Post-tensioned Steel Research Articles

Self-centering rocking steel frame with column mid-height uplift: Experimental and numerical investigation

This paper proposes a self-centering rocking steel frame with column mid-height uplift (SCRSF-CMU) that exhibits high post-yield stiffness and energy dissipation capacity. The hysteretic performance of the SCRSF-CMU was investigated through cyclic loading tests. A numerical model of the SCRSF-CMU was established and validated against experimental results. Subsequently, the seismic performance of the SCRSF-CMU was compared with that of the self-centering rocking steel frame with column base uplift (SCRSF-CBU) using nonlinear time history analysis. Finally, the seismic responses of the SCRSF-CMU and SCRSF-CBU under varying earthquake intensities were analyzed using the endurance time analysis. The results indicate that the designed SCRSF-CMU demonstrates excellent lateral force resistance, energy dissipation, and self-centering capabilities. The rocking effect and the restoring force of the post-tensioned steel strands effectively controlled the residual lateral displacement of the specimens. The multi-scale numerical model of the SCRSF-CMU accurately captured its hysteretic behavior and deformation patterns. Compared to the SCRSF-CBU, the SCRSF-CMU exhibited superior rocking deformation capacity, post-yield stiffness, and hysteretic energy dissipation. Under MCE excitation, both SCRSF-CMU and SCRSF-CBU showed uniform inter-story drift distribution with minimal residual deformation, creating a satisfactory condition for the post-earthquake repair work if necessary. The high post-yield stiffness of the SCRSF-CMU was more effective in reducing both maximum and residual displacements. Endurance time analysis revealed that SCRSF-CMU and SCRSF-CBU exhibited relatively uniform inter-story drift distribution under SLE, DBE, and MCE earthquakes. Under FE excitation, the inter-story drift ratio of both structures were nearly identical; however, under DBE and MCE excitations, the maximum roof drift ratio and inter-story drift ratio of the SCRSF-CBU were larger, indicating that the SCRSF-CBU had higher deformation demands than the SCRSF-CMU.

Shear Strengthening of RC Beams Incorporating Post-Tensioned Bars and Engineered Cementitious Composite Reinforced with Palm Fronds

This paper investigates, experimentally and numerically, the shear strengthening of Normal Concrete (NC) beams using post-tensioning steel bars and Engineered Cementitious Composite (ECC) reinforced with chemically cured Palm Fronds (PFs). The benefits of strain-hardening ECC and the tensile strength of PFs cured with 6% wt Alkali NaOH solution beside post-tensioned bars have been employed herein. Seven full-scale Reinforced Concrete (RC) beams were fabricated and experimented with under three-point loading until failure. The test parameters include the strengthening technique, type, and configuration of the material used for strengthening. The strengthening process has been implemented through two techniques: Externally Bonded Reinforcement (EBR) and Near-Surface Mounted (NSM) Reinforcement. The strengthening materials have been configured and placed in horizontal, vertical, and inclined positions. The effectiveness of the strengthening methods has been evaluated by examining their cracking propagations, load-deflection responses, collapse modes, elastic stiffness, and absorbed energy. It was found that the proposed strengthening systems could significantly control the crack pattern and failure mode, and they could enhance the ultimate load amplitude up to 37% and 50% for NSM ECC with PFs and EBR post-tensioning steel bars, respectively. Nonlinear three-dimensional finite element models of the tested beams were developed and validated with the test data, where it was found that finite element models predict the structural performance of tested beams with a maximum error of only 2%.

