 92.7% of the intact beams, respectively. A theoretical model of the spliced beams with bamboo scrimber plates was proposed and verified by tests data. Comparisons of the analytical and the test results reveal that the model can predict the moment capacity of the spliced beams with bamboo scrimber plates corresponding specific failure mode in this test.

BEARING CAPACITY, DEFORMABILITY AND CRACK RESISTANCE OF A DAMAGED BEAM REINFORCED WITH FIBER CONCRETE IN THE COMPRESSED ZONE

The paper presents the results of the study of the load-bearing capacity, deformability and crack resistance of a damaged beam reinforced with fiber concrete in the compressed zone. A beam with 40% damage is considered. The research was conducted in two stages. At the first stage, tests of prisms and cubes made of concrete and fiber concrete were carried out, which showed that the introduction of steel fiber into the composition of concrete in the amount of 2% by volume increases the compressive strength by 15.3%. The initial modulus of elasticity of fiber concrete of the specified mixture is 38.0% higher than that of ordinary concrete of this composition. According to the results of experimental studies of prisms, a diagram of concrete deformation, the nature of changes in relative linear deformations of fiber concrete, as well as graphs showing a comparison of the nature of deformation of concrete and fiber concrete were constructed. At the second stage, the beam sample was tested on a specially designed stand. Before concreting, a foam insert was installed in the zone of planned damage, the shape and dimensions of which corresponded to the planned damage. After the concrete set to 70% strength, the liner was removed, and the formed cavity was filled with a 2% fiber concrete mixture. A beam with 40% cross-sectional damage in the mid-compression zone and a near-rectangular damage shape was found to have a load-bearing capacity of 92.0 kN, or 93.9% of the load-bearing capacity of an undamaged beam. Cracking started at the 4th loading stage, when the load value was 26.0kN, i.e. 28.3% of the bearing capacity of the damaged beam. At the same time, 5 cracks formed in the area of pure bending. At the fifth stage, two more cracks appeared. At the 8th and 9th loading stages, 4 more cracks formed. A total of 12 cracks were formed. The maximum final crack opening width was 0.6 mm. Thus, the strengthening of a beam with 40% damage in the compressed zone by the method considered in the work allows you to achieve its bearing capacity, which is 93.9% of the bearing capacity of an intact beam.

EXPERIMENTAL STUDIES ON THE STRENGTHENING OF A BEAM DAMAGED IN THE TENSILE ZONE

The paper presents the results of a study of the bearing capacity of a beam damaged during hostilities, which was reinforced with steel-reinforced concrete. Consider a beam with 40% damage in the stretched zone. Before concreting, a foam insert was installed in the zone of planned damage, the shape and dimensions of which corresponded to the planned damage. After the concrete set to 70% strength, the liner was removed, and the formed cavity was filled with a 2% fiber concrete mixture. This is one of the options for beam strengthening in a complex program of testing damaged beams, which involves the study of a series of beams with different types of damage, the damage zone (tension and compression) and its dimensions, geometry and method of strengthening. For testing, the authors developed a special stand. The plane-transverse load bending of the beam under study is created with the help of a hydraulic jack and a metal I-beam with a traverse, which transmits two equally concentrated forces to the beam. The generated load is controlled by a model dynamometer of the Tokar system and a ring dynamometer, which acts as a support. Experimental studies have established that a beam whose cross-section is 40% damaged in the middle stretched zone, and the shape of the damage is close to rectangular, has a bearing capacity of 91.0 kN, which is 92.38% of the bearing capacity of an intact beam (98.5 kN ). Cracking started at the 5th loading stage, when the load value was 32.5kN, i.e. 35.7% of the bearing capacity of the damaged beam. At the same time, 4 cracks were formed. At the sixth stage, three more cracks appeared. At stages 9-12 of loading, 9 more cracks formed. The maximum final crack opening width was 1.1 mm. At the same time, 6 cracks formed in the zone of clean bending. During the entire testing process, the fiber concrete liner worked with the beam as a single unit. It can be argued that the strengthening of a beam with 40% damage in the stretched zone in the manner considered in the paper allows to achieve its bearing capacity, which is 92.38% of the bearing capacity of an undamaged beam.

