FRP Type Research Articles

Effect of concrete strength on the seismic performance of circular reinforced concrete columns confined by basalt and carbon fiber-reinforced polymer

This paper investigated the effect of concrete strength on the seismic performance of circular reinforced concrete (RC) columns confined by basalt and carbon fiber-reinforced polymer (BFRP and CFRP). Eight confined columns and four control columns were tested under a low cyclic lateral load. The variables in the test included concrete compressive strength (i.e., 22.4 MPa, 31.4 MPa, 42.5 MPa and 57.8 MPa) and FRP type (i.e., basalt and carbon fiber). The test results demonstrated that all the columns exhibited flexural failure after confinement. The strength, ductility and energy dissipation capacity of the confined columns were effectively enhanced. With the same confining stress, the peak loads of the BFRP- and CFRP-confined columns were nearly the same. However, the BFRP-confined columns with low and moderate concrete strength showed larger ductility and energy dissipation capacity compared with the CFRP-confined counterparts, and these capacities of the CFRP-confined column with a concrete strength of 57.8 MPa were slightly better than those of the BFRP-confined equivalent. This showed that the FRP jackets with larger modulus had better confinement effect on the columns with higher concrete strength. Finally, formulas for calculating the load carrying and ductility capacities of different FRP-confined circular RC columns were proposed based on the experimental results.

Determination of Bending Moment Resistance of L-Type Doweled Joints Reinforced With Glass-Fiber-Reinforced Polymer Woven Fabrics (GFRPWF) and Basalt-Fiber-Reinforced Polymer Woven Fabrics (BFRPWF)

In this study investigated the bending moment resistance of L-type doweled joints reinforced with glass-fiber-reinforced polymer woven fabrics (GFRPWF) and basalt-fiber-reinforced polymer woven fabrics (BFRPWF). Dowels produced from Scots pine, oak, beech and chestnut wood were used in the doweled joints. While the GFRPWF and BFRPWF were fixed with epoxy adhesive, the dowels were fixed with polyvinyl acetate (PVAc-D3/D4) glue. Test were carried out to determine the bending moment resistance of doweled joints. Experimental results showed that joints connected with oak dowel has been the highest bending moment resistance, and the joints of Scots pine dowel has been the weakest bending moment resistance. The bending moment resistance of oak dowel was approximately 23%, 33%, and 61% higher than for joints constructed with beech, Chestnut and Scots pine, respectively. The bending moment resistance value reinforced with the BFRPWF (55.62 N.m), and the lowest was in unreinforced joints (32.06 N.m). The mean bending moment resistance of reinforced joints (GFRPWF, BFRPWF) was 31% and 74% higher than unreinforced samples (control), respectively. In general, it has been found that the bending moment resistance of doweled joints is influenced by wooden dowel species and FRP types.

Advancements in the Study of FRP-Reinforced Timber Columns under Axial Compression

FRP reinforcement technology, with its numerous outstanding advantages, has been widely applied to the strengthening of timber column structures, making related research of significant social and engineering practical relevance. This paper reviews the research achievements in the axial compression performance of FRP-reinforced timber columns from both domestic and international sources. It analyzes advancements in four aspects: types of FRP, number of FRP layers, the impact of knots, and models of ultimate compressive strength and finite element models. A comprehensive analysis and comparison of existing research shortcomings and unresolved issues are provided. Finally, some references and suggestions for further research and application of FRP-reinforced timber columns are offered.

Behavior of large-scale LRS FRP-confined steel-reinforced recycled aggregate concrete square columns under axial compression

The combination of environmentally friendly large rupture strain fiber-reinforced polymers (LRS FRPs) and recycled fine and coarse aggregates presents a promising alternative to overcome the scarcity of natural river sand and natural gravels. Recycled aggregate concrete (RAC) can obtain sufficient ductility and strength by the confinement of LRS FRPs, and these two green materials are particularly suited to sustainable construction. However, existing research on LRS FRP-confined RAC is very limited and primarily focused on small-scale specimens. The objective of this paper is to investigate the axial compression performance of large-scale steel-reinforced RAC square columns wrapped with LRS FRP and promote the practical application of this sustainable structural system. The experimental variables include the effective confinement stiffness ratio (ρk,eff) and the type of LRS FRP (i.e., polyethylene naphthalate (PEN) FRP and polyethylene terephthalate (PET) FRP). Test results showed that the application of RAC had a negligible effect on the axial compression behavior of large-scale LRS FRP-confined square columns. The behavior of the test columns was primarily influenced by ρk,eff. Finally, evaluations were conducted on the existing models of LRS FRP-confined concrete with square cross-sections, based on the compilation of available test results from large-scale specimens.

