Yield Line Research Articles

New proposal for the bending moment capacity of tubular T-joints in carbon steel and stainless steel structures

The expected failure mode of T-joints between rectangular hollow sections subjected to bending moment with a ratio of the brace width (b1) over the chord width (b0) below 0.85 (i.e., β=b1/b0≤0.85) is the chord face failure, produced by yielding. This paper presents the development of a numerical model to reproduce this phenomenon, calibrated against experimental laboratory tests, which is then used to carry out a large parametric study, where the influence of the main geometric parameters involved in the joint resistance –the chord width (b0), the chord thickness (t0), the chord radius (R0), the brace width (b1), the brace height (h1) and the weld thickness (a)– is assessed for two different materials: S275 carbon steel and EN 1.4301 austenitic stainless steel. The results derived from the parametric study suggested that a different yield line mechanism may develop for higher β-values (β≥0.45) than that considered in current European and American codes. Hence, a new formulation for estimating the bending resistance of T-joints exhibiting chord face failure modes is presented based on a different yield line mechanism developed in this paper. This formulation includes additional geometric parameters that are dismissed in the current formulation, such as the chord radius and the weld thickness, which are found to have a non-negligible influence on the joint resistance. Moreover, the proposed formulation is adjusted in order to be used for joints with lower β-values without losing accuracy. Additionally, the new proposed formulation is adapted for stainless steel joints by combining it with the Continuous Strength Method (CSM) formulation with promising results. Finally, the soundness and safety of the proposed formulation is statistically demonstrated.

Lint percentage and boll weight QTLs in three excellent upland cotton (Gossypium hirsutum): ZR014121, CCRI60, and EZ60

BackgroundUpland cotton (Gossypium hirsutum L.) is the most economically important species in the cotton genus (Gossypium spp.). Enhancing the cotton yield is a major goal in cotton breeding programs. Lint percentage (LP) and boll weight (BW) are the two most important components of cotton lint yield. The identification of stable and effective quantitative trait loci (QTLs) will aid the molecular breeding of cotton cultivars with high yield.ResultsGenotyping by target sequencing (GBTS) and genome-wide association study (GWAS) with 3VmrMLM were used to identify LP and BW related QTLs from two recombinant inbred line (RIL) populations derived from high lint yield and fiber quality lines (ZR014121, CCRI60 and EZ60). The average call rate of a single locus was 94.35%, and the average call rate of an individual was 92.10% in GBTS. A total of 100 QTLs were identified; 22 of them were overlapping with the reported QTLs, and 78 were novel QTLs. Of the 100 QTLs, 51 QTLs were for LP, and they explained 0.29–9.96% of the phenotypic variation; 49 QTLs were for BW, and they explained 0.41–6.31% of the phenotypic variation. One QTL (qBW-E-A10-1, qBW-C-A10-1) was identified in both populations. Six key QTLs were identified in multiple-environments; three were for LP, and three were for BW. A total of 108 candidate genes were identified in the regions of the six key QTLs. Several candidate genes were positively related to the developments of LP and BW, such as genes involved in gene transcription, protein synthesis, calcium signaling, carbon metabolism, and biosynthesis of secondary metabolites. Seven major candidate genes were predicted to form a co-expression network. Six significantly highly expressed candidate genes of the six QTLs after anthesis were the key genes regulating LP and BW and affecting cotton yield formation.ConclusionsA total of 100 stable QTLs for LP and BW in upland cotton were identified in this study; these QTLs could be used in cotton molecular breeding programs. Putative candidate genes of the six key QTLs were identified; this result provided clues for future studies on the mechanisms of LP and BW developments.

A study on the effect of opening location on ultimate load capacity of an orthogonal solid slab

The aim of the research is to study the effect of the position of the opening on the ultimate load capacity of the orthogonal solid slab. A yield line theory is used for the prediction of the ultimate load capacity of an orthogonal concrete slab with and without rectangular corner opening subjected to uniformly distributed load (UDL). In this study, two locations of the opening are considered: the rectangular opening provided at the corner and the interior corner of the slab. All possible governing, geometrically admissible, collapse mechanisms were identified, virtual work equations were derived, and to solve the equations a computer program has been developed. The same aspect ratios of the slab and the opening, and opening sizes up to 0.4 times the slab length the were considered. Four boundary conditions of the slab with different opening sizes are considered to present the design charts for affine coefficients.

