Prestressed Beams Research Articles

Analysis of load carrying capacity of bridges strengthened by extracorporeal prestressing after five years of operation: a case study

PurposeThe application of reinforcing old bridges by adding external prestressed steel bundles is becoming more and more widespread. However, the long-term safety performance test of the strengthening method is rarely carried out. In this paper, the bearing capacity of a 420 m prestressed concrete (PC) continuous girder bridge after five years of strengthening is analyzed.Design/methodology/approachThe bridge model of the bridge structure and strengthening scheme is established by the finite element software of the bridge. The theoretical load-bearing capacity of the bridge under the latest standard load grade is obtained by finite element analysis. The actual bearing capacity of the bridge is obtained by field test. Through the comparative analysis of theory and practice, the health state of the bridge after five years of reinforced operation is judged. The damage to the overall stiffness and external prestressing of the bridge is also analyzed.FindingsThe results of deflection and strain show that the stiffness and strength of the secondary side span and the middle span decrease slightly, and the maximum reduction of bearing capacity is 4.5%. The static stiffness of the whole bridge decreases as a result of cracks, and the maximum decrease is 21%. In the past five years, the relaxation loss of the external prestressing of the bridge is 3.31–3.97%, which is the main reason for the decrease in bearing capacity.Originality/valueThrough the joint analysis of the bridge stiffness and the loss of external prestressing, the strengthening condition of the bridge after five years of operation is effectively analyzed. The strengthening effect of the external prestressed steel beam strengthening method is analyzed, which can provide a reference for similar bridge strengthening.

Flexural behavior of glulam beams reinforced by bonded prestressing tendons

The rapid progression of mass timber structures towards greater spans presents a challenge for the flexural behavior of glulam beams. In this study, this challenge was addressed by reinforcing the glulam beams with prestressing tendons which were bonded to the glulam beams by epoxy resin. The objective of this study is to investigate the influence of prestressing force levels and bonded types on the flexural behavior of prestressed glulam beams. Four-point bending tests were conducted on twelve glulam beams prepared by unreinforced, unbonded prestressed or bonded prestressed techniques. Experimental results revealed that the glulam beams exhibited increased ductility under prestressing force. Compared with unreinforced beams, the prestressed beams demonstrated a remarkable increase of up to 78.8 % in flexural capacity and 13.5 % in flexural stiffness. For the prestressed beams, the flexural capacity increased as prestressing force increases. Compared with the unbonded prestressed beams at the same prestressing force level, the bonded ones exhibited higher flexural capacity and flexural stiffness. Additionally, the bonded prestressed beams exhibited a slight increase in tendon stress at the end of the prestressing tendon during loading, indicating favorable bonding behavior of epoxy resin. Numerical models were developed to predict the non-linear flexural behavior of prestressed beams, and the numerical results showed good agreements with the experimental results. Parametric analysis based on the numerical models was conducted on the prestressed beams at various prestressing force levels. The positive effect of the bonded prestressed method on the flexual behavior of glulam beams was further substantiated.

STUDY ON CONSTRUCTION MONITORING AND CONTROL OF MULTI-SPAN PRESTRESSED CONCRETE CONTINUOUS BEAM BRIDGE

This article focuses on the construction monitoring and control of a pre-stressed concrete continuous beam bridge, consisting of 13 spans. The goal is to ensure that the bridge structure meets the design requirements throughout the entire construction process. By comparing the theoretical and measured values of the bridge’s alignment and stress during the cantilever construction, closure, and completion phases, it can be observed that the deflection deformation of the bridge is generally in agreement with the theoretical calculations. After the completion of the entire bridge, the measured elevations of each section have an error range of -18mm to 20mm compared to the design elevations, which satisfies the specifications. A comparison analysis of the measured and theoretical stress values at the root and mid-span of the cantilever indicates that the stress difference at the root is within the range of -0.2MPa to 0.2MPa, and the stress differences at the mid-span after completion are 0.03MPa (upper) and 0.09MPa (lower), all of which meet the structural design and code requirements. By establishing a gray GM (1,1) model and using gray system theory, the deflection error during the construction process is predicted and controlled. The prediction accuracy of different methods is compared to determine a reasonable prediction method suitable for long-span pre-stressed continuous beam bridges, providing reference for similar engineering projects.