Seismic behavior of hybrid post-tensioned special steel moment frames

Generally, conventional moment-resisting frames are prone to substantial residual displacements. To overcome this disadvantage, self-centering systems were introduced. Post-tensioned self-centering (PTSC) moment-resisting systems are a variation of conventional moment-resisting systems that drastically reduce the large residual displacements of the moment frames. However, one of the uncommon drawbacks identified in PTSC systems is their low energy dissipation. This study aims to compensate for this by innovatively combining conventional self-centering systems with special moment-resisting frames (SMRF) in various formats to retain the advantages of both systems. Another disadvantage of PTSC systems is the high cost and complexity of the structural design procedure required to maintain an elastic response in the framing beam-column elements. To address this issue, a practical and cost-effective design procedure was proposed. The study also included the influence of different dual SMRF-PTSC frame actions and base column connection types. A set of 35 structures comprising 4, 8, 12, and 16-story buildings were considered for nonlinear static/dynamic analysis and seismic response assessment. The nonlinear static analyses were carried out in a cyclic format due to the self-centering characteristics of the system. Additionally, 22 far-field records per FEMA P695 were chosen for the time history analyses. The results show that structures equipped with post-tensioned self-centering connections (PTSC) designed according to the proposed procedure are successful in drastically decreasing residual drifts. However, the total elimination of residual drifts relies on providing a self-centering connection for the base level columns and considering an overstrength factor for the base level columns' moment capacity design. The proposed value in this investigation was derived as 5, which significantly strengthens the base level columns while resulting in an overall notably cost-efficient PTSC-equipped frame. In the case of dual frames, the conventional SMRF spans should not exceed the number of PTSC-equipped spans, as doing so will diminish the self-centering characteristics of the lateral system.

Seismic performance of friction damped posttensioned steel frame equipped with SMA strands

The post-tensioned friction dissipating (PTFD) connection for steel frames has drawn significant attention from researchers due to its excellent seismic performance. A simplified numerical algorithm suitable for modeling the SMA strands is proposed. The simplified numerical model of the SMA-PTFD is established. Parametric analysis is performed based on hysteresis analysis and transient dynamic analysis to reveal the influence of SMA strands on the seismic performance of SMA-PTFD frames. The changing rule of seismic response of SMA-PTFD frames, along with the fmax for SMA strands and the Fmax for the friction device, is systematically investigated. The value of the objective function can be reduced by about 50 % when the fmax is increased from 1 kN to 13 kN. The fundamental frequency is 1.25 Hz for three analyzed conditions. The value of the second frequency is significantly affected by Fmax. The values of the second frequency are 1.5 Hz, 1.58 Hz, and 1.42 Hz. The characteristics of seismic response, including displacement and cable force, are deeply studied. The seismic response is also investigated in the frequency domain. The results presented in this work reveal the collaborative energy dissipation mechanism of the friction device and SMA strands.

Corrosion-induced fragility of existing prestressed concrete girder bridges under traffic loads

Italian and European transportation networks include a significant number of existing bridges, built since the early ‘60s, characterised by simply supported prestressed concrete (PC) girders with post-tensioned steel tendons. Corrosion of tendons, which may lead to significant loss of structural capacity, cannot be detected by simple visual inspections and requires advanced and expensive testing by bridge owners. Therefore, procedures aimed at risk-informed prioritisation of advanced inspections and possibly retrofit are needed. The paper presents a study on the fragility of existing PC girder bridges considering traffic loads, accounting for corrosion-induced effects. An automated framework is proposed, aiming at the efficient probabilistic structural assessment of the investigated bridge typology accounting for different critical corrosion scenarios and the influence of knowledge-based uncertainty related to geometric and mechanical properties. To simulate corrosion effects, prestressing steel tendon geometric and mechanical characteristics are modified through a specific algorithm able to estimate variations in flexural and shear bearing capacity of critical cross-sections. To simulate the traffic loads, a simplified analysis is performed by using code-based traffic load models. In the paper, the framework is tested with reference to a dataset of case-study superstructures. The obtained fragility curves are deeply discussed, highlighting the effects of the number of girders and span length on the corrosion-induced increase in fragility. Although the proposed methodology presents some simplifications, it could improve the current practices of risk prioritisation, by supporting transportation authorities in ensuring the safety of the existing bridge stock.

Experimental research on seismic performance of dry-wet combined precast concrete beam-to-column connections

In order to enhance on-site assembly efficiency and construction organization flexibility, a new type of dry-wet combined precast concrete beam-column connection was proposed. The prefabricated beams and columns were joined together using local post-tensioned tendons to create a temporary frame structure with dry connections. Subsequently, the wet connections between the prefabricated beams and slabs were established by pouring cast-in-place top concrete. A monolithic connection and four full-scale precast connections were subjected to reversal cyclic loading, with each designed incorporating distinct types of post-tensioned (PT) tendons, bonding conditions, and grouting materials. The test results indicate that the new connection exhibits flexural failure at the beam ends. In comparison to cast-in-place connections, it demonstrates enhanced deformation capacity, comparable ductility, higher stiffness, and reduced energy dissipation due to slippage of the PT tendons and steel bars. However, the viscous damping exceeds 15 %, thereby satisfying the seismic resistance requirements. The high-strength mortar grouting material satisfactorily fulfills the anchoring requirements of steel bars within the corrugated steel ducts, whereas the prestressed grouting material falls short in this regard. The overall performance of the new connection can be further enhanced by improving the grouting material and implementing local unbonded measures.

