Prestress Level Research Articles

Experimental and numerical studies on low velocity impact behaviors of curved prestressed concrete shells

This study investigates the behavior of curved prestressed concrete (CPC) shells under low-velocity impact loads. The dynamic response of CPC shells under impact loading was studied by conducting impact tests and numerical simulations, with the impact process divided into three stages. The failure modes, impact force, displacement response, and energy dissipation of the specimens were analyzed to reveal the effects of prestress level, curvature, and initial impact momentum on the impact performance of CPC shells. Shear and flexural failure modes were observed in the six specimens under impact loading, along with three types of local damage: concrete indentation, crushing, and spalling. As curvature decreases, the failure mode transitions from shear to flexural failure. However, the prestress level and impact momentum did not change the failure mode of the specimens. Prestress induced both pressure strengthening and flexural weakening effects on the specimens, which collectively influenced their impact performance. Additionally, it was observed that prestress and curvature interactively affect the impact performance of the specimens. Furthermore, under higher initial impact momentum, the CPC shell experienced more severe shear damage.

Experimental Study on Seismic Behavior of a New Separately‐Anchored Self‐Centering Beam‐Column Connection

ABSTRACTPost‐tensioned self‐centering (PTSC) structures that use PT tendons to assemble precast members and provide structural resistance have demonstrated superior seismic performance and self‐centering capacity. Current PTSC frames generally serially connect all beams in a floor. This assembly method would induce interferences among different spans and increase the risk of progressive failure once local damage occurs in a bay. This paper proposes a new type of PTSC joint to avoid such serial connection of beams. By employing steel beams to serve as the anchorages of PT tendons, each bay of the frame is separately prestressed. The composite prestressed beams can be readily fixed to columns by high‐strength bolts, hence facilitating the construction of such separately‐anchored self‐centering (SASC) frame building. External friction dampers are installed to enhance the energy dissipation capacity of SASC connections. Eight full‐scale cyclic loading tests are performed to compare the performance of the new SASC connections with conventional PTSC joints and also comprehensively evaluate the seismic behavior of SASC connections with different parameters. The test results validate the excellent damage mitigation abilities of both types of connections while the superior mechanical performance of the new SASC connections. In addition, the effects of key design parameters such as initial prestress level, damper force, and tendon number on the seismic behavior of the SASC connection are evaluated, and design recommendations for the application of the proposed precast beam‐column connection are also provided.

Shear Behaviour of the Post-tensioned Segmental Precast Concrete Pontoon Deck with the GFRP Rods

The present experimental and numerical study evaluated the structural performance of segmental concrete pontoon decks reinforced and post-tensioned with GFRP rods. Four large-scale decks were tested and the load-displacement response, strain behaviour of rods, concrete, and failure mechanism in four different prestressing levels were assessed. It was found that a small post-tensioning of 7.4% of the rod's ultimate tensile strength reduced the self-weight deflection by 92% and increased initial stiffness by 8.7 times compared to segmental decks without prestressing. Failure in prestressing decks typically began with concrete crushing at the joint with an increased compression depth due to increased initial post-tension; however, the ultimate failure mechanism of the hand-tight deck was governed by the interlaminar shear of the rod. A finite element model was developed and verified against test results A parametric study evaluating the influence of the post-tensioning at higher load, rod depth, concrete properties, rod number, and deck geometry was implemented. It was shown that increasing the post-tension load and depth of the rod improved the stiffness and reducing the spacing can result in a more uniform compression stress in the joint. This study provides design recommendations for ACI 440.4 R-04, by considering the concrete compression depth between joints rather than the depth of the FRP rod and contributes to a more accurate load estimation of the concrete crushing caused by joint openings. The results of this research could rectify the present problems with the construction design of maritime infrastructure and offer an innovative solution.