Prediction of progressive collapse resistance of RC frames using deep and cross network model

Compressive membrane/arch action at small deformations and resistance evolution path at large deformations are two key factors in determining whether an RC frame structure can resist progressive collapse. In this study, two deep learning models based on deep and cross network (DCN) are developed to predict the progressive collapse resistance of RC frames. DCN model I is constructed to predict the compressive membrane/arch action resistance, while DCN model II is developed to predict the resistance displacement curve considering the dynamic effect. 464 records regarding structural collapse were collected through extensive literature review and stringent data filtering. They were randomly divided into 80% and 20% for training and testing the two models, to which the column removal scenario, with or without slab, boundary condition, beam net span, beam section, beam reinforcement ratio, and material property were selected as input features. Moreover, Shapley additive explanations (SHAP) method was introduced to interpret the proposed DCN model. The results indicated that the performance of DCN model I in predicting the compressive membrane/arch action resistance was satisfactory with an MAPE value of 10.66% and an R2 value of 0.9799, respectively, while being more accurate than the existing yield line theory and Park’s compressive arch calculation model. The proposed DCN model II can further capture the evolution of the dynamic resistance of RC frames accurately. The two DCN models have been deployed online to public for application.

Combining ability estimates for quality and non-quality protein maize inbred lines for grain yield, agronomic, and quality traits

IntroductionBiofortified maize varieties could contribute to the fight against hunger and malnutrition of the increasing human population and help meet the high demand of maize for human consumption, industrial use and feed for animal and poultry. The understanding of the genetic mechanisms conditioning the inheritance of grain yield and other agronomic and quality traits is essential in the development of superior maize genotypes. The main objective of this study was to determine the combining ability for grain yield and other agronomic traits of QPM and non-QPM inbred lines crossed with two QPM and two non-QPM testers.Materials and methodsA total of 130 hybrids were obtained by crossing 10 non-QPM and 23 QPM lines with four elite testers (two QPM and two non-QPM). The 130 single cross hybrids were evaluated at 13 sites in 2018 and 2019.Results and discussionThe results showed significant general combining ability (GCA) for lines and testers as well as significant specific combining ability (SCA) for hybrids for most of the measured traits. Non-additive gene action controlled the inheritance of grain yield while agronomic and quality traits were controlled by additive gene action. QPM lines 11, 14 and 28 and non-QPM tester CML444 showed desirable GCA effects for grain yield, indicating that these lines in combination with tester CML444 should be considered when targeting development of superior maize genotypes with QPM traits.ConclusionsBased on the SCA values, crosses 120, 108, 105, 99, 85, and 41 were identified as the best hybrids across the locations. It is recommended that maize breeding programs targeting the development of high yielding QPM hybrids should exploit QPM lines with high GCA values for heterosis to be realized. In addition, the identified superior hybrids may be further evaluated and consequently promoted for commercial release which could increase incomes of farmers and help to alleviate poverty, hunger and malnutrition in southern Africa and sub-Saharan Africa at large.

Evaluation of YLT method to estimate the load carrying capacity of one-way patched reinforced concrete slab under concentrated load

An unsaturated polyester resin (UPR) mortar was applied to repair the damage to the tension zone's one-way reinforced concrete (RC) slabs. The load carrying capacity of the patched RC slab is of interest to justify the effectiveness of the repair. The Yield Line Theory (YLT) may be used to estimate the load carrying capacity of patched RC slabs under concentrated load. The results of the YLT are compared with the experimental results to evaluate the validity of the YLT method. The results confirm that patching alters the yield line formation, mainly when the concentrated load is applied close to the patching zone. Subsequently, the YLT method provides a higher load carrying capacity estimation deviation for slabs with a loading point near the patching zone. On the other hand, the YLT method estimates load carrying capacity accurately when the loading point is away from the patching zone.

Experimental and Numerical Investigation of Compressive Membrane Action in GFRP-Reinforced Concrete Slabs

Experimental and numerical analyses of eight in-plane restrained slabs (1425 mm (length) × 475 mm (width) × 150 mm (thickness)) reinforced with glass fiber-reinforced polymer (GFRP) bars are reported in this paper. The test slabs were installed into a rig, that provided 855 kN/mm in-plane stiffness and rotational stiffness. The effective depths of the reinforcement in the slabs varied from 75 mm to 150 mm, and the amount of reinforcement changed from 0 to 1.2% with 8, 12, and 16 mm bar diameters. A comparison of the service and ultimate limit state behavior of the tested one-way spanning slabs shows that a different design approach is necessary for GFRP-reinforced in-plane restrained slabs that demonstrate compressive membrane action behavior. Design codes based on yield line theory, which considers simply supported and rotationally restrained slabs, are not sufficient to predict the ultimate limit state behavior of restrained GFRP-reinforced slabs. Tests reported a higher failure load for GFRP-reinforced slabs by a factor of 2, which was further validated by numerical models. The experimental investigation was validated by a numerical analysis, and the acceptability of the model was further confirmed by consistent results obtained by analyzing in-plane restrained slab data from the literature.