The Impact of Increased Traffic and Explosion Loads on the Concrete Bridges Baniwalid Bridge - Case Study

The Baniwalid Bridge is located at the entrance of the city. This bridge was implemented during the seventies of the last century and was opened to traffic in the eighties. It is considered the main artery for traffic, linking the two sides of the city. Its length is about 500m, and its width is 20m. It has two directions; each direction is 8 meters wide. The construction system of the bridge consists of 31 average spans, each of which is 14.5 meters long, and each span consists of 18 pre-stressed beams, with a height of 0.72 meters and a width of 1.00 meters. Traffic increased within the city in previous years as a result of the closure of the coastal road, which led to a change in the movement of freight and land transport to eastern and southern Libya through the cities of Baniwalid and Gharyan, where the bridge was subjected to very high traffic loads that far exceed the design loads. In this study, the bridge was inspected, some previous reports were reviewed, and the construction status of the bridge was determined in general. There are many cracks in the bridge due to water, shells and increased traffic. The foundations were also exposed to erosion due to torrential rains. In general, the bridge needs immediate maintenance.

Field Test and Numerical Study of Three Types of Frame Beams Subjected to a 600 kN Anchoring Force

Frame beams with anchor cables constitute a crucial method for slope reinforcement projects. With the development of fabricated structures, there has been an increasing focus on precast prestressed frame beams with anchor cables. This paper presents a field test conducted in Yunnan, China and numerical simulations to analyze the structure behavior of three types of frame beams with a 600 kN anchoring force: cast-in-situ frame beams, precast prestressed frame beams, and precast prestressed frame beams with connections. The results showed that: (1) Although all three types of frame beams met the design requirements for a 600 kN anchoring force capacity, the volume of precast prestressed frame beams constituted only 57% of that of the cast-in-situ frame beams. (2) The maximum bending moment for the precast prestressed frame beams with connections was 60 kN·m less than that for the cast-in-situ frame beams. (3) The field test results for bending moments exceeded the values obtained from the numerical simulation. When using a numerical simulation to study the bending moments of the anchor frame beams, it is acceptable to apply appropriate amplifications to the numerical results. (4) Among the three types of frame beams with cables, the precast prestressed frame beams with connections exhibited the best structural performance.

Vibration reliability of steel beams prestressed by drawing

Introduction. Vibrations of building structures and mechanism parts were analyzed. The need to investigate the oscillation processes and vibration reliability of steel beams prestressed by web drawing was formulated. The subject of study is structural steel. The object of study is bimetallic steel beam prestressed without rods.Materials and methods. The scientific inquiry is based on the basics of structural mechanics of buildings and structures: superposition principle, differential equation of deflection curve of a bar, energy method, and methods of determination of stress-strain state of prestressed steel bars.Results. A comparative analysis of vibration reliability of non-prestressed beams and prestressed structures of equal bearing capacity was performed. Rotations of the beam supporting nodes loaded by prestressing forces and external impacts were determined by integration of differential equation of deflection curve of a split bar. The support moments in rigid supporting nodes of structures were determined on the basis of superposition principle. The developed methods of stressed condition of prestressed bars are the basis for determination of normal stresses in the sections of beams under study. The resultant stresses were obtained by algebraic addition of prestresses and stresses from external loads. Dynamic parameters of bearing capacity of beams were determined on the basis of works by I.M. Rabinovich and V.A. Kiselev. The oscillation circular frequency of conventional and prestressed beams was established, analytical expressions for determination of angular velocity of prestressed bending elements were formulated, and the dynamic deflections and factors of structures were determined. It is found that the circular frequency of prestressed beams hinged in supporting nodes compared to the circular frequency of conventional beams decreases by a factor of 1.4 and by a factor of 5.6 in beams with rigid supports. Angular velocity decreases by a factor of 1.4 (hinge supports) and 6.8 (rigid supports), respectively. The deflections of prestressed beams are reduced by a factor of 1,87: 11,9. There is a significant reduction in the stressed condition of prestressed structures.Conclusions. A hinged traditional beam under external and vibration loads in limit state is in the material yield zone and does not meet the first and second limit state conditions. These structures have the lowest vibration reliability. Prestressed structures are more reliable. With rigid supporting nodes, the moments of prestressing forces coincide with the supporting moments and produce hogging with the vector opposite to the external load deflection vector. In the limit state, total deflections are less than the external load deflections. Stresses in the structure decrease. Since load moments and beam deflections are initial parameters for dealing with dynamic strength tasks, we may state that prestressed beams with rigid supporting nodes have an increased vibration reliability.