Effect of high-strength SCC with and without steel fibres on the shear behaviour of dry joints in PCSBs

The structural behaviour of precast concrete segmental bridges (PCSBs) heavily relies on the strength of the joints between segments. Multi-keyed dry joints are currently the most commonly used solution in these discontinuity zones. Employing high-strength concrete is becoming increasingly common in civil engineering given its higher strength and improved durability. It specifically allows higher prestressing levels in PCSBs. Using self-compacting concrete enhances workability and adding steel fibres improves mechanical properties. The existing scientific literature includes experimental tests to analyse the shear behaviour of castellated dry joints in different concrete types. However, no experimental tests appear specifically for the castellated dry joints made with high-strength self-compacting concrete (HS-SCC) with and without steel fibres. Therefore, this experimental study conducted 31 push-off-type tests to analyse the behaviour and shear capacity of dry joints made of HS-SCC by investigating the influence of adding steel fibres to the concrete mix. The study examined crack patterns, load-displacement behaviour, failure modes and different (cracking, ultimate and residual) loads. The addition of steel fibres improved joints’ shear capacity. However, brittle behaviour was observed after reaching ultimate load when using HS-SCC, even when steel fibres were added to the concrete mix. Finally, the adequacy of existing formulations was analysed. Standard AASHTO proved to be on the unsafe side for the castellated dry joints specimens made of HS-SCC without steel fibres, and provided a good approximation for the specimens with steel fibres.

A flexibility approach for geometric nonlinear static analysis of guyed masts

The present study proposes a novel flexibility-based approach for the large displacement analysis of guyed masts. The guyed mast is modeled as an equivalent beam–column supported by catenary cables, and the exact force–displacement relations of sagging cables and slender beam–column are accounted for with sufficient rigor. The proposed method starts with formulating two mutually exclusive sets of second-order force–displacement equations, one for the mast and the other for the cables. Flexibility matrices are derived in an incremental form for an Euler–Bernoulli beam–column using the well-known Variational Iteration Method (VIM). Since an exact Lagrangian multiplier is used in the correction functional, the displacements obtained from this numerical method are also exact. The cable behavior is studied using Irvine’s model, which is the most accurate and realistic one since it represents the equilibrium configuration of the cable using a catenary curve. But, the model is non-algebraic and is unsuitable for complex structures. Hence, Irvine’s equations are recast into an incremental form to obtain exact incremental flexibility matrices. Then, displacement compatibility is re-established between the mast and the cables at their interfaces. This method can effectively address the eccentric compression on the mast shaft from the supporting guy cables, stay slackening, postbuckling of the mast, and trace the mast’s nonlinear response for large displacements. A multi-level guyed mast is analyzed to demonstrate the practical application of the proposed method. Classic examples of single-level guyed towers are used to illustrate the behavior in the postbuckling and post-slackening region. The sensitivity of a guyed mast to cable prestress levels, as well as mast shaft imperfections, are also discussed. The solved examples are also analyzed using commercial finite element software packages, and comparisons are drawn regarding their accuracy in capturing the load–deflection response under large displacements.

Carbon fiber reinforced polymer (CFRP) laminates: flexural strengthening method for prestressed concrete beams with anchorage loss

Abstract Post-tensioning (PT), a method of pre-stressing, involves the use of high-strength steel strands/ tendons to reinforce concrete or other materials. On the contrary, Carbon Fiber-Reinforced Polymers (CFRP) are lightweight, high-strength materials with used to strengthen concrete structures by adhering the polymer to the concrete element. Challenges with post-tensioned elements include reverse curvature of the post-tensioning strands, tendon misplacement, and frequent damage in the anchorage and dead-end zones. These difficulties frequently cause bulging of the surrounding concrete, even at lower stress levels, and can lead to concrete bursting when tension exceeds certain threshold. This study investigates into the potential of CFRP strengthening technique to improve the flexural capacity of post-tensioned concrete beams with anchorage loss. Through an experimental program, the study compares the performance of control beams to those reinforced with different layers of CFRP. The results of this study demonstrated that there was a significant increase in flexural capacity, ranging from 45.31% to 78.62% for single layers and 87.17% to 153% for double layers of CFRP sheet. Additionally, the research examines how different levels of prestressing and CFRP wraps influence crack formation and delamination patterns of carbon fiber, with promising results. It was also noted that optimal usage of CFRP fibers and tendons is found to be critical. The study suggests exploring alternative fiber types and orientations for future study.