Experimental and theoretical analysis of FRP-confined square lightweight aggregate concrete columns under axial compression

The structure of an FRP-confined square lightweight aggregate concrete (LWAC) column was investigated, and it was found to significantly decrease the self-weight while improving the deformation capacity and bearing capacity. Twelve FRP-confined LWAC columns and three unconfined LWAC columns underwent monotonic axial compression tests. The influences of the FRP thickness and type on the compressive performance, stressstrain relationship and strain cloud maps were investigated based on digital image correlation (DIC) technology. Both types of FRP materials demonstrated a noticeable enhancement in both the strength and deformation capacity of LWAC, with CFRP having the greatest effect on strength and BFRP having the greatest effect on ductility. Compared to LWAC columns without confinement, the compressive strength of LWAC confined by BFRP or CFRP increased by 9.4∼21.9% and 24.9∼53.3%, respectively, and the ultimate strain increased by 10.6–14.2 times and 8.0–10.9 times, respectively, with increasing the thickness of FRP. DIC technology was used to accurately measure changes in the strain and the crack development of the specimens, thereby obtaining an accurate rupture strain of the FRP material. The existing models were evaluated using test data, and new models were proposed for FRP-confined square LWAC.

Comparative study of models predicting punching shear capacity of strengthened corroded RC slab-column joints

ABSTRACT Degradation in reinforced concrete (RC) members associated with rebar corrosion in old buildings is one major concern that can significantly affect the strength and serviceability of RC structures. Strengthening existing structures using FRP can comprise complex assessment and design processes. This study addresses the critical issue of modeling the behavior associated with steel reinforcement corrosion in RC slab-column joints (SCJs). Three modeling methods, namely artificial neural network (ANN), Eureqa’s symbolic regression algorithm, and analytical modeling, are proposed to predict the punching shear (PS) capacity of corroded RC SCJs by accounting for the changes in material properties due to corrosion and the strengthening provided by different types of FRP. The accuracy of the proposed models is validated through comparisons with experimental results and a verified finite element (FE) model that considers material deterioration and bond degradation. The results demonstrate that the proposed models offer more accurate PS capacity predictions than existing design codes. Among the considered prediction models, the ANN model exhibits superior performance and is recommended for PS capacity prediction. A practical design tool in the form of a graphical user interface (GUI) was created to facilitate the assessment and prediction of the PS behavior of corroded RC SCJs. Engineers can conveniently use this GUI to evaluate and predict the performance of such joints.

Experimental and Numerical Study of CFRP Laminate Strengthened Concrete Beams Under Hygrothermal Environment

Carbon fiber reinforced polymer (CFRP) laminates are widely used to strengthen and retrofit deteriorated concrete structures, yet their long‐term performance and durability under varied environmental conditions remain critical areas of investigation. This study comprehensively examined the behavior of small concrete beams externally bonded with CFRP laminates under three distinct hygrothermal regimes: immersion in water at 23, 45, and 60°C for up to 112 days. The experimental program encompassed direct tension pull‐off testing of the CFRP–concrete assembly and four‐point bending tests on the beams. Pull‐off tests revealed complex failure modes, with bonding epoxy failure (43%) and concrete substrate cohesion failure (39%) being dominant. Notably, pull‐off strength exhibited nonmonotonic trends across all environments, suggesting that environmental degradation is not solely time‐dependent. Flexural capacity increased by 20%, 49%, and 11% for room temperature (RT), moderate temperature (MT), and high temperature (HT) conditions, respectively, after 112 days, highlighting the synergistic effect of CFRP strengthening and ongoing concrete curing. A calibrated three‐dimensional finite element model, developed using Abaqus, accurately replicated the experimental results and facilitated parametric studies on factors influencing CFRP‐strengthened beam performance. This included concrete compressive strength, number of CFRP layers, laminate thickness, and FRP type. The study elucidates the complex interplay between environmental exposure, material properties, and structural performance, contributing valuable insights for enhancing durability predictions and design guidelines for CFRP‐strengthened concrete structures in diverse climatic conditions.