ЭЛЕМЕНТЫ ОЦЕНКИ РЕСУРСА СТАЛЬНЫХ БАЛОК, ПРЕДВАРИТЕЛЬНО НАПРЯЖЕННЫХ ВЫТЯЖКОЙ СТЕНКИ

The article presents possible ways to determine service life of steel single-span beams with prestressed web. The authors implement the method for searching coefficients of optimal distribution of material over the cross section of a symmetrical, monometallic steel I-beam. Basing on structures theory the study determines the maximum permissible moments of external loads for ordinary and prestressed beams. It formulates analytical expressions characterizing the first and second limit states of prestressed beams and establishes the resource of their bearing capacity. As a result of performed analysis, analytical dependences of prestressed beams stiffness are determined and structures resource is established according to this criterion. The study determines height of beams and its change with span variations and actual uniformly distributed load. Resource height of prestressed beams is established in comparison with height of conventional bending structures. Load-bearing capacity of beams with prestressed web is 1,8 times higher than the corresponding capacity of conventional beam and their resource is 180 %. Deflections of prestressed beams are 77,3 % less than deflections of traditional beams and stiffness resource is 1,29. Height of conventional beam is 1,847 times higher than height of prestressed structure. Service life of prestressed beam is 187%. Key words: prestressing, optimal design, load-bearing capacity, rigidity, service life.

Numerical and digital image correlation study of the flexural behavior of prestressed ultra-high-performance concrete beams made from locally available materials

This paper presents finite element simulations of the flexural behavior of three prestressed ultra-high-performance concrete (UHPC) beams based on the concrete damaged plasticity model (CDPM) available within Abaqus. A novel numerical model that applies the prestressing force through surface traction is proposed. The flexural deformation of the prestressed UHPC beams is simulated from the application of the prestressing force through failure under flexural loading. Material properties were measured and informed values for CDPM input parameters. The model was compared with four-point loading tests previously conducted to study the flexural behavior of large-scale prestressed UHPC beams. Digital image correlation (DIC), supplemented with traditional sensors, was used during the test to monitor behavior. The primary results based on the numerical modeling are as follows: • The model is validated to accurately simulate the flexural behavior of prestressed UHPC beams, both in global deflection and local strain. • The prestressing process, including camber deformations, is effectively simulated. • The new approach to apply prestressing force in the model can be applied in scenarios requiring large prestressing forces. • The numerical results are also validated through comparison with DIC results. The new numerical modeling approach will be effective for guiding experimental studies and design of prestressed UHPC beam elements.

Corrosion effects on the flexural performance of prestressed reinforced concrete beams

An experimental campaign aimed at understanding the behavior of corroded prestressed beams is carried out to investigate the effects of low corrosion levels spreading along the entire beams. The results show that corrosion affects the flexural stiffness, the beams' crack pattern, and the failure conditions. Analytical models, implemented to simulate the experimental investigation, allowed a better interpretation of the obtained results, showing that the flexural performance of the corroded beam is governed by both a prestress loss and a reduction of the strand’s mechanical properties, such as ultimate strength and strain.

Experimental and Numerical Study on the Flexural Behaviors of Unbonded Prestressed I-Shaped Steel Encased in Ultra-High-Performance Concrete Beams