Finite Element Modeling and Artificial Neural Network Analyses on the Flexural Capacity of Concrete T-Beams Reinforced with Prestressed Carbon Fiber Reinforced Polymer Strands and Non-Prestressed Steel Rebars

The use of carbon fiber reinforced polymer (CFRP) strands as prestressed reinforcement in prestressed concrete (PC) structures offers an effective solution to the corrosion issues associated with prestressed steel strands. In this study, the flexural behavior of PC beams reinforced with prestressed CFRP strands and non-prestressed steel rebars was investigated using finite element modeling (FEM) and artificial neural network (ANN) methods. First, three-dimensional nonlinear FE models were developed. The FE results indicated that the predicted failure mode, load-deflection curve, and ultimate load agreed well with the previous test results. Variations in prestress level, concrete strength, and steel reinforcement ratio shifted the failure mode from concrete crushing to CFRP strand fracture. While the ultimate load generally increased with a higher prestressed level, an excessively high prestress level reduced the ultimate load due to premature fracture of CFRP strands. An increase in concrete strength and steel reinforcement ratio also contributed to a rise in the ultimate load. Subsequently, the verified FE models were utilized to create a database for training the back propagation ANN (BP-ANN) model. The ultimate moments of the experimental specimens were predicted using the trained model. The results showed the correlation coefficients for both the training and test datasets were approximately 0.99, and the maximum error between the predicted and test ultimate moments was around 8%, demonstrating that the BP-ANN method is an effective tool for accurately predicting the ultimate capacity of this type of PC beam.

Flexural behaviour of stone slabs with prefabricated prestressed CFRP-reinforced stone strips

A strengthening technique incorporating prefabricated, prestressed, carbon-fibre-reinforced polymer (CFRP)-reinforced stone strips for stone slabs was proposed. To investigate the flexural behaviour of strengthened stone slabs, an experimental campaign consisting of 11 stone-slab specimens was conducted by considering the reinforcement ratio, the prestress level, the length of stone strip and the strengthening method as the main parameters. By installing strain gauges on the CFRP bars and stone slabs, the stress-transfer efficiency between different components of the strengthened stone slab during prestressing and strengthening processes were monitored. The results showed that the temporary device could effectively maintain the prestress imposed in the CFRP bars and transfer it to the stone slabs to be strengthened. Further four-point bending tests indicated that the prefabricated stone strips shifted the failure mode of bare stone slabs from brittle fracture to ductile, with obvious deflection and multiple flexural cracks. The load plotted against deflection responses of the strengthened slabs showed three stages, and a significant increase in the load-carrying and deformation capacities was observed when compared to those of the bare stone slabs. Finally, simplified theoretical models for predicting the flexural strength and initial stiffness of the strengthened stone slabs were proposed and assessed.

Innovative design and sensing performance of a novel large-strain sensor for prestressed FRP plates

Owing to the low measuring range of traditional fiber Bragg grating (FBG) sensors and the complexity, imprecision, and lack of practicality in existing large-strain sensors, this paper introduces a novel type of large-strain sensor based on pre-relaxation and continuous sensing technology. This design aims to realize the whole-process strain monitoring of prestressed fiber reinforced polymer (FRP) plates. Static tensile tests were conducted on 9 large-strain sensor specimens. The effects of pre-relaxation degree, section number, pre-tension time, and prestressing level were evaluated. The results reveal that, the pre-relaxed sensor, proved its efficacy in capturing the strain pertinent to the post-tensioned operational state of the FRP plate, and a sensing performance of up to 18,923 με can be facilitated and further extended by a pre-relaxation and continuous sensing technique. Moreover, it is recommended that during the fabrication of the large-strain sensor, two pre-tensions be applied, with a prestressing level between 115% and 125% of the pre-relaxation degree.