Compressive behavior and modeling of concrete wrapped by hybrid low-high elongation capacities FRP

This paper experimentally investigated the monotonic and cyclic compressive behavior of concrete confined with hybrid carbon fiber-reinforced polymer (CFRP) and large rupture strain (LRS) FRP. A total of 34 concrete cylinders wrapped by FRP were prepared and tested under monotonic/cyclic axial compression. The effects of FRP types and thickness on the failure mode, efficiency factor, hybrid effect, stress-strain response, and energy dissipation were carefully investigated. Test results verified that the hybrid confinement mechanism can fully utilize the advantages of both types of FRP and avoid their essential shortcomings. LRS FRP effectively improved the utilization of CFRP and increased the deformation and energy dissipation capacity of concrete. Hybrid inner CFRP and outer LRS FRP serve as a confinement device that can achieve a progressive failure mechanism for concrete. In addition, an analysis-oriented model was developed and constructed to simulate the monotonic stress-strain behavior of hybrid-wrapped concrete. This analysis-oriented model focuses on the lateral stress-strain relationship and the localized CFRP fracture effect. Finally, a cyclic stress-strain model of hybrid-wrapped concrete was developed using the analysis-oriented model as an envelope model. The proposed model can accurately capture monotonic/cyclic stress-strain behaviors.

Bond Behavior of Recycled Tire Steel-Fiber-Reinforced Concrete and Basalt-Fiber-Reinforced Polymer Rebar after Prolonged Seawater Exposure

The integration of basalt-fiber-reinforced polymer (BFRP) rebars into concrete design standards still remains unrealized due to limited knowledge on the performance of the rebars in concrete, particularly in terms of bond durability in harsh conditions. In this work, we investigated the bond durability characteristics of BFRP rebars in fiber-reinforced self-compacting concrete (FRSCC) structures. To this aim, a number of 24 FRSCC pullout specimens reinforced with either BFRP rebar or glass-fiber-reinforced polymer, GFRP, rebar, which is a commonly used type of FRP, were fabricated. Half of these specimens were submerged in simulated seawater for a two-year span, while the other 12 similar specimens were maintained in standard laboratory conditions for comparative purposes. Subsequently, all 24 specimens underwent monotonic and fatigue pull-out tests. The exploration in this study focused on investigating the influence of the environmental condition, reinforcement type, and loading type on the bond stress versus slip relationship, maximum bond stress, and failure mode of the specimens. Based on the results obtained and by adopting the durability approach of industry standards for prediction of the bond retention of FRP-reinforced concrete, the bond strength retention between BFRP/GFRP and FRSCC after 50 years of exposure to seawater was estimated. The outcomes of the study are expected to enhance engineers’ confidence in the use of FRP, especially BFRP, for constructing durable and sustainable reinforced concrete structures in aggressive environments.

Confinement-based direct design method for fibre reinforced polymer confined CFST short columns

The paper presents a detailed analysis of the behaviour of circular and square concrete filled steel tube (CFST) short columns strengthened externally with carbon or glass fibre reinforced polymer sheets (CFRP or GFRP, respectively). A thorough review of existing test information is presented and discussed, and the most salient parameters in terms of the overall strength are identified. There are a large number of influential and inter-related parameters which affect the load-carrying capacity, including the geometry, cross-sectional shape, type of steel, concrete strength, boundary and loading conditions, and type of FRP. It is shown that existing design approaches do not reliably predict the strength for the full range of possible parameters. Therefore, this paper proposes a new design model to calculate the axial compressive strength of FRP-confined concrete filled steel tubular (CFST) short columns with either a circular or square cross-section. The method accounts for the various complexities which affect the behaviour, yet presents a user-friendly, performance-based design expression. It is based on an evaluation of the lateral confining pressure provided by the both the FRP and the steel tube to the concrete core. This is employed in the confinement-based direct resistance calculations. The paper validates the approach by comparing its capacity predictions with a large database of experimental results and alternative design models available in the literature. The results show that the proposed model provides much accurate strength predictions with greater reliability for the full range of parameters examined, than existing methods.