Investigating the seismic performance and developing the fragility curves of self-centering steel frames with augmented nonlinear viscous damping: A numerical simulation

This paper focuses on investigating the seismic performance of post-tensioned steel frames equipped with nonlinear viscous dampers. The aim is to increase the ductility and seismic energy dissipation capacity of these structures. Finite element (FE) models were created using the Abaqus software and validated against reference experimental data under cyclic loading. Two types of post-tensioned moment-resisting frames (PT-Frames) were developed: a conventional PT-Frame and a PT-Frame with two pairs of nonlinear viscous dampers acting as knee braces (each brace pair, contains two dampers connected in parallel, thus there are 4 dampers used in total). Various analyses, including modal analysis, cyclic loading, and incremental dynamic analysis (IDA), were conducted using earthquake records mentioned in FEMA P-695. Fragility curves were plotted based on the IDA results. The findings indicate that the augmented nonlinear viscous damping significantly increases the natural fundamental period of vibration in PT-Frames (133 % increase observed). It also enhances the absorption and dissipation of input seismic energy (800 % increase in cumulative dissipated seismic energy observed). Moreover, it reduces the probability of damage exceeding the damage index value for different performance levels (collapse prevention, life safety, and immediate occupancy) by average values of 115 %, 61.72 %, and 25.126 %, respectively. These improvements help mitigate damage to the structural components.

Removal of Support or Pier Without Jacks: Jimeno-Lleyda Methodology as a Derived Technology for Post-Tensioned Steel Structures

The removal of supports is a common necessity when there is a change of architectural use or a span change in a bridge. The present document proposes a simple technical solution that allows defining a procedure of cutting and bridging a support without the use of jacks. From this method statement, a post-tensioning technology for steel structures is derived.

Hybrid-self-centring steel frames: Insights and probabilistic seismic assessment

This paper comprehensively discusses the seismic performance of steel moment-resisting frames with hybrid-self-centring connections (SMRF-HSCC) employing energy dissipation sequences by probabilistic seismic assessment. The hysteretic model of the HSCC was first developed based on experimental results, and a simplified nonlinear-spring-based model to simulate the behaviour of the connection was proposed and verified by physical test data. A series of codified prototype structures were developed, considering the fracture behaviour of post-tensioned (PT) steel strands in the connections. The seismic performance of prototype structures was assessed in terms of nonlinear static analyses and nonlinear dynamic analyses. The results indicated that the hysteretic response of SMRF-HSCC exhibited trilinear hysteretic features with the expected energy dissipation sequences. The influence of the high-mode effects on SMRF-HSCC was mitigated with the increase in energy dissipation and post-yield stiffness of the structure. Finally, the fragility analyses of the prototype structures were further performed, and the risk assessment was also made considering a 50-year service period. The collapse probability and the exceedance probability of target residual drift over a 50-year service period of SMRF with conventional self-centring connections showing flag-shaped hysteresis were higher than that of SMRF-HSCCs. The results also confirmed that the collapse probability and exceedance probability of target residual drift over a 50-year service period of SMRF-HSCC can be adjusted by reasonably modulating the arrangement of the HSCCs.

Post-tensioned steel beam-column connections with reduced length BFRP tendons

The seismic behavior of the traditional top and seat angle beam-column connection was experimentally evaluated using a half-scaled prefabricated exterior beam-column connection subassembly. Then, an ensemble of three post-tensioned beam-column connections using reduced length basalt fiber reinforced polymer (BFRP) tendons was tested with three different tendons' post-tension (PT) force levels of 15.9, 30, and 50% of the tendons' ultimate strength. Following that, another group of three additional subassemblies containing both reduced length BFRP tendons, as post-tensioning devices, and top and seat angles, as energy dissipation (ED) devices, was tested with the same three post-tension force levels used in the previously tested group. Finally, an analytical model was proposed to capture the moment-relative rotation response of the traditional top and seat angle and the connection combining both the top and seat angles and the BFRP tendons. The results showed that connections containing BFRP tendons only, with the lowest PT force level, provided the same envelope of the top and seat angle connection, and further enhancement could be achieved by increasing the PT force level. Also, the addition of the BFRP tendons to top and seat angle connection improved the connection strength, initial stiffness, post-yield stiffness, and reduced the residual drift. In addition, the proposed analytical model predicted the moment-relative response well, which ensures the reliability of the model in designing such connections.