Prestressed steel wires impact on axial bearing capacity of ultra-large section jacking prestressed concrete cylinder pipe (JPCCP): Field experiment and simulation

Jacking prestressed concrete cylinder pipe (JPCCP) represents an innovative composite structure for pipe jacking applications. As a critical component of the JPCCP, the stress levels and stress loss of the prestressed steel wires significantly influence the axial bearing capacity during the jacking process, subsequently impacting the long-term safety and durability of the pipeline. This study presents a field loading experiment conducted with China’s largest JPCCP project. The results reveal tension and relaxation phenomena in the prestressed wires at various positions throughout the jacking process, and the wires’ deformation in the pipe’s central section was greater than that at the bell-spigot end. Following the initial jacking, the stress loss of the prestressed wires was the highest, with significantly reduced deformation in subsequent jacking stages, culminating in a maximum stress loss of 29.0 MPa. Utilizing ABAQUS, a numerical model of the JPCCP incorporating multiple interlayer relationships was developed and validated against experiment data. The study further analyzes the effects of steel wire spacing, prestress level, and prestress loss across different concrete layers, and examines the damage to key areas of the pipe under ultimate compression jacking. The findings indicate that the inner concrete at the spigot end is more prone to damage and yielding, predominantly due to cross-sectional mutations, additional bending moments, and tensile stresses. Based on these findings, specific design and construction proposals are proposed. This study provides an in-depth analysis of the impact of prestressed steel wires on the axial bearing capacity of ultra-large section JPCCP, offering valuable insights into its design and construction.

Evaluation of the shear behavior of RC beams strengthened with prestressing BFRP grids

The shear behavior of reinforced concrete (RC) beams strengthened with prestressing basalt-fiber-reinforced polymer (BFRP) grids was experimentally evaluated. Parameters, including grid type, concrete strength, and prestress direction and level, were numerically investigated. Equations for the shear capacity of prestressing grid-strengthened beams were derived. The results showed that using BFRP grids with a 30 % prestress level increased the number of mid-span flexural cracks in the strengthened beam but reduced their length. Compared to the control beam, the load capacity under the serviceability limit state was enhanced by 48 %. The strain responses of the grids exhibited a linear stage followed by a nonlinear stage due to diagonal cracks. The maximum strains of longitudinal and transverse grid tendons in the prestressed strengthened beam decreased by 15 % and 30 %, respectively, compared to the non-prestressed beam. The BFRP grids showed a comparable strengthening effect to low-modulus carbon-fiber-reinforced polymer grids. Increasing concrete strength greatly improved the shear capacity of RC beams. The enhancement effect was greater for transverse tendons with a 30 % prestress level than for longitudinal tendons with a 60 % prestress level. The derived equation accurately predicted shear capacities in experiments or simulations within an error range from −4.7–1 %.

Study on the performance of cast-in-situ concrete wet joints in PCSBs under cyclic loading

The closure section of precast concrete segmental bridges (PCSBs) usually adopts the wet joint, the regular longitudinal reinforcement is discontinuous, which makes the section the vulnerable part. To study the performance of the wet joint in the closure section under cyclic loading, six specimens considering loading mode, interface treatment method, setting of regular reinforcement and prestressing are tested. Results show that the damage of the wet joint accumulates and the plasticity develops under cyclic loading, the specimens undergo residual deformation, strength attenuation and stiffness degradation. Increase in prestressing level can delay the cracking, the cracking load of specimens with a prestressing level of 8MPa and 10MPa is 21.9% and 32.8% respectively higher than that of the specimen with a stress level of 6MPa, and the results also confirm that excessive prestressing level cannot significantly improve the shear strength of the specimens. When the controlled displacement is small, the residual deformation of the specimen is small and the strength attenuates slowly; with the increase in controlled displacement, the residual deformation of the specimen increases and speeds up, the strength decreases continuously, and the development of the crack tends to be stable, leading to the leveling off of degradation of the stiffness.