Assessment of damage evolution of concrete beams strengthened with BFRP sheets with acoustic emission and unsupervised machine learning

Basalt fiber reinforced polymer (BFRP) is an emerging material that can be used to strengthen or repair concrete structures. This paper experimentally investigates the flexural failure process of concrete beams strengthened by BFRP sheets under four-point loading conditions using acoustic emission (AE)-based nondestructive evaluation and unsupervised machine learning techniques. Both damaged beams and repaired beams were tested and compared with intact beams regarding their mechanical performance and AE signature. Test results showed that BFRP sheets enhanced the load-bearing capacity of the beams significantly, and AE signals were sensitive to the initiation and development of damages. The damage process and mechanisms of different beams have been investigated by analyzing AE signals regarding various AE parameters, and particularly, the failure process and damage mechanisms were investigated via b-value and k-means clustering analyses. This research provides theoretical guidance for evaluating the reinforcing effect of BFRP sheets for concrete beams based on AE techniques.

BEARING CAPACITY OF A BEAM DAMAGED DURING COMBAT ACTIONS STRENGTHENED WITH THE USE OF FIBER CONCRETE

The paper presents the results of a study of the load-bearing capacity of a beam damaged during hostilities, which was reinforced with steel-reinforced concrete. A beam with 20 percent damage in the compression zone is considered. Before concreting, a foam insert was installed in the area of the planned damage, the shape and dimensions of which corresponded to the planned damage. After the concrete was set to 70% grade strength, the liner was pulled out, and the resulting cavity was filled with a 2% mixture of fiber concrete. This is one of the beam strengthening options in a comprehensive damaged beam testing program, which involves the study of a series of beams with different types of damage, varying damage zone (tensile and compression) and its magnitude, geometry and method of strengthening. The authors developed a special stand for testing. The load-bearing capacity of the damaged beam reinforced with fiber concrete was 80.6 kN, or 89.5% of the load-bearing capacity of the intact beam. Cracking started at the 4th load stage, when the load value was 16.1 kN, or 20% of the bearing capacity of the damaged beam. At the same time, 10 cracks formed in the zone of pure bending, the opening width of which did not exceed half the price of the microscope division, which is 0.005 mm. At the next eight stages of loading (up to 48.4kN), no new cracks were observed, and the width of the opening of all the ones that had previously formed doubled - it reached 0.01mm. At the 12th, 13th and 19th stages of loading, 4 more cracks appeared. The maximum final crack opening width was 1.2 mm. Up to a load of 68.5kN, which is 85% of the load-bearing capacity of the damaged beam, the reinforced concrete liner works with the beam almost as a unit, and then the compressed zone of concrete squeezes out the liner. It is claimed that the strengthening of a beam with 20% damage in the compressed zone in the manner considered in the work allows to achieve its bearing capacity, which is almost 90% of the bearing capacity of an undamaged beam.

Crack localisation in composite cantilever beams using natural frequency measurements

ABSTRACT Crack localisation is a fundamental step of damage identification. Most of the published research on crack localisation based on natural frequency consists in model updating which requires a great deal of calculation. This paper presents a simple method of crack localisation in composite cantilever beam-type structures. The proposed method consists of classifying the reduction of the first four measured natural frequencies and deducing the damage position from a table. For these purposes, a finite element model is first used to study the direct problem: the vibration behaviour of an intact beam and the changes caused in the damaged state. Then it is shown that the classification of the frequency reduction ratio is different for each damaged zone. Consequently, the beam is discretized into several areas according to the classifications of the first four frequency ratios. Therefore, this discretization is represented in a table to be used in damage localisation. The robustness of the suggested technique is first tested numerically by using the Abaqus/CAE finite element software environment. Then, the applicability of the localisation method is validated experimentally on a cracked glass fibre-reinforced epoxy beam. The results show that the proposed method can successfully localise damage in composite beams.