A novel type of traditional composite member-unbonded prestressed I-shaped steel encased in a UHPC (PSRUHPC) beam is proposed to reduce the brittleness of UHPC beams and improve their bearing capacity. A PSRUHPC beam, an unbonded prestressed UHPC (PRUHPC) beam, and an I-shape steel UHPC (SRUHPC) beam were manufactured, and their flexural static performances were assessed using a flexural comparison test. The test results reveal that the flexural process of the PSRUHPC beam is similar to that of ordinary reinforced concrete beams, and UHPC crushing in the compression zone is a sign of failure. Due to the bridge coupling effect of steel fiber, the crushed concrete still maintains good integrity without bursting, the UHPC in the tension zone remains functional after cracking, and the cracking inflection point of the load–deflection curve was not obvious. The PSRUHPC beam showed a significantly improved bearing capacity and flexural stiffness, its load–deflection curve exhibited significantly more energy consumption, and its bending ductility performance was improved, with better deformation properties. Compared with PRUHPC beams, PSRUHPC beams show a bearing capacity increase of 55.3%, a cracking load increase of 11.9%, and a displacement ductility coefficient increase of 76.2%. Compared with SRUHPC beams, PSRUHPC beams show a 15.4% increase in bearing capacity, a 50.2% increase in cracking load, and a 12.1% increase in displacement ductility coefficient. The application of prestress can significantly improve the stiffness of the beam prior to cracking. The cracking loads of prestressed ordinary concrete beams and steel-reinforced concrete beams account for 20–30% of their ultimate loads, which value was 40–50% for the tested beams. The change trend of strain in the section steel and UHPC is roughly the same at the same height, and the strains of the two deviated after most of the section steel yielded under tension, but they can generally work together. When the tested beams were cracked, multiple cracks appeared, which were fine and dense. The magnetic flux sensor cable force-monitoring system can better monitor the strand stress increment of unbonded prestressed steel UHPC beams, where the prestressed strand did not yield tension under the final state; the load–strand stress increment curve was basically the same as the load–deflection curve, and the stress increment of the unbonded steel strand positively correlated with the midspan deflection. Finite element simulation was used to verify the test results, and we determined the reinforcement ratios for non-prestressed and prestressed reinforcement, as well as the ratio of a steel-containing section, the effective prestress, the height of prestressed reinforcement, the position and strength of I-shaped steel, and whether or not the prestressed reinforcement was bonded. The effects of these parameters on the bearing capacity and displacement ductility coefficient of PSRUHPC beams were studied. The results can provide a reference for subsequent theoretical design calculations.

A spatial stability theory of thin-walled steel beams pre-stressed by spatially inclined un-bonded cables and its FE formulation

A spatial stability theory of mono-symmetric thin-walled steel beams pre-stressed (PS) by spatially inclined cables is firstly derived using an energy method where it is assumed that deviators are rigid. Its FE formulation is then presented under bonded/un-bonded multi-deviator conditions. After that, validity and accuracy of the present formulation is demonstrated through numerical examples. Finally, effects of initial tension, deviator numbers, inclined cable profiles, and un-bonded/bonded conditions on lateral-torsional buckling (LTB) of the PS bi-/mono-symmetric beams are investigated under external loadings. Particularly, new findings on LTB characteristics of the PS beams are presented with a specific emphasis on the effects of increasing initial tension.

LTB analysis of pre-stressed steel beams using mono-symmetric thin-walled beam and spatially inclined un-bonded cable elements

A FE procedure is proposed for spatial buckling analysis of thin-walled steel beams that are pre-stressed (PS) by spatially inclined cables. Here, the beams are simply supported, and their cross section can be bi/mono-symmetric. Also, the pre-stressing cables are connected to several deviators under bonded/un-bonded conditions. For lateral–torsional buckling (LTB) analysis of the PS beams, a thin-walled beam element for the steel beam and solid beam elements for the deviator members are firstly formulated using total potential energies. After that, the potential energies of two-node bonded and multi-node un-bonded cable elements are rigorously derived, and the corresponding elastic and geometric stiffness matrices are explicitly presented. Finally, the validity and accuracy of the present FE formulation are demonstrated through numerical examples, and a set of parametric studies is conducted to investigate the effects of initial tension, multi-deviators, vertical and lateral eccentricities, and flexible deviators on the LTB of the PS beams.

Experimental study of moment redistribution before yielding in precast prestressed concrete beams made continuous

AbstractThe bending stiffness distribution of beams composed of simple‐span precast prestressed beams, which are made continuous by deck reinforcement at intermediate supports, is not constant. As the structure undergoes loading, the deck slab at the intermediate support cracks earlier than the prestressed span soffit and due to that the bending stiffness distribution changes along the beam length. The effect of nonconstant bending stiffness distribution on the moment redistribution of the structure before the yielding is studied experimentally and analytically. Two continuous beams with spans of 10 m + 10 m were manufactured, loaded to failure, and studied. It was concluded that the studied structure undergoes considerable moment redistribution before yielding although it would be designed for zero redistribution at the ultimate limit state. If this elastic redistribution is neglected in the structural analysis, the service limit state sagging moment at midspan may end up on the unconservative side. Elastic redistribution can be predicted quite accurately with the help of nonlinear analysis or roughly with simplified idealization as proposed in this article.