Flexural Response of Prestressed FRP Strengthened Reinforced Concrete Beam under Static Load

The motive of building sustainable structures and strengthening the structural members is important to overcome the problems associated with poor initial design and/or construction, accidental events, and degradation related to the environment. This paper aims to assess the flexural behavior of a prestressed basaltic fiber-reinforced polymer- (FRP-) strengthened reinforced concrete (RC) beam under static load through the finite-element method using ABAQUS CAE that is validated with experimental results from relevant literature. To achieve the desired objective, 18 models were prepared based on prestressing level, thickness of basalt FRP (BFRP), width of BFRP, length of BFRP, bond between concrete and BFRP, and type of FRP as study parameters. The results indicate that the use of prestressed BFRP is efficient in strengthening the flexural strength of the RC beam. Compared to nonstrengthened specimens, the flexural capacity of the specimens strengthened with BFRP at prestressing levels of 0%, 15%, 35%, and 45% show enhancement of 6.09%, 9.17%, 13.89%, and 17.57%, respectively. While increasing the width, length, and thickness of the prestressed BFRP section, increased yielding and ultimate load capacity of the specimen have been obtained; however, the ductility has been reduced up to 13.87% with increasing the BFRP thickness. The result also shows that the specimen strengthened with prestressed BFRP has better ductility than the prestressed carbon FRP (CFRP)-strengthened specimen; however, the model strengthened with prestressed CFRP has shown higher load-carrying capacity. It is also noticed that a cohesive bond better suited the experimental specimen than the fixed interference of the concrete surface, and relative to the cohesive bond, the fixed interference has shown a 17.4% higher ultimate load carrying capacity.

Performance-Based Environmental Assessment of FRP-Confined Concrete Stub Columns: Investigation on FRP Types

Performance-Based Environmental Assessment of FRP-Confined Concrete Stub Columns: Investigation on FRP Types

Seismic behaviour of shear critical square RC columns strengthened by large rupture strain FRP

This paper presents an experimental study on the seismic behaviour of shear critical square columns strengthened by large rupture strain (LRS) FRP under reversed cyclic lateral load together with constant axial load. The experimental program included 2 control columns, 6 LRS FRP-strengthened columns, and 2 CFRP-strengthened columns. The tested specimens’ failure modes, hysteretic responses, ductility, and cumulative energy dissipation were carefully analyzed. The influences of axial load ratio, FRP layers, and FRP type on the seismic performance of these columns were investigated. Compared with the control column, the ductility ratio and energy dissipation of the column wrapped by 3-layer LRS FRP at a low axial load ratio were raised by 491.7 % and 6498.3 %, respectively. The advantage of LRS FRP over CFRP in seismic retrofitting for shear critical RC columns was demonstrated through comparative analysis for the first time. Although the tensile stiffness of 1-layer PET FRP is much smaller than 1-layer CFRP, the ductility ratio and cumulative energy dissipation of the 1-layer PET FRP-strengthened column under a low axial load ratio were still slightly larger than that of the column wrapped by 1-layer CFRP. The CFRP-strengthened column under a high axial load ratio showed sudden explosive failure, while the LRS FRP-strengthened columns exhibited progressive failure. In addition, the axial flexure shear interaction (ASFI) method considering buckling of longitudinal reinforcement in FRP-confined concrete was developed and verified by comparing test results and predicted envelope curves.

Predictive models of behavior and capacity of FRP reinforced concrete columns

This paper proposes a new model for predicting the axial capacity and behavior of Fiber Reinforced Polymerreinforced concrete (FRP-RC) columns using a promising variant of Genetic Expression Programming (GEP). Current design codes, such as the ACI 440.1R-15 and the Canadian Code CSA S806, disregard the compressive contribution of FRP bars when used in compression members. The behavior of concentrically short FRP-RC columns has been widely investigated in the past few years; however, limited research has been dedicated to investigating the effect of load eccentricity and the slenderness ratio of FRP-RC columns. In addition, the methodologies adopted for including the effect of column slenderness remain a subject of debate, as no solid conclusions are withdrawn in this regard. In this paper, the experimental results of FRP-RC columns are gathered from the literature and used to formulate two GEP models to predict the axial capacity based on load eccentricity. The experimental data includes columns reinforced with different FRP types and subjected to concentric and eccentric axial compressive loads. In addition, the database comprises short and slender columns. The proposed GEP models are functions of concrete compressive strength, longitudinal reinforcing bars ratio, FRP bars elastic modulus, eccentricity level, and column dimensions. For the aim of comparison, a preliminary evaluation of previously suggested empirical equations/models for estimating the axial capacity of FRP-RC columns was carried out over the collected database. The proposed models showed superior accuracy in axial capacity prediction with coefficients of determination R2 equals to 0.978 and R2 equal to 0.992 for eccentric and concentric axial load, respectively. The proposed models were found to give reliable estimates of the axial capacity of columns reinforced with FRP longitudinal bars. Finally, a parametric study to evaluate the effect of each variable on the proposed models was conducted.