Analytical model for RC beams with embedded prestressed Fe-SMAs

Prestressed iron-based shape memory alloy (Fe-SMA) strengthening is an effective means to enhance the performance of reinforced concrete (RC) structures. The applied prestress level significantly influences the strengthening efficiency. However, the absence of a reliable model predicting the applied prestress hinders the efficient design of prestressed Fe-SMA strengthening solutions. To fill this gap, the current study proposes an analytical model, with which a constant zone and a transfer zone are identified in strengthened RC beams. The constant zone, with zero interfacial shear stress, sustains a constant prestress level, while the transfer zone, experiencing non-zero shear stress, gradually reduces the Fe-SMA tensile stress from the prestress level to zero. Validated through experiments, the proposed model accurately predicts the applied prestress levels and prestress-induced deflections in RC beams strengthened with Fe-SMAs and more conventional carbon fiber reinforced polymers (CFRPs). Further analysis reveals that the transfer zone length ranges from 4 to 7 characteristic lengths, and it is proportional to the logarithm of the applied prestress level. Simplifying a constant prestress level within the beam span yields sufficiently accurate prestress analysis.

Threshold Voltage Recovery Time Measurement Technique Post VTH Instability in Normally-Off p-Gate GaN High Electron Mobility Transistors

In this study, we propose a simple measurement technique to quantitatively measure the time taken by threshold voltage of normally-off p-GaN AlGaN/GaN HEMTs to recover from a nominal operational gate stress-induced instability. The proposed technique eliminates the requirement to perform a full transfer characteristic sweep post-stress, thereby eliminating the measurement-induced instability effect, often colluding precise recovery time measurement. The rate of recovery and extracted recovery times hold significance in empirically correlating the location of traps in the p-GaN or AlGaN barrier region causing VTH instability. The gate of the HEMT is stressed at nominal operational drive voltages 1.5 V, 2 V, and 4 V for various time intervals from 500 μs to 100 s, and the time taken for the drain current to recover to prestress levels measured at near-threshold voltage (~1.1 VTH) is measured as the threshold voltage recovery time. With increasing gate stress voltages, 2DEG gets trapped at relatively deeper trap energy levels at the AlGaN/GaN interface requiring more emission time during the process of recovery, mandating larger recovery times. At higher stress voltage of 4 V, the Schottky gate leakage current is high enough enabling injected holes to cross the AlGaN barrier and counter-compensate for the deeply trapped 2DEG, requiring relatively the same recovery times as lower stress voltages where the gate leakage is negligibly small. With increasing stress time, the amount of 2DEG trapped increases, requiring more recovery time to de-trap and beyond a certain time, saturation of the trap density occurs causing the recovery time to plateau.

Experimental characterization of indented dry connections for precast double‐curved concrete shells

AbstractThis paper presents the experimental validation of a connections system to connect segmented precast long‐span thin‐shell structures made with lightweight ultra‐high‐performance fiber‐reinforced concrete (UHPFRC). The work comprises the segmentation of the large‐span ultra‐thin shell to meet the requirements of prefabrication (construction and transport limitations), and the design and characterization of the connections. Once the assembling of the shell required the use of post‐tensioned unbonded prestressing, an indented dry connection was chosen. The connections are experimentally characterized with in‐plane and out‐of‐plane shear tests for different prestressing levels. The results are presented and discussed, demonstrating the balanced behavior of the indented dry connection under shear loading. The connections exhibited high ductility in shear, capitalizing on the use of a UHPFRC to fabricate the shell. The prestressing also demonstrated its efficacy, significantly enhancing both the stiffness and the capacity of the indented dry connection.