Flexural behaviours of pretensioned prestressed concrete-UHDC composite beams reinforced with CFRP bars

Prestressing fiber reinforced polymer (FRP) bars is widely acknowledged as an effective method for exploiting their high strength. However, compared to FRP reinforced concrete structures, prestressed FRP reinforced concrete structures exhibit weaker deformation capacity. To address this issue, ultra-high ductile concrete (UHDC) was employed to enhance the flexural behaviours of pretensioned prestressed concrete (PPC) beams reinforced with carbon fiber reinforced polymer (CFRP) bars, while additional aluminium alloy ribs (ARs) were utilized to ensure proper anchorage. A total of eight beams were designed and tested, consisting of four PPC beams and four PPC-UHDC composite beams, which featured different types of CFRP bars, reinforcement ratios and UHDC placement. The test results revealed that the CFRP-reinforced PPC-UHDC composite beams exhibited significantly improved flexural performance in terms of cracking load, ultimate load and ultimate displacement. For specimens with lower reinforcement ratio, the UHDC effectively controlled the cracks and promoted uniform strain in the CFRP bars, leading to increased ultimate load capacity and ultimate displacement. For specimens with higher reinforcement ratios, the flexural performance was comprehensively improved when the UHDC was placed in the compression zone. Numerical analysis was conducted to further investigate the flexural behaviours of PPC-UHDC composite beams under various conditions.

A novel smart steel strand based on optical-electrical co-sensing for full-process and full-scale monitoring of prestressing concrete structures

ABSTRACT As the main load bearing component, the steel strand has a significant impact on the safety of civil infrastructure. Real-time monitoring of steel strand stress distribution throughout the damage process is an important aspect of civil infrastructure health assessment. Hence, this study proposes an optical-electrical co-sensing (OECS) smart steel strand with the DOFS and CCFPI embedded in. It can simultaneously measure small strains in the initial damage phase with high accuracy and obtain information in the large deformation phase with relatively low precision. Several experiments were carried out to test its sensing performance. It shows both DOFS and CCFPI have good linearity, repeatability and hysteresis. In comparison to DOFS, CCFPI has a relatively lower accuracy and resolution, but a large enough measurement range to tolerate the large strain in the event of a steel strand failure. To verify the reliability of the proposed smart steel strand in real structures, the strand strain distribution in the full damage process of bonded prestressed beams under four-point bending loading was monitored using the smart steel strand as a prestressing tendon. The strain measured by the OECS steel strand is shown to reflect the deformation and stiffness variation of prestressed beams under different load.

Numerical Investigation of Flexural Behavior of Reinforced Concrete (RC) T-Beams Strengthened with Pre-Stressed Iron-Based (FeMnSiCrNi) Shape Memory Alloy Bars

Shape memory alloy (SMA) is a material that can change shape in response to external stimuli such as temperature, stress, or magnetic fields. SMA types include nitinol (nickel-titanium), copper-aluminum-nickel, copper-zinc-aluminum, iron-manganese-silicon, and various nickel-titanium-X alloys, each exhibiting unique shape memory properties for different applications. Reinforced concrete (RC) T-beams strengthened and pre-stressed with Fe-SMA bars are numerically investigated for their flexural response under the influence of various parameters. The bars are embedded in a concrete layer attached to the beam’s soffit. Based on the numerical results, it was found that increasing the compression strength from 30 to 60 MPa slightly improves the beam’s strength (by 2%), but it significantly increases its ductility by approximately 45%. As opposed to this, the strength and ductility of the pre-stressed T-beam are considerably improved by using a larger diameter of Fe-SMA bars. Specifically, using 12 mm Fe-SMA bar over 6 mm resulted in 65% and 47% greater strength and ductility, respectively. Furthermore, this study examines the importance of considering the flange in the flexural design of pre-stressed beams. It is seen that considering a 500 mm flange width enhanced the ductility by 25% compared to the rectangular-section beam. The authors recommend further experimental work to validate and supplement the calculations and methodology used in the current numerical analysis.