Experimental investigation of self-centering beam-to-column connections with different ribbed top and seat angles

This study experimentally investigated the seismic behavior of a novel self-centering beam-to-column connection with the different ribbed top and seat angles. The connections were composed of square concrete filled steel tubular (CFST) column, H-shaped steel beam, angles with or without stiffening rib, and post-tensioned (PT) high-strength steel tendons. Eight half-scale specimens were designed and tested under cyclic loading. The influences of stiffening rib type including plane rib and multi-wave rib, PT tendon distance, and with or without PT tendons upon the performance of the connection were evaluated experimentally. The results show that the connections installed PT tendons exhibited the double linear hysteretic feature with a slight narrow hysteretic loop due to the friction of the components, the connections assembled the angles or ribbed angles took on the fuller and more stable hysteretic loop, and the connections installed the PT tendons and ribbed angles exhibited the double-flag shaped hysteretic curve. The employment of plane or multi-wave ribbed angles significantly increased the initial rotational stiffness and ultimate moment. For the connection combined the PT tendons and ribbed angles, the average residual rotation angle ratio and the maximum equivalent viscous damping ratio reached about 0.095 and 0.07 at the drift ratio of 2%, respectively. The distance of PT tendons did not affect the hysteretic behavior of the connection. The PT tendons could provide the excellent self-centering behavior of the connection.

Corrosion effects on strands of PT bridges

In recent years, partial failures and collapses involving existing Post – Tensioned (PT) bridges highlighted the need for their structural assessment. Most of existing bridges are approaching the end of their nominal life and constitutive materials have undergone, over the decades, relevant degradation phenomena with dangerous consequences at both local and global level. A good knowledge of material properties, structural details and of the actual maintenance condition of the bridge is then required, especially if we consider that hidden defects – i.e. defects that are not visible without specific investigations – can be responsible of the activation of unexpected brittle failures. Corrosion of prestressing steel cables represents one of the most relevant aspect to investigate, being related to phenomena (such as localized pitting or hydrogen embrittlement) that cannot be detected without specific investigation techniques but that are responsible for relevant decrease of the mechanical properties of materials and modification of the failure modality. Predictive models calibrated basing on experimental results, may represent in presence of aggressive environmental conditions may represent an efficient tool for describing corrosion effects on the mechanical properties of strands and evaluating residual performance.The present work shows preliminary results of a wide experimental test campaign executed on corroded steel strands extracted from an existing prestressed concrete bridge with post-tensioned steel cables; hydrogen embrittlement effects are well visible on the mechanical properties of corroded strands. The peculiarity of the work lies in the availability of naturally corroded strands, with well-known external agents (rain, air, etc.) and exposure period. Preliminary results of FEM analyses on models calibrated basing on experimental tests’ results are even presented.

Experimental investigation of bearing capacity of 3D printed concrete segmental girder

3D concrete printing (3DCP) technology represents a new approach to producing contemporary concrete structures. The application of sophisticated equipment such as a 3D printer has brought numerous advantages, which were noted through significant practical application. Currently, 3DCP technology is being developed in two main directions: on-site production of entire structures and prefabricated construction. However, 3DCP technology has not yet reached its full potential in prefabrication as the connections between individual segments and their capacities under horizontal and vertical loads, have not yet been extensively investigated. This paper focuses on the experimental testing of the bearing capacity of a beam constructed by connecting individual segments of 3D printed concrete. The segments are connected using post-tensioning steel bars. The experimental program included testing a single segment as well as a segmental girder in a 3-point test. In the case of the individual segment, failure occurred due to the loss of tensile capacity of the concrete. For the segmental beam, failure occurred when the shear capacity was reached. Shear fracture was accompanied by diagonal cracks extending from the point of force application towards the beam supports.