Stability Conditions and Stiffness Variability of General Tensegrity Systems with Kinematic Joints

Abstract Tensegrity systems represent promising candidate mechanisms with in-situ stiffness variability through changing the cables' prestress levels. However, prestress-based stiffness behaviors of tensegrity systems with arbitrary kinematic joints have not been analyzed systematically. This paper adopts the natural absolute coordinates for static modeling of tensegrity systems consisting of rigid members and tension elements. Then, a generic stiffness analysis method is developed to formulate the reduced-basis tangent stiffness matrix, which is found to include three parts: positive semi-definite material and geometric stiffness matrices, and an indefinite constraint stiffness matrix. Based on these findings, a systematic stability-checking procedure is derived to determine prestress and super stability, which are qualitative indicators of the softening and stiffening effects in different tensegrity systems. Then, we proceed to quantify the range of prestress-based stiffness variability by formulating semidefinite programming problems that numerically pinpoint the maximum and zero stiffness points. Furthermore, this paper reveals the composable nature of multiple self-stress states, enabling the composability of stiffness properties in mechanism designs. Several numerical examples verify the efficacy and versatility of the proposed method and demonstrate interesting stiffness behaviors of tensegrity systems with kinematic joints.

Vascular endothelial cell morphology and alignment regulate VEGF-induced endothelial nitric oxide synthase activation.

Nitric oxide (NO) production by endothelial nitric oxide synthase (eNOS) inhibits platelet and leukocyte adhesion while promoting vasorelaxation in smooth muscle cells. Dysfunctional regulation of eNOS is a hallmark of various vascular pathologies, notably atherosclerosis, often associated with areas of low shear stress on endothelial cells (ECs). While the link between EC morphology and local hemodynamics is acknowledged, the specific impact of EC morphology on eNOS regulation remains unclear. Morphological differences between elongated, aligned ECs and polygonal, randomly oriented ECs correspond to variations in focal adhesion and cytoskeletal organization, suggesting differing levels of cytoskeletal prestress. However, the functional outcomes of cytoskeletal prestress, particularly in the absence of shear stress, are not extensively studied in ECs. Some evidence suggests that elongated ECs exhibit decreased immunogenicity and enhanced NO production. This study aims to elucidate the signaling pathways governing VEGF-stimulated eNOS regulation in the aligned EC phenotype characterized by elongated and aligned cells within a monolayer. Using anisotropic topographic cues, bovine aortic endothelial cells (BAECs) were elongated and aligned, followed by VEGF treatment in the presence or absence of cytoskeletal tension inhibitors. Phosphorylation of eNOS ser1179, AKT ser437 and FAK Tyr397 in response to VEGF challenge were significantly heightened in aligned ECs compared to unaligned ECs. Moreover this response proved to be robustly tied to cytoskeletal tension as evinced by the abrogation of responses in the presence of the myosin II ATPase inhibitor, blebbistatin. Notably, this work demonstrates for the first time the reliance on FAK phosphorylation in VEGF-mediated eNOS activation and the comparatively greater contribution of the cytoskeletal machinery in propagating VEGF-eNOS signaling in aligned and elongated ECs. This research underscores the importance of utilizing appropriate vascular models in drug development and sheds light on potential mechanisms underlying vascular function and pathology that can help inform vascular graft design.