Cyclic and monotonic performance of unstiffened extended end-plate connections having thin end-plates and large-bolts

This study presents the findings of comprehensive numerical and experimental programs on unstiffened extended end-plate connections (UEECs) having thin plates and large sized bolts. The main goal of the research program is to analyze the effects of variables influencing the capacity of these connections. Six specimens were subjected to cyclic and monotonic loading to achieve this goal. For the experimental part, the thickness of end-plate was chosen as the variable. The thickness of end-plates was selected to ensure failure modes governed by the bending capacity of end-plates. A comprehensive numerical study consisting of 156 finite element models where the parameters are I-section types, width and thickness of end-plate, edge distance, distance from flange to bolt row, bolt diameter and weld thickness was performed. The results showed that the connections with thin end-plates can perform high ductility and strength. Moreover, the design methods given by AISC 358-16 and EN1993-1-8 conservatively predict the plastic moment capacity of UEECs. According to numerical findings, the average ratios of actual to estimated plastic moment capacity by AISC 358-16 and EC3:1-8 are 2.77 and 3.13, respectively. These ratios alter to 3.70 and 3.93 for the experimental results. The yield line mechanism and the spacing between the plastic hinges are to cause this underestimate. An expression for the observed yield line pattern is developed to estimate the plastic moment capacity more correctly. The actual to estimated plastic moment capacity ratios according to proposed expressions are averagely 1.23 and 1.29 for the outcomes of the experimental and numerical study, respectively.

Behavior of thread-fixed one-side bolts bolted T-stubs with arc-shaped flange to steel tube under tension

Tensile tests and Finite Element (FE) analysis were conducted on the Thread-fixed One-side Bolts (TOBs) bolted T-stub with arc-shaped flange to steel tube in this paper. Critical parameters were determined as the thickness of tube wall, the outer diameter of steel tube, the thickness of arc-shaped flange, and the center angle between bolts. Test results revealed that the connection would encounter three typical failure modes, which were: failure mode 1, thread shear failure with yielding of tube wall; failure mode 2, complete yielding failure of tube wall; failure mode 3, thread shear failure with yielding of T-stub arc-shaped flange. Developed FE models are verified and used to analyze the yield line pattern of tube wall, the hoop stress distribution of cross-section of tube wall, and the shear acting on bolt shank. Based on the experimental and numerical results, preliminary analytical models and design methods are proposed to estimate the tensile yield strength of specimens under different failure modes.

The Use of Nutritional Rice Specific Resistance for Control of Pathogen Pyricularia oryzae

Apart from being a source of energy, rice is also a source of protein and microelements that are useful for human health, such as B vitamins, iron (Fe), zinc (Zn), anthocyanins, and folic acid. Blast disease caused by the fungus Pyricularia oryzae is an important disease in rice crops worldwide. The aim of the study was to evaluate the resistance of nutritionally specific rice lines to blast disease. The nutritionally specific rice tested were preliminary yield lines and multilocation trials. The pathogens of P. oryzae used were 4 races, namely races 173, 133, 073 and 033. Observations and analysis of resistance to blast disease were carried out based on the IRRI SES method. The results for the preliminary yield trial line showed that the B15068C-MR-1-2-7-KN-2 line showed a resistant response to 4 races of blast pathogen with a disease scale of 1 and as many as 11 special rice lines showed a resistant response or moderately resistant to 4 races, while the multilocation trial lines obtained as many as 3 special rice lines and the variety of Inpari 19 which had a resistant or moderately resistant response to 4 races of P. oryzae. These nutritionally specific rice lines can be used as gene donors for resistance or proposed as varieties that have blast disease resistance. while the multilocation trial lines obtained as many as 3 special rice lines and the variety of Inpari 19 which had a resistant or moderately resistant response to 4 races of P. oryzae. These nutritionally specific rice lines can be used as gene donors for resistance or proposed as varieties that have blast disease resistance. while the multilocation trial lines obtained as many as 3 special rice lines and the variety of Inpari 19 which had a resistant or moderately resistant response to 4 races of P. oryzae. These nutritionally specific rice lines can be used as gene donors for resistance or proposed as varieties that have blast disease resistance.

Assessment of Bread Wheat Genotypes (Triticum aestivum L.) with GGE Biplot and AMMI Model in Multiple Environments

Wheat is one of the products with the widest cultivation area and adaptation ability in the world. Although the heritability of the variety is important in grain yield, the environment and genotype x environment interaction is significantly effective. This study was carried out in 6 different environments. According to the Additive Main Effect and Multiplication Interaction (AMMI) model; genotype, environment and genotype x environment interaction were found to be effective on grain yield, respectively, by 9.40%, 56.79% and 16.28%. It has been determined that, there is a positive relationship between grain yield and the number