Beam Depth Ratio Research Articles

A novel approach for quantifying dynamic impacts on steel frames induced by instantaneous interior column loss

This research presents an innovative approach to accurately quantify dynamic impacts on the steel frame structure resulting from the instantaneous loss of an interior column. This methodology effectively calculates the dynamic amplification factor (DAF) when the steel frame reaches its collapse limit state and predicts the structure's deformation under such a scenario. Central to this approach is the conversion of the static load-deformation curve, pertinent to a scenario of interior column loss, into a dynamic force load-deformation curve using the concept of energy balance. A comprehensive parametric analysis was conducted to study how different structural parameters, such as beam depth, span, slab thickness, rebar diameter, and slab aspect ratio, affect the enhancement factor (i.e., the ratio of collapse resistance to yield resistance). A pragmatic formula for determining enhancement factor was subsequently suggested. Moreover, this study delved into how these structural parameters influence the dynamic amplification factor at the collapse state, revealing a notable dependency of dynamic amplification factor on the slab aspect ratio that an increasing aspect ratio correlates with a rising dynamic amplification factor trend. The manuscript also presented a detailed methodology for computing the dynamic deformation of frame structures in the event of an instantaneous interior column loss. The results of the case study show that the proposed method closely matches the accuracy of numerical analyses, with differences falling within a 15% range.

Experimental study on the effectiveness of strengthening of reinforced concrete beams with opening in shear span using CFRP sheets

In reinforced concrete beams, the opening is frequently required for the passage of utility ducts and/or pipes. The presence of such web openings leads to a reduction of the strength and stiffness of the beam. To ensurethe safety of the reinforced concrete beam, a strengthening system around the opening is necessary. This paperaims to contribute to a better understanding of the shear behavior of reinforced concrete beams with openingsin the shear span, strengthened with Carbon fiber-reinforced polymer (CFRP) sheets. The study is based on anexperimental program carried out on six beams. All beam specimens were 850 mm long with a cross-sectionof 150 × 250 mm and a shear span to beam depth ratio (a/d) of 1.48. One beam without any openings served asthe control specimen, while the remaining five beams featured circular or rectangular openings within the shearspan and with/without shear strengthening using CFRP sheets around the openings. The test results obtainedfrom this experimental program provide insights into the shear behavior of beams with openings, both with andwithout strengthening using CFRP sheets. Additionally, the potential advantages and effectiveness of employingCFRP strengthening techniques for opening strengthening are investigated and discussed.

Determination of critical collapse resistance of steel framed-structure: Fast manual calculation

This paper proposes a fast manual calculation method for determining the critical collapse resistance (CCR) of steel frame structures caused by an edge column loss. The critical collapse deformation (CCD) of the frame structure in an edge column loss is determined prior to calculating the CCR. Systematic parametric analysis is performed to examine the impacts of floor aspect ratio, slab rebar, slab thickness, beam depth, and beam span on the CCD of the frame structure. It is found that the CCD of the frame structure caused by the edge column loss can be determined by the beam depth, beam span and floor aspect ratio. When the beam span is increased by one beam depth, the CCD of the frame structure is increased by 0.2 times of the beam depth. The slab rebar and slab thickness have minimal effects on the CCD of the frame. When the rebar diameter and slab thickness are decreased by 50 % and 30 % respectively, the change of the CCD of the frame structure is within 10 %. A hardening factor is introduced to calculate the CCR of the frame in an edge column loss, defined as the ratio of the CCR to the yield resistance of the frame. Through more than 20,000 parametric analyses, it is found that the hardening factor can be determined by the normalized CCD (NCCD, the ratio of CCD to the yielding deformation) and the span-to-thickness ratio (STR) of the slab. For the STR of 40 and NCCD of 32, the hardening factor of the frame structure in an edge column loss is more than 3.0. A detailed process for calculating the CCR of the frame structure in an edge column loss is given. The results in the case study demonstrate that the error between the proposed method and the numerical analysis is within 10 %.