Axial stress-strain behavior of pre-stressed CFRP confined concrete columns

Bonded carbon fiber reinforced polymer (CFRP) confined concrete presents issues such as stress hysteresis and easy detachment at the interface between CFRP and concrete. Applying prestress to CFRP can improve this situation. To investigate the stress-strain behavior of prestressed CFRP strengthened plain concrete columns (PC) under axial compression, a total of 1 unreinforced concrete column, 9 bonded CFRP strengthened concrete columns, and 27 prestressed CFRP strengthened concrete columns were designed. Including CFRP layers and the level of prestress were taken as the study factors, and axial compression tests were conducted on each specimen to analyze their axial compression performance. The test results indicated that applying prestress to CFRP results in the core concrete being constantly subjected to triaxial compression, with initial transverse compressive strain and longitudinal tensile strain, thereby increasing the initial stiffness of the core concrete. In contrast to bonded CFRP-strengthened columns, the ultimate axial stress, ultimate axial strain, and initial stiffness of prestressed CFRP-strengthened columns increased with the level of CFRP prestress, with a more pronounced improvement observed in columns wrapped with a higher number of layers of CFRP. For a 4-layer CFRP strengthened column prestressed at 0.3, the ultimate axial stress and ultimate axial strain increased by up to 13 % and 20 %, respectively, compared to bonded 4-layer CFRP strengthened columns, with the initial stiffness increasing by up to 30 %. On the other hand, applying prestress to CFRP can significantly enhance the effective utilization of CFRP, but it is negatively correlated with the number of CFRP layers. Compared to bonded 1-layer CFRP strengthened columns, the effective utilization rate increased from 0.63 to 0.91, a 44 % increase, when prestressing CFRP at 0.3. Finally, based on existing relevant research, a peak stress and strain model considering the ratio of confinement stiffness to strain ratio was proposed. Based on the fundamental assumptions of curve analysis, the design-oriented axial stress-strain model suitable for prestressed CFRP strengthened concrete columns was established, with good match between theoretical and experimental curves.

Influence of the Initial Prestress Level on the Distribution of Regions of Dynamic Instability of Geiger Domes

This paper provides a parametric analysis of cable–strut tensegrity domes subjected to periodic loads. This analysis aims at determining the main regions of dynamic instability (unstable regions). From the point of view of the physical interpretation of the phenomenon, if the load occurs in these regions, the amplitudes of the resulting vibrations increase, posing a risk to the durability of the structures. The consideration includes cable–strut structures called Geiger domes. Four dome design solutions known from the literature are compared, i.e., regular (patented by Geiger) and modified domes with a closed and an open upper section. In contrast to conventional cable–strut structures, Geiger domes are characterized by a self-equilibrated system of internal forces (initial prestress), which affects the shape and range of unstable regions. The main purpose is to answer the question as to which type of design solution is more sensitive to the risk of excitation vibrations. A nondimensional parameter λ is introduced for this quantitative assessment. This parameter reliably determines the change in the area of unstable regions as the initial prestress level increases. The range of the parameter λ is defined as a value between 1 and 0. In the case of λ=1, there is potential for the excitation of unstable motion, whereas in the case of λ=0, such a risk is absent. The analysis presented in this paper can be employed in the process of optimizing the initial prestress level, which will constitute the subsequent stage of this research. A geometrically non-linear model is used to evaluate the behavior of the considered structures.

Fast fracture in toughened glass when impacted randomly by Ice

Modelling the triggering of fracture at a pre-existing flaw is an evolving method of predicting ultimate failure in glass. This fracture mechanics approach of modelling has been shown to give more reliable predictions than a calibrated probabilistic distribution model (as is commonly adopted) when dealing with hail impact which is highly transient in nature. The dynamic stress intensity factor controlling fast crack growth is sensitive to the complex stress state surrounding the critical flaw. Finite element simulations of localised stresses in 3D could incur high computation cost which is compounded by the need to repeat computations until convergence and to simulate multiple strikes in emulating a storm scenario. In this study, closed-form expressions were developed to waive away the need of any simulations. With hail impact, boundary conditions of the glass panel need not be factored into the modelling, as the highly transient stresses are wave controlled. Input parameters are the thickness and level of prestress in glass; offset of position of strike from the known crack and its depth; and the size, velocity, and temperature of the ice impactor. Results from 40 test scenarios involving 5 offset distances, 3 crack depths, 2 glass thicknesses, and 2 sizes of ice were used to validate the prediction, and to reveal the sensitivity of the outcome of the impact to changes in the impact position relative to the known crack.