DAMAGE DETECTION IN A STEEL BEAM USING VIBRATION RESPONSE

Changes in vibration signals, natural frequency and modal parameters were used for damage detection in a steel beam. Several tests were performed on simply supported steel beams having open transverse cracks with varying depths and locations. Frequencies for the first three vibration modes were generated from the analytical, numerical, and experimental models. Analytical frequencies were calculated assuming Euler-Bernoulli beam and solving partial differential equations. Vibration signals were collected using a portable digital vibrometer and analyzed through Fast Fourier Transform. The finite element beam models were calibrated using experimental results. The graphical plots of the normalized frequency from the experimental study and FE models showed similar pattern for the first mode. The nodal points were identified as the locations where the damaged frequency equals the frequency of an intact beam. The existence of damage in the beam specimen was confirmed by comparing the natural frequency of a beam at its intact and damaged states. Equations relating normalized frequency with varying crack depth and location were proposed.

Experimental Study of Glued Laminated Timber (Glulam) from Jackfruit Wood and Coconut Wood for Timber Beams of Level Houses in East Nusa Tenggara

Wood is a construction material that is familiar to the wider community. Wood can be used in construction. The purpose of this study was to determine the specifications of the physical properties, mechanical properties, tensile strength and flexural strength of laminated wood (glulam), in jackfruit and coconut wood beams originating from the East Nusa Tenggara region in multi-storey house buildings. The tests carried out included testing the water content, testing the tensile strength and bending strength, testing the tensile strength and bending strength on glulam beams using epoxy glue adhesives. The results of this study showed that jackfruit wood and coconut wood aged 15 years and 20 years had an average moisture content of 15 years, namely 15% and 26%, the average specific gravity was 0.54 (tons/m3) and 0.46 (tons/m3). Meanwhile, the average water content for 20 years is 15% and 32%, the average specific gravity is 0.58 (Ton/m3) and 0.45 (Ton/m3). The tensile strength of intact and glulam wood of jackfruit and coconut wood was obtained from laboratory results on SNI 7973-2013 calculations, the average tensile strength of intact jackfruit and coconut wood was 84.40 MPa and 80.73 MPa. The flexural strength of intact beams and glulam of jackfruit and coconut wood aged 15 years was obtained from laboratory results on SNI 7973-2013 calculations of the flexural strength of intact beams for 15 years, the average being 71.81 MPa and 26.07 MPa. At 15 years of age, the flexural strength of glulam beams was the highest variation 1 and variation 2 (Jackfruit, Coconut, Jackfruit) mean 76.00 MPa and 41.85 MPa. The flexural strength of intact beams and gulam of jackfruit and coconut wood aged 20 years was obtained by laboratory results on SNI 7973-2013 calculations of flexural strength of intact beams, which were 80.27 MPa and 29.73 MPa respectively. At the age of 20 years, the highest flexural strength of glulam beams were variations 1 and 2 (Coconut, Jackfruit, Coconut) with an average of 80.40 MPa and 48.76 Mpa.

Experimental investigation on seismic performance of self-centering frictional cast-in-situ beam-column joints

Excessive residual deformation makes it difficult to repair reinforced concrete frame after earthquakes, and self-centering techniques have been widely adopted to mitigate residual displacement of structures. Therefore, a self-centering frictional cast-in-situ beam-column joint (SCFJ) is developed. This SCFJ mitigates damage and residual displacement via reduced beam section and self-centering frictional connectors (SFCs). The construction and working mechanism of the SCFJ are first studied, after which cyclic loading tests of SFCs, SCFJs and an ordinary reinforced concrete joint (ORCJ) are carried out. The damage evolution process, strength, hysteresis characteristics, and residual displacement of these joints are systematically discussed. The results indicate that the proposed SCFJ exhibits excellent self-centering characteristics with limited damage, while having comparable energy dissipation with ORCJ. Specifically, the damage of the SCFJ mainly occurs in the reduced beam section, and the reinforcement in the intact beam section and column is always elastic. The number and width of cracks in the SCFJ are significantly less than those of the ORCJ under the same displacements. Even if the drift ratio of the SCFJ reaches 2.5%, its residual drift ratio remains less than 0.5%, which is only 40% of the residual drift ratio of the ORCJ, thus facilitating rapid post-earthquake repair.