Shear span behavior of reinforced concrete beams with circular and rectangular openings

In reinforced concrete (RC) beams, opening is frequently required for the passage of utility ducts and/or pipes. The presence of such web openings leads to a reduction of the strength and sitffeness of the beam. This paper aims to contribute to better understanding the shear behavior of RC beam with web opening in the shear span. The study is based on an experimental program carried out on three RC beams. All beam specimens were 850 mm long with a cross section of 150 × 250 mm and a shear span to beam depth ratio (a/d) of 1.48. One beam without any openings served as the control specimen, while the remaining two beams featured circular or rectangular openings within the shear span. The test results obtained from this experimental program offer insights into the shear behavior of beams with openings. Furthermore, a simplified calculation was conducted to determine the shear strength of the test specimens, considering the influence of openings. This calculation provided a deeper understanding of how openings contribute to the reduction in the shear strength of RC beams.

Size effect tests on shear strength of Basalt FRP-RC deep beams with different shear-span ratios

Basalt Fiber Reinforced Polymer (BFRP) bars appear effective in reducing corrosion-related damage and are gradually used as substitute for Steel bars in engineering practices. However, most of available efforts are focused on the size effect of BFRP-reinforced concrete (BFRP-RC) deep beams without web reinforcement, while less efforts have been studied on BFRP-RC deep beams with web reinforcement. Moreover, the quantitative influence of the shear-span ratio on the shear capacity of BFRP-RC deep beams is always in dispute. The purpose of the work is to investigate the quantitative influence of beam depth and shear-span ratio on the shear behavior of BFRP-RC deep beams with web reinforcement. A total of sixteen specimens were tested by considering the beam depth (i.e., 300 mm ∼ 1200 mm) and the shear-span ratio (i.e., 0.8, 1.3 and 1.8) as test variables. Twelve beams were reinforced with BFRP bars while the other four beams were reinforced with steel bars to act as controls. The corresponding size effect of BFRP-RC deep beams with web reinforcement was quantitatively studied, and the applicability of current design codes and scientific calculation methods were discussed. The results indicate that: 1) the increase of shear-span ratio reduces the nominal ultimate shear strength but has an ignorable influence on the size effect; 2) the nominal ultimate shear strength of BFRP-RC deep beams declinebyabout 46% as the beam depth increases from 300 mm to 1200 mm (both horizontal and vertical web reinforcement ratio are 0.51%); 3) the size effect of FRP-RC deep beams is not reasonably considered in current design codes, while, Jin’s theoretical model can scientificallyreflect the effect of beam depth and shear-span ratio on the nominal shear strength.

Parametric study and design method on unequal depth beams to corner column joints with H-damper

The paper presents the parametric studies and design method of unequal depth H beams-HSS steel column corner joints with H-dampers. According to corresponding experimental studies, nineteen numerical models were created by ABAQUS and their reliability was validated by comparative tests. The design methods and corresponding calculation of H-dampers with three perforated shapes (diamond, ellipse, and vertical) are exhibited. The primary analyzed variables were beam depth ratio (Dbs/Dbw), H-damper types, limb breadth (B), and limb length (lf) of H-dampers. Then, the bearing capacities and initial stiffness of beams and bearing capacities and energy dissipation in H-dampers were studied through parametric analysis. The results indicated that T-connectors and H-dampers could elevate the bearing capacity and initial stiffness of shallow beams. H-dampers exhibited better energy dissipation performance. Besides, web-perforated forms of dampers affected the beams and dampers. Wider limb breadth and shorter limb length enhanced the bearing capacity and initial stiffness of beams, and reduced energy dissipation of H-dampers.

Failure mode classification and deformability evaluation for concrete beams reinforced with FRP bars

The failure mode of fiber-reinforced polymers reinforced concrete (FRP-RC) beams is a concern in the capacity evaluation. Therefore, developing a robust method to identify the failure mode of FRP-RC beams is warranted. This paper proposes a support vector machine (SVM) algorithm, together with comprehensive compiled experimental databases and a validated analytical model, to identify the failure mode of FRP-RC beams. The SVM analysis yields “data-driven classification rules” that not only achieved superior performance over ACI 440 guidelines but are also valid for a large range of design parameters. The proposed classification rules are a function of the balanced reinforcement ratio (ρfb) and height to depth ratio (h/b) of FRP-RC beams. In addition, the verified classification rules recommend increasing the transition zone defined by ACI 440 from 1.4ρfb to 1.55ρfb. The study also utilized the verified analytical model to conduct a comprehensive deformability evaluation of FRP-RC members. The results indicate that FRP-RC beams have sufficient deformability before failure regardless of the failure mode. Moreover, to ensure minimum deformability requirements for FRP-RC beams, a limit should be specified on the modulus of elasticity -to-the ultimate tensile strength of the FRP ratio. Based on the analysis, a proposed limit of 200 is recommended.