Structural Behaviour of Polystyrene Foam Lightweight Concrete Beams Strengthened with FRP Laminates

Lightweight concrete (LWC) is one of the most important building materials nowadays. Many research studies were focused on LWC produced using lightweight aggregates. However, limited work was cited for LWC produced using polystyrene beads. In this study, LWC beams strengthened with carbon fibre reinforced polymer (CFRP) and glass fibre reinforced polymer (GFRP) were experimentally tested to investigate the improvement in their flexural and shear behaviours. LWC in this investigation was achieved by partial replacement of normal aggregate by polystyrene beads and resulted in approximately 30% less weight compared to Normal weight concrete. Fourteen Reinforced Concrete (RC) LWC beams of 100 mm by 300 mm cross section having an overall length of 3250 mm were tested under four-point bending. These beams were designed, detailed, and tested to obtain flexural and shear mode of failure. These beams were divided into two groups based on the intended failure mode. In each group, six beams were strengthened using CFRP and GFRP laminates, while the remaining one beam was used as control. The tested parameters were the type of FRP, the width of the laminates used in shear strengthening, and the number of layers used in flexural strengthening. It was found that strengthening of LWC beams using CFRP and GFRP layers resulted in increasing the loading capacity and decreasing deflection as compared to control. The strengthening with CFRP and GFRP is also suitable in reducing the crack width and crack propagation which is more significant in LWC beams. The experimental results were also compared with the expressions in codes for forecasting the strength of LWC beams and it was that these expressions are compatible with the experimental results.

Compressive Behavior of Predamaged Concrete Cylinders Repaired with Jute and Basalt FRP Composites: A Comparative Study

Natural fibers have become a research hotspot in composite materials recently. This study investigated the axial compressive behavior of predamaged concrete repaired by jute fiber–reinforced polymer (JFRP) composites. Basalt FRP (BFRP) was also utilized to repair the predamaged concrete for comparison. Thirty FRP-jacketed concrete cylinders with a diameter of 150 mm and a height of 300 mm were designed and fabricated. Plain concrete cylinders were axially preloaded to three predamage levels, then repaired by JFRP and BFRP composites, and reloaded to evaluate the compressive behavior after repair. The results showed that the predamage of concrete had a noticeable adverse effect on the compressive behavior of JFRP- and BFRP-repaired concrete. Compared with the JFRP-jacketed intact concrete, the compressive strength and initial elastic modulus of the JFRP-repaired predamaged concrete decreased by 6%–18% and 16%–54%, respectively. However, the compressive strength and ultimate strain of the predamaged concrete were still improved by 5%–41% and 82%–291% after JFRP repair, respectively, when compared with those of the plain concrete. On the contrary, the ultimate axial strain and lateral strain capacities of JFRP- and BFRP-repaired concrete were insignificantly affected by the concrete predamage. Under similar confinement ratios, the compressive strengths of JFRP- and BFRP-jacketed intact concrete were close to each other, whereas the axial strain–lateral strain relationship and the variations of the Poisson’s ratios were highly dependent on the FRP types and the number of FRP layers. Based on the test results and data collected from the open literature, an ultimate strength model, an ultimate axial strain model, and a stress–strain relationship model were newly developed for JFRP-repaired predamaged concrete.