Residual Performance of Reinforced Concrete Beams Damaged by Low-Velocity Impact Loading

With the advancement of material science and infrastructure design technology, there is an increased need to reflect various loading scenarios in the design of civil infrastructures, including extreme loads such as impact and blast. However, structural behavior under extreme loads has been observed to be very different from that under static loads due to the high-rate loading condition. Therefore, extensive experimental and analytical studies have been conducted to explain the structural behavior under impact loading. From these efforts, various discussions have been presented on the impact behavior and the evaluation of the impact resistance of structures. However, despite the fact that the repair or reinforcement of structures damaged by impact loads is a critical issue, studies of the residual performance of impact-damaged structures are insufficient. This paper presents an experimental study to improve the understanding of the residual performance of impact-damaged structures. A total of 29 RC beams were tested under static loads to examine the effect of impact-damage on the residual behavior of RC beams. Of these, 8 RC beams were intact, and the other 21 RC beams suffered impact loading through drop weight impact tests and were damaged prior to the static flexural tests. The residual performance was evaluated by comparing the maximum load capacity, flexural stiffness, and displacement ductility of impact-damaged beams and intact beams. The comparison indicated that the flexural stiffness and displacement ductility of the impact-damaged RC beams decreased significantly, whereas their flexural strengths did not exhibit a significant difference. Predictive models for flexural stiffness and displacement ductility of the impact-damaged beams were suggested from the test results, and through these, the residual performance of the impact-damaged structure could be evaluated.

Intermediate crack-induced debonding in CFRP-retrofitted notched steel beams at different service temperatures: Experimental test and finite element modeling

Carbon fiber-reinforced polymer (CFRP)-retrofitted steel beams are likely exposed to significant service temperature variations due to seasonal and daily temperature changes. However, there is lacking research on the structural performance of CFRP-retrofitted steel beams under service temperature variations. This paper presents an experimental study of fourteen beams including one intact beam, one notched beam and twelve CFRP-retrofitted notched beams tested at various service temperatures from -20°C to 80°C. The structural properties including load-deflection curves, load capacities at initial and ultimate debonding, crack mouth opening displacements at the notch and the CFRP strain measurements were examined and compared at different service temperatures. The debonding loads of CFRP-retrofitted beams were increased with the temperatures from -20°C to 60°C and decreased at 80°C. A formula was proposed to derive the local bond-slip behavior of the CFRP-to-steel interface at different temperatures from the CFRP strain measurements. The shear stiffness of the interface generally decreased with the service temperature growth, while the interfacial fracture energy first increased and then decreased. A finite element model was proposed to gain insight into the effects of interfacial thermal stress and temperature-dependent bond properties on the bond behavior and structural performance of CFRP-retrofitted beams at different service temperatures.

Evaluating Flexural Performance of Repaired Reinforced Concrete Beams under Static and Repeated Loading Using Non-Destructive Methods.

Deterioration of concrete structures is one of the major issues faced by the construction industry. Repair and rehabilitation are necessary to extend the service life of such structures. This study aims to investigate the effect of repair material type, length of repaired region, and loading regime on the structural characteristics of the repaired reinforced concrete (RC) beams. To achieve this goal, a total of 30 repaired and non-repaired RC beams were prepared and tested under static and repeated loading conditions. Three types of sounding-based non-destructive test (NDT) methods are employed to determine the material deterioration and sub-surface delamination after repeated loading. Results showed that under static loading conditions, full-length repaired beams had better performance than 1/3-span repaired beams. Beams repaired with cementitious repair mortar containing modified binder and cementitious repair concrete in full length had a yield strength that was 14% and 9%, respectively, higher than that of beams repaired in 1/3 span. All RC beams with full-span repair outperformed the intact beams. After repeated loading, beams repaired with cementitious repair with modified binder over full length showed a 14% improvement in yield strength compared to control samples. It was found that repair materials that had a high compressive and flexural strength are beneficial. The resonant frequency drops correlate well with the yield strength results. The formulas proposed by Canadian Standards Association (CSA) 23.3 can effectively predict the moment resistance of both intact (control) and repaired RC beams. The ratio of experimental moment resistance values to its predictions ranges from 0.91 to 1.04.