Real fracture toughness of FRC and FGC: size and boundary effects

The present dilemma is how to simulate the real crack in full depth (FD) fiber-reinforced concrete (FRC), FD FRC, to get the actual fracture toughness of such fibrous composites, i.e., through-thickness pre-cracks are inappropriate for such materials. To overcome this dilemma, a new technique was adopted to create a pre-matrix crack (MC) without cutting the fibers bridging the two surfaces of the pre-crack. The main objective of the present work is to study the size and boundary effects on the real fracture toughness of MC-FD FRC and functionally graded concrete (FGC). Forty-eight MC-FD FRC and MC-FGC beams with three different span to depth ratios L/d equal 4, 5, and 6, and three different beam depths of the same beam span have been tested under three-point bending. All beams have the same pre-MC length to beam depth ratio (ao/d) of 1/3. Hooked end steel fibers of 1% fiber volume fraction produced FRC. FGC beams consist of three equal layers, FRC layer at the tension side, normal strength concrete layer at the middle of the beam, and high strength concrete layer at the compression side. The applied load versus all beams' crack mouth opening displacement (CMOD) curves have been analyzed. The present load/CMOD results showed that beams having constant L/d ratios are recommended to capture independent size effect parameters. The size effect law (SEL) and boundary effect model (BEM) are good candidates to predict the size effect. According to the maximum non-damaged defect concept, the SEL is more reliable in predicting MC FD FRC fracture toughness than BEM.

Prestressing Effects on Full Scale Deep Beams with Large Web Openings¨: An Experimental and Numerical Study

Most studies on deep beams have been made with reinforced concrete deep beams, only a few studies investigate the response of prestressed deep beams, while, to the best of our knowledge, there is not a study that investigates the response of full scale (T-section) prestressed deep beams with large web openings. An experimental and numerical study was conducted in order to investigate the shear strength of ordinary reinforced and partially prestressed full scale (T-section) deep beams that contain large web openings in order to investigate the prestressing existence effects on the deep beam responses and to better understand the effects of prestressing locations and opening depth to beam depth ratio on the deep beam performance and behavior. A total of seven deep beam specimens with identical shear span-to-depth ratio, compressive strength of concrete, and amount of horizontal and vertical web reinforcement ratios have been tested under mid-span concentrated load applied monotonically until failure. The main variables studied were the effects of depth of the web openings and the prestressing location on deep beam performance. The test results showed that the enlargement in the size of web openings substantially reduces the element’s shear capacities while prestressing strands location above the web openings has more effect at increasing the element’s shear capacities. The numerical study considered three-dimensional finite element models that have been developed in Abaqus software to simulate and predict the performance of prestressed deep beams. The results of numerical simulations were in good agreement with the experimental ones.

Fracture parameters of flyash and GGBS based Alkali activated concrete

In the world of concrete, Geopolymer concrete is an innovative and eco-friendly construction material which shall be produced by the chemical reaction of inorganic molecules to reduce CO2 emission and in engineering design safety is an essential parameter which needs to have greater attention when the failure consequences are severe. Cracking plays an important role in concrete structures by indicating major structural problems when subjected to loading. Fracture mechanics is a powerful tool for advanced study and the prime objective is to predict if a structure will fail or not by the presence of a crack. The study intends to assess the effect of the beam depth (75 mm, 150 mm and 300 mm) and molarities (6 M & 8 M) on the fracture parameters of geopolymer concrete beams. The geopolymer notched concrete beams were modelled using finite element analysis software (ANSYS 2021 R1) to study the fracture parameters of AAC. The fracture parameters like fracture energy, fracture toughness and stress intensity factor are investigated for the beams of varying sizes with varying notch depth ratios (ao/D = 0.15, 0.3, 0.45) defined as per RILEM specifications and analyzed under three-point bending test conditions using ANSYS. The results are obtained by developing the FEM model of beams using ANSYS. This study found that the fracture energy, fracture toughness and stress intensity factors values are increased with the increase in beam size & molarity and decreased with an increase of notch to depth ratio and it is also found that load-carrying capacity is decreased with the increase of notch depth to beam depth ratio.