Lateral Load Behavior of Self-centering Frame with Y-Eccentrically Braced Substructure: An Experiment and Numerical Analysis

A novel self-centering frame with Y-eccentrically braced structure (SC-YEBFs) has been proposed in this paper to solve the problem that the storey drift of structure may exceed the specified limit in standards when self-centering beam-column joints are applied in high-rise and larger spans buildings, and the SC-YEBFs not only has the self-centering performance of self-centering frame system, but also has the high lateral stiffness and energy dissipating capacity of Y-Eccentrically braced frame. To study the lateral load behavior and influencing factors of SC-YEBFs, cyclic loading tests of two scaled specimens of SC-YEBFs substructure (SCS) were conducted, and seven finite element models corrected by the experiment were established to perform parametric analysis. The experiment and finite element analysis results indicated that the shear link has greatly increased the lateral stiffness and energy dissipating capacity of the self-centering structure, at the same time, it has maintained a good self-centering performance and replace ability. With an increase in the cross-sectional area and initial prestress of post-tensioned steel strands, the lateral load capacity and self-centering performance can be improved. The self-centering performance can be effectively improved by reducing the friction coefficient at the rotation connections. SC-YEBFs further extending the application field of self-centering structural systems, and making it possible to be applied to high-rise and larger spans structures.

Analytical investigation of multi-joint rotation behavior of PTPS-CFDST column under lateral loading

The post-tensioned precast segmental concrete-filled double-skin steel tube (PTPS-CFDST) column is an innovative composite column that has recently been proposed and verified to exhibit excellent seismic resilience performance, being a promising solution for low-damage seismic design in accelerated bridge construction. Under lateral loading, this type of new column behaves with multiple joint rotations with laterally unconstrained post-tensioned (PT) tendons, which cannot be accurately predicted by the existing analytical models. This study firstly presents a new multi-joint rotation analytical model for the PTPS-CFDST column under lateral push-over loading, with the positional influence of PT tendons considered. The proposed model is then validated against experimental and numerical results, demonstrating its accurate prediction of lateral force capacity, global column deformation, and local joint openings. In addition, a comparison between the one-, two- and three-joint analytical models is conducted, and the results reveal that the two- and three-joint analytical models achieve accurate results. Finally, parametric studies considering the initial prestressing force, thickness of steel tube and hollow ratio are performed, which further validates the accuracy, applicability, and versatility of the proposed model. This research enhances the analytical understanding of the multi-joint rotation behavior of the PTPS-CFDST column, which may provide references for the seismic design of this new type of column.

Experimental Study on Behavior of Precast UHPC Beam-Column Joints Subjected to Cyclic Loading

Ultra-performance concrete (UHPC) is a new material with many outstanding features such as compressive and tensile strength that are both very high compared to conventional concrete. In precast reinforced concrete structures, the beam-column joint is one of the most important parts. In this type of connection, the beam is connected to the column through post-tensioned prestressing steel bars (PC bars), making the connection resistant to bending moments as well as shear forces. This paper presents the behavior of this type of connection under the effect of seismic loads on the following criteria: flexural resistance, moment-rotational relationship, change of PC bars’ prestress during and after cyclic loading.

Collapse performance of post-tensioned steel frames considering influence of infill walls

The aim of this paper is to study the effect of infill walls on load resisting behaviors of post-tensioned (PT) steel frames against collapse. Three planar PT steel frames are simulated using finite element (FE) method, one of which has no infill wall while the other two are installed with infill walls. The applied loads, lateral displacements, failure patterns, stress developments in infill walls, resisting mechanisms, as well as re-centering capabilities of three PT steel frames are studied and the role that infill walls play is discussed. Parametric analyses are conducted to investigate influences of magnitude of PT forces and critical material properties. Results indicate that infill walls work as compressive struts, significantly increasing initial stiffness, resistance and story drifts of PT steel frames, and play as energy dissipation devices during the collapse process. The existence of opening makes the stiffness distributed discontinuously throughout infill walls, greatly changing the failure pattern and increasing story drifts of PT frames. The resistances of infilled PT steel frames increase with increasing PT forces, bed joints strength and masonry unit strength in the initial stage. A design scheme is also developed to precisely predict the collapse resistance of infilled PT steel frame structures.