Efficacy of CFRP/BFRP laminates in flexurally strengthening of concrete beams with corroded reinforcement

This paper aimed at quantifying the effect of reinforcement corrosion level on the deformability and the flexural strengthening performance of Carbon and Basalt-Fibre-Reinforced Polymers (CFRP and BFRP) sheets on fifteen large-scale reinforced concrete (RC) beams. The main investigated parameters included reinforcement corrosion levels (0–30% by mass), FRP types and numbers of FRP layers (0–4 layers). The test results showed that the CFRP/BFRP laminates substantially reduced the crack width by up to 89%/85%. The flexural resistance of the corroded beams was, thus, improved by up to 103%/41%. By increasing the flexural resistance of corroded beams up to 41%, the BFRP laminates were a cost-effective strengthening option. Corrosion of the steel reinforcement resulted in the more effective mobilisation of the CFRP/BFRP laminates. This led to an increase in the strengthening effectiveness (improvement of beam flexural resistance) of the CFRP/BFRP laminates in the corroded beams by 14%/6% on average compared to the non-corroded beams. This increase tended to be more pronounced with a higher reinforcement corrosion level. In this paper, the authors propose an empirical formula to include the effect of reinforcement corrosion levels on FRP debonding strain. The proposed formula was verified showing an acceptable agreement with the experimental data from this study and other previous studies.

Parameters affecting the behaviour of RC beams strengthened in shear and flexure with various FRP systems

An experimental investigation was carried out on rectangular RC beams strengthened with FRP in different strengthening forms in shear and flexure. The parameters examined in this study are as follows: The shear span to effective depth ratio (a/d), the number of FRP layers in shear, strengthening form (completely wrapping, U-wrapping, and side-bonding), FRP types (Glass or Carbon), and FRP strips width to spacing ratios (wf/sf). The experimental results showed that strengthening with FRP enhanced the load-carrying capacity, deflection capacity, initial stiffness, and ductility capacity with respect to the reference beams. Increasing the number of FRP layers in shear did not provide a proportional increase in the contribution of FRP to shear strength. The FRP types, FRP strips width to spacing ratios (wf/sf), the number of FRP layers in shear, a/d, and strengthening form affect the cracking patterns and loads of tested beams compared to reference beams. In addition, strengthening with FRP could change the failure modes of RC beams from brittle shear failure to more ductile flexural failure. It was also found that the equations used to calculate FRP contribution to shear strength (ACI 440.2R (2017), Fib-TG 9.3 (2001), Khalifa (2002), Triantafillou (1998), Bukhari (2010)) overestimated the FRP contribution and gave unconservative results, especially for U-wrapped and side bonded beams compared to the experimental results.

Consideration of Critical Parameters for Improving the Efficiency of Concrete Structures Reinforced with FRP.

Fibre-reinforced polymer materials (FRP) are increasingly used to reinforce structural elements. Due to this, it is possible to increase the load-bearing capacity of polymer, wooden, concrete, and metal structures. In this article, the authors collected all the crucial aspects that influence the behaviour of concrete elements reinforced with FRP. The main types of FRP, their characterization, and their impact on the load-carrying capacity of a composite structure are discussed. The most significant aspects, such as type, number of FRP layers including fibre orientation, type of matrix, reinforcement of concrete columns, preparation of a concrete surface, fire-resistance aspects, recommended conditions for the lamination process, FRP laying methods, and design aspects were considered. Attention and special emphasis were focused on the description of the current research results related to various types of concrete reinforced with FRP composites. To understand which aspects should be taken into account when designing concrete reinforcement with composite materials, the main guidelines are presented in tabular form.

The behavior of concrete beams strengthened with NSM CFRP strips: a numerical parametric study

A non-linear finite element (NLFE) model was developed to predict the flexural response of concrete beams, strengthened with near surface-mounted (NSM) carbon fiber-reinforced polymer (CFRP) strips. The model was employed for predicting the influence of a wider spectrum of key parameters, concrete compressive strength (25–55 MPa), NSM FRP strips number (2–4) or spacing (20–35 mm), bond length (100–450 mm), FRP type (carbon, glass, and basalt) and loading pattern (four-point, three-point, and distributed load), upon the performance of these beams. The results showed a clear improvement in the performance of the CFRP-strengthened concrete beams when made at a higher-strength class of concrete. Using a higher number of NSM FRP strips of the same cross-sectional area contributed to enhancing the mechanical performance noticeably. Moreover, the model developed was capable of capturing the negative impact of using a lower spacing for a constant number of NSM CFRP strips. The impact of the FRP strips' type varied upon the mechanical property predicted and the strength grade of concrete used in the casting of the beams. The load resistance of NSM FRP-strengthened specimens was the highest under three-point load configuration, followed, in sequence, by distributed and four-point loads, respectively.