Numerical and analytical studies of flexural behaviour of prestressed UHPC joints

This study numerically and analytically investigates flexural behaviour of precast ultrahigh performance concrete (UHPC) segments connected by post-tensioned prestressing strands with or without epoxy on keyed joint surfaces. The analytical formulas are proposed for calculation of joint opening load and ultimate flexural capacity, and a numerical model is established to investigate flexural behaviour of the jointed beam. The joint surfaces without epoxy are simulated by a pair of contact elements with a friction coefficient of 0.6. For the joint surfaces with epoxy, besides the contact elements, a spring element is defined for consideration of the epoxy and an optimized force–displacement relationship is first proposed and input for the spring property. The previous test data and data from one intact beam with low reinforcement ratio tested in the present study are used for validation of the analytical and numerical calculations. The numerical results agree well with the test results in terms of load-midspan deflection, load-joint opening displacement as well as failure modes. Based on the validated numerical model, the effect of number of prestressing strands and beam depth on the flexural behaviour of the prestressed jointed beam is investigated. This study will promote prestressed UHPC joints’ application in practical engineering.

Notch-type damage influence on the frequency of the principal mode of the composite cantilever beam flexural vibrations

The results of calculation investigations aimed at the determination of the influence mechanisms of the surface damage in the form of a rectangular notch and fibers’ orientation on the frequency of the principal mode of the composite cantilever beam flexural vibrations are presented. The three-dimensional finite element model of the beam made of the unidirectional carbon-fiber-reinforced plastic with the local surface rectangular notch-type damage has been developed using the effective modulus concept to determine the composite material elastic properties. Its adequacy is corroborated via the comparison of the determination results of the principal frequency of flexural vibrations of the intact beam as a function of the degree of anisotropy in composite material with the known experimental data. In this paper has been found the mechanisms of influence of the damage parameters (notch depth and its location along the beam length) and the degree of anisotropy of the elastic properties in composite material, which is defined by the angle of the fibers, on the variation of the frequency of the principal mode of flexural vibrations. It is established that there is such a notch location along the beam length for its specified depth and width, the so-called transition point, where the natural frequency of vibrations of the damaged and intact beams are equal independent of the angle of the fibers. This fact indicates that there is a simultaneous damage effect on both the variation of flexural stiffness of the beam and its inertia properties. The location of the transition point depends on the notch depth and fibers’ orientation. With the larger distance of the notch from the transition point to the free end, the principal frequency of vibrations of the damaged beam becomes larger as compared with that one for the intact beam.

Damage severity for cracked simply supported beams

This paper investigated the static and dynamic behaviors of isotropic cracked simply supported beam using finite element analysis (FEA), ANSYS software. Modal and harmonic vibration analysis of intact and damaged beam were performed in order to extract mode shapes of bending vibration, natural frequencies and obtain frequency response diagram. Static finite element analysis of undamaged and damaged simply supported beam was carried out to determine zero frequency deflection, then stiffness of intact and cracked beam was computed using conventional formula. Crack damage severity of damaged beam was calculated and it is noticed that as crack position is increased from left hand support of beam up to central point and crack depth is increased, then crack damage severity increases. The effect of mode shape pattern is investigated and it is found that the amount of decreasing of natural frequency is proportional to the normalized mode shape at position of crack. The exhibited correlation between results for damaged beam revealed that crack damage severity is proportional to zero frequency deflection and inversely proportional to first mode frequency.