Performance assessment of post-tensioned concrete-filled steel tube beams using unbonded tendons with uncertainty quantification

The centerpiece of many research projects is evaluating the structural performance of the concrete-filled steel tubes (CFSTs). When these structural elements are employed as flexural members, some parts of the concrete infill are subjected to tension, and consequently the concrete is cracked so that the confinement effect is reduced. Therefore, the application of tendons and modification of the CFST configuration are deployed to improve the serviceability of the CFST beams. A non-linear finite element (FE) model considering the effects of the material and geometrical non-linearity and initial imperfection is developed. Concurrently, an analytical model based on the plastic stress distribution method (PSDM) is proposed to compare the results. In addition, a probabilistic assessment along with the uncertainty quantification is conducted to calculate the reliability indices and the sensitivity of the beams to the variation of the input variables. The results of the study demonstrate that the implemented measures considerably enhance the moment capacity and serviceability performance of the CFST beams. Moreover, the sensitivity analyses show the significance of the variables on the model output with different steel yield stress values and the importance is ordered as the steel tube width followed by the steel tube thickness and the concrete strength.

Reliability-based design optimization of post-tensioned self-centering rocking steel frame structures

This paper reports the Reliability-Based Design Optimization (RBDO) of post-tensioned self-centering rocking steel frame structures with buckling-restrained bracing systems. The objective was to investigate the reliability index, optimization of self-centering structures to reach minimum weight using metaheuristic algorithms, and their application in linear and nonlinear reliability problems. For this purpose, three steel structures (10-, 15-, and 20-storey structures) were each evaluated with three steel framing systems (buckling-restrained bracing, post-tensioned self-centering multiple rocking steel frame with buckling-restrained bracing, and post-tensioned self-centering single rocking steel frame with buckling-restrained bracing), making a total of nine models. Subsequently, specific 2D frames of the structural models were numerically simulated using nonlinear dynamic analysis (NDA) in OpenSees software. Optimization was carried out in two stages: with and without considering the uncertainties. Finally, for calculating the failure probability and structural reliability index, Monte-Carlo Simulation (MCS) was employed. Results indicate that, although considering the reliability index leads to heavier structures, structural safety was increased and failure probability was reduced to even lower specified levels. Furthermore, among the incorporated algorithms, the Colliding Bodies Optimization (CBO) and Charged System Search (CSS) algorithms proved to have superior performances in terms of accuracy and converging time. On average, using these two algorithms for cases without uncertainty resulted in maximum weight reductions of 36%, 30%, and 32% for 10-, 15-, and 20-storey structures. In addition, for cases with uncertainty, these two algorithms with reliability index (β) of 2 respectively reduced the weight of 10-, 15-, and 20-storey structures by 21%. Also, it was shown that not considering the uncertainties can increase the failure probability by up to 23%.

Shaking table test on seismic behavior of posttensioned precast segmental Concrete-Filled double skin steel tubular piers

Posttensioned precast segmental bridge piers have proven to be an attractive solution for accelerated bridge construction and seismic resilience. Although extensive research efforts have been made to understand the seismic performance of such piers under quasi-static loading and unidirectional/bidirectional ground motions, there is limited information available regarding to their dynamic behavior when subjected to tri-directional ground motions. Therefore, this study performed shaking table tests on an innovative posttensioned precast segmental concrete-filled double skin steel tubular (CFDST) pier to explore its seismic behavior under a set of tridirectionally applied far-field ground motions. A total of six 1/5 scaled piers were investigated with different design details, including one monolithic pier as reference, two posttensioned precast segmental piers without internal energy-dissipating (ED) bars but different amounts of prestressing tendons, and three posttensioned precast segmental piers with different amounts of ED bars. It has found that the relative displacement responses decreased with increase in amounts of prestressing tendons or ED bars. The segmental piers without ED bars twisted obviously when PGA reached 0.3 g under tri-directional ground motion excitations, while the segmental piers with ED bars did not due to additional shear resistance across joints provided by ED bars. Moreover, the dynamic responses of segmental piers with and without vertical ground motion excitation were compared in details to investigate the effect of vertical ground motion on their seismic behavior. It has found that the change in vertical acceleration response due to vertical ground motion excitation was a significant importance compared to the change in lateral accelerations, relative displacements and tendon force increment. In consequence, the axial compressive force as well as shear resistance across joint provided by dead load reduced by almost 33% due to appearance of vertical ground motion at the PGA of 0.7 g.