Multilinear model for progressive collapse response of reinforced concrete frames under penultimate column removal scenario

When local damage occurs due to unexpected events, compressive arch action (CAA) and catenary action (CTA) increase the progressive collapse resistance beyond the conventional plastic hinge mechanism. To investigate the progressive collapse behavior, large-scale structural tests and/or finite element analysis are performed, which are time-consuming and requires in-depth professional knowledge. In the present study, a multilinear model was developed to evaluate the progressive collapse resistance of moment sub-frames after the removal of a penultimate column. To estimate the load-carrying capacity and corresponding deformation at each mechanism, the effects of boundary condition, and the geometric and material properties of the beam section on the structural performance were considered. The validity of the proposed method was verified by comparison with the existing test results of moment sub-frames under progressive collapse. Further, a parametric study was performed to investigate the effects of concrete strength, reinforcement ratio, beam section size, and beam span on the progressive collapse resistance of the substructure. The analysis results showed that increasing the beam depth or beam top rebar ratio significantly increased the progressive collapse resistance.

Shear behavior of panel zone with an eccentricity between beam depths: Parameter study and design methodology

Recently, beam-CFST column connections with an eccentricity between beam depth have been used in engineering practices to fulfill the design requirements of high-rise and large-span space structures. According to the comparison between the numerical data with the current design code, AIJ (1987), and Eurocode (2005), this paper presents a design method to evaluate the shear performance of connection panel zone with an eccentricity between beam depths. The proposed design methods directly superimpose the contribution of the infilled concrete and the outer steel tubular, which take the effect of beam-depth ratio (h2/h1), size effect (D), aspect ratio (H/D), width-to-thickness ratio (D/t), and axial-force ratio (n) into consideration. The design methods showed high accuracy and could be applied to assess the shear performance for connections with an eccentricity between beam depths.

Numerical analysis of ultimate load and crack propagation in a concrete beam with longitudinal small hole

This analytical study aims to investigate the flexural behavior of simply supported RC beams having longitudinal hole with circle cross section under monotonic two point loads. The commercial FE program ABAQUS was used for simulating and implementing the specimens behavior that tested experimentally in previous researches. The overall specimens investigated were thirteen RC rectangular beam specimen, the first one was solid while the others with longitudinal circular hole. The specimens with holes divided into three groups, each one has a specified hole diameter 25 mm, 40 mm, and 50 mm. The distance from center of hole to the top section face was variable where the hole would be completely in the stress block, below it, or partially within it. The validity of the simulated model were verified by comparing the available load deflection data with the implemented one, where good agreement were noticed. The simulated models could introduce the ultimate load, first cracking load and its propagation in addition to the maximum attended deflection. It is concluded that the existence of a longitudinal hole with a percentage of diameter to beam depth ratio below 20% with different positions from top surface of the cross-section to the center of the hole values caused decreasing in ultimate load not exceeding 5% compared with the solid beam.

Weight function calculation method for analyzing mixed-mode shear cracks in reinforced concrete beams

Based on a virtual crack extension (VCE) technique in finite element method (FEM), this paper proposes a rational method of calculating weight functions for inclined shear cracked RC beams with any geometry. As an inclined shear crack in an RC beam is geometrically determined by the absolute dimensions, shear span to beam depth ratio, crack inclined angle and crack initiation location, the relations between the weight functions and these parameters are investigated by either following theoretical equations or varying the parameters in a certain range. The range is determined to enclose the geometries of inclined critical shear cracks of a large set of RC beams which were tested under a bending load but failed due to the propagation of a critical inclined shear crack. Moreover, a method of calculating the weight functions of a shear cracked RC beam with any geometrical properties is developed numerically using the weight functions calculated and provided in this study. As a result, it is possible that the shear behaviors of RC beams can be even studied conveniently but also comprehensively following the theoretical fracture mechanic approach.