Evaluation of experimental techniques for performance estimation of post-tensioned concrete beams

Structural health monitoring (SHM) techniques have become a significant subject in structural evaluation due to the development of non-destructive methods used to monitor and assess the integrity of structures. This paper aims to investigate the effect of damage on the flexural performance indicators and dynamic characteristics of post-tensioned concrete (PC) beams, using both static and vibration tests. The beams were tested at several load levels to reproduce different load stages of a PC member: pre-cracking, during and after the formation of initial cracks, and finally, during and after the formation of larger significant cracks. The performance of the elements is evaluated based on static data, energy calculations, and the three criteria of ACI 437 recommendations. Data from the vibration tests were used to identify the changes in modal parameters after different load levels. Acoustic emission data analysis and results were used to classify the level of damage. Experimental bending stiffness and crack length determination via visual inspection was used as control parameters to assess the deterioration levels of the beams. The outcomes of this study show the relationship level among the different experimental responses obtained: flexural performances, the presence of damage in the beams, and natural frequencies. By considering the relationships of the SHM techniques and their individual findings, the evaluation of performance indicators or damage classification in rectangular concrete prestressed beams reveals that the main limitation is the required knowledge about the previous response of the system.

A Novel Smart CFRP Cable Based on Optical Electrical Co-Sensing for Full-Process Prestress Monitoring of Structures.

Carbon-fiber-reinforced polymer (CFRP) is a type of composite material with many superior performances, such as high tensile strength, light weight, corrosion resistance, good fatigue, and creep performance. As a result, CFRP cables have great potential to replace steel cables in prestressed concrete structures. However, the technology to monitor the stress state in real-time throughout the entire life cycle is very important in the application of CFRP cables. Therefore, an optical-electrical co-sensing CFRP cable (OECSCFRP cable) was designed and manufactured in this paper. Firstly, a brief description is outlined for the production technology of the CFRP-DOFS bar, CFRP-CCFPI bar, and CFRP cable anchorage technology. Subsequently, the sensing and mechanical properties of the OECS-CFRP cable were characterized by serious experiments. Finally, the OECS-CFRP cable was used for the prestress monitoring of an unbonded prestressed RC beam to verify the feasibility of the actual structure. The results show that the main static performance indexes of DOFS and CCFPI meet the requirements of civil engineering. In the loading test of the prestressed beam, the OECS-CFRP cable can effectively monitor the cable force and the midspan defection of the beam so as to obtain the stiffness degradation of the prestressed beam under different loads.

Arch Action Model for the structural assessment of existing prestressed concrete bridges

AbstractStructural assessments of existing older prestressed concrete bridges according to the currently applicable standards and guidelines in Germany generally reveal significant deficiencies in shear reinforcement. Large‐scale tests within the scope of research activities commissioned by the Federal Highway Research Institute (BASt) were carried out at TU Dortmund University to analyze the shear load‐bearing behavior of continuous prestressed concrete beams in more detail. The Arch Action Model (AAM) was derived from the Simplified Arch Action Model (SAAM) to provide a possible analysis method for determining shear contribution from concrete. Thus, the shear capacity of prestressed beams can be determined in a more realistic manner than using the truss model underlying the current state of standardization. The paper at hand provides information and explanations about the SAAM and AAM with regard to their application to real‐world structures for structural bridge assessments.

Numerical analysis of bonded and unbonded prestressed RC beams using cohesive and non-compatible rod elements

This research presents a numerical approach to simulate prestressed RC beams. It combines state-of-the-art finite element models to simulate the concrete (including fracture), tendons, passive reinforcements, and the rebar–concrete interaction. This provides more realistic simulations and rich details on deformability, crack patterns, and axial and contact stress distributions in passive reinforcements and tendons. Concrete fracture is simulated using cohesive elements with a constitutive model based on the plasticity theory and fracture mechanics, enabling crack development and propagation prediction. Reinforcements are simulated using rod elements with incompatible nodes. Special contact elements link rod to bulk elements and are placed along the reinforcements and at tips. These contact elements also predict relative displacements between rebars and concrete. Prestressing is simulated by setting initial stresses in tendons and applying forces to its nodes simultaneously. The approach also includes two numerical techniques to improve the convergence of the highly nonlinear problem. Five experimental beams are simulated. In all cases, the numerical load–deflection curves agree with the experiments. Fracture patterns also match rupture modes. Finally, contact stress discontinuities in tendons due to crack development are examined in more detail.