Incorporation of Smart Concrete in Large-Scale RC Beams for Evaluating Self-Sensing and structural Properties

Only using a small number of samples in the absence of reinforcement, the concrete self-monitoring behaviour is tested, which is inaccurate for real-world structures. The behaviour of concrete is primarily tested, which can be inaccurate for structures in real time. This study examined the self-sensing ability of large-scale reinforced concrete beams that are 1500 mm long and 125 mm wide embedded with smart concrete at top and bottom surfaces for a length of 350 mm. As shear failure is catastrophic, the present study focused on evaluating RC beams' self-sensing property failing under shear, and shear reinforcement was not given for the same reason. A total of six RC beams, 3 of are 250 mm deep and 3 are 350 mm deep with variable reinforcement ratios, were tested in a four-point bending test to study the self-sensing properties such as strain and crack/damage sensing. Mechanical/structural properties of all the beams have been documented, along with self-sensing properties. The results obtained showed that partially placed smart concrete in the RC beam's pure bending region successfully sensed all strain and damage/cracks without any impact due to beam depth and reinforcement ratio. During testing, it was observed that 250-mm-deep beams failed due to flexure/concrete crushing, and 350-mm-deep beams failed due to shear. In particular, smart concrete's self-sensing property showed promising results for the beams that failed due to flexure by representing all the cracks developed in the pure bending region. Fraction change in resistance (FCR) has also been obtained for all the beams during self-sensing testing, and this FCR has been successfully co-related with concrete strain in compression and steel strain in tension. An empirical equation was also derived separately for beams that failed in shear and flexure, which provides a co-relation between FCR and concrete or steel strain.

Numerical investigation and design method of bolted beam-column joint panel with eccentricity in beam depths

With the development of long-span space structures and high-rise buildings, more and more unequal-depth beams are applied to meet the demand of different shear performance and flexure moments on each side of the column. The author developed a new type of the bolted unequal-depth beam-column joint with a T-shape connector. Outer annular stiffeners were used to retrofit the hollow square sectional column with the connection region and improve the seismic performance. Limited literature was reported to justify current guidance on designing the T-shape connector. This paper analytically investigates the shear performance of the bolted unequal-depth beam-column joint with a T-shape connector in detail. Three cruciform beam-column joint specimens and thirteen three-dimensional nonlinear finite element models were tested under the cyclic loadings. The 3D analytical models were verified by the tested data. In addition, a parametric analysis was conducted to present the influence of four parameters on the shear performance of the panel zone, which are three levels of beam depth ratio, four levels of width-thickness ratio of steel column, four levels of axial force ratio, five levels of beam-flange-to-column-width-ratio. The analytical results demonstrated that due to the T-shape connector, the beam depth ratio has a limited effect on the shear performance. However, the width-thickness ratio was the main parameter that acts on the shear performance of the panel zone.

Experimental and numerical study of seismic performance of high-strength steel fabricated framed-tube structures with replaceable shear links

Steel moment-resisting frames (MRFs) dissipate earthquake energy via the deformation of plastic hinges at beam-ends. To ensure that such plastic hinges are long enough to serve their purpose, their designs are based on a minimum span–depth ratio of beams as per seismic design codes. However, in steel framed-tube structures (SFTSs), deep spandrel beams having large cross-sections with flexural plastic hinges at beam-ends cannot be adequately developed, which is the reason behind SFTSs presenting lower ductility and energy dissipation capacities. To address this issue, high-strength steel (HS)-fabricated SFTSs with bolted web-connected replaceable shear links (HS-FTS-RSLs) have been proposed. In HS-FTS-RSLs, shear links are fabricated from conventional steel and placed in the middle of the deep spandrel beams to behave as ductile fuses that dissipate seismic energy, and the spandrel beams and columns use HS. In this study, a 2/3-scaled HS-FTS-RSL specimen with a very short shear link was fabricated, and cyclic loading tests were performed to investigate the hysteretic behavior of the specimen. The finite-element models (FEMs) of four full-scale sub-structures of HS-FTS-RSLs were established. Subsequently, the effects of the length of the very short bolted web-connected shear links on the cyclic performance of the HS-FTS-RSLs were investigated via nonlinear numerical analyses. The test results showed that the specimen developed the expected failure modes and showed good ductility and energy dissipation capacities. The shear link entered the plastic stage to dissipate energy, while spandrel beams and columns remained in the elastic stage under the cyclic loads. Moreover, the use of a shorter shear link was shown to yield a higher load-carrying capacity and initial elastic lateral stiffness; however, a lower ductility and energy dissipation capacity for HS-FTS-RSLs were induced. The performance of the specimen was comparable to that of the original sub-structure specimen after replacement of the shear link. The expected post-earthquake recoverability and resilience of the structure could be achieved via replacement of the shear link. The acceptable residual interstory drift, which simplifies the replacement of the bolted web-connected shear link, was 0.23%. The length ratios e/(Mp/Vp) of very short bolted web-connected shear links should not be lower than 0.53 in HS-FTS-RSLs, as per the numerical analysis results. The overstrength factor of the very short bolted web-connected shear link could reach 1.9, which is much higher than the proposed value of 1.5 for the shear link in the eccentrically braced frame in AISC 341–16.

Collapse Responses of Concrete Frames Reinforced with BFRP Bars in Middle Column Removal Scenario

Six concrete beam-column frame sub-assemblages reinforced with basalt fiber-reinforced polymer (BFRP) bars in the frame beams were designed to investigate the collapse resistance after a middle column removal. Effect of parameters, including span to depth ratio of frame beams, prestressing, as well as material types of stirrups in the beams, on the collapse resistance of the sub-assemblages, was investigated. Experimental results showed that the initial stiffness of the frame beams was apparently lower due to low elastic modulus of BFRP bars. The collapse resistance of the sub-assemblages presented wave-like increasing tendency with the vertical displacement of the failed middle column, and it mainly attributed to the cracking or crushing of concrete and rupture of BFRP bars in the frame beams. Top longitudinal BFRP bars at the beam ends near to the side column (BESCs) and bottom longitudinal BFRP bars at the beam ends near to the middle column (BEMCs) kept tensile during the loading process, which played an important role in resisting structural collapse. Adjacent structural members such as frame beams and columns could provide horizontal reaction forces to constrain the free deformation of the residual sub-assemblages after the middle column failed, and it was beneficial to mitigate the structural collapse risk. The vertical deformation of the frame beams was nearly linear and proportional to the vertical displacement of the failed middle column. Finally, the dynamic increase factor (DIF) of collapse load was discussed using energy conservation method, and a calculation method of DIF for prestressed concrete frame structures was developed. It was suggested that the DIF values for the non-prestressed frame structures reinforced with BFRP bars in the beams should be taken as 2.0, while those for the prestressed sub-assemblages can be taken between 1.44 and 2.0.

Characterization on tensile behaviors of fracture process zone of nuclear graphite using a hybrid numerical and experimental approach

This paper reports an experimental and numerical study on the fracture properties of nuclear graphite NG-CT-01 produced in China. Three-point bending tests were performed on center-notch beams and electronic speckle pattern interferometry (ESPI) technique was employed to measure the full-field deformation of the beams. Besides, finite element analysis was performed by using extended finite element method to simulate the fracture behavior of graphite. Numerical results were compared with the experimental results and excellent agreement was obtained, validating the reliability and accuracy of the numerical model. Based on the strain field measured by ESPI technique, the formation and evolution of the fracture process zone (FPZ) in graphite were observed. The tension softening curve (TSC) of the graphite was determined by using a hybrid numerical and experimental approach. The influences of initial crack length to beam depth ratio on the fracture responses of graphite beam, including the load-displacement curves, double-K fracture parameters, TSCs and the length of the FPZ, were evaluated. In order to explain the correlation between the tension softening behaviors and the fracture mechanism of the FPZ, a tri-linear model was proposed. Furthermore, double-K fracture criterion was employed to predict the crack propagation in graphite.

DESIGN METHOD ON PANEL-ZONE SHEAR BEHAVIOR OF CONNECTION BETWEEN SQUARE COLUMN AND H-SHAPED-STEEL UNEQUAL-DEPTH BEAM WITH EXTERNAL-DIAPHRAGM

To evaluate the panel-zone shear behavior of a H-shaped steel unequal-depth beam-to-column connection with external-diaphragm, seven specimens are fabricated and tested under cyclic loading. Based on the test results, twenty three-dimensional solid models with different parameters are established, and the nonlinear finite element analysis has been carried out. The results show that the shear failure modes can be classified to an entire panel zone mode and a partial panel zone mode by introducing the concept of the minimum column-beam strength ratio of the connection. Moreover, the shear behavior of the panel zone is affected by various parameters, including beam depth ratio (db1/db2), the size of external diaphragms, and width-to-thickness ratio (D/t) of a steel column. Furthermore, based on the yield line theory, test results and numerical results, the design formulas on shear strength have been proposed and the calculated results show a good agreement with the test results and numerical results. The proposed formulas can evaluate the shear strength of the panel zone with adequate accuracy and be adopted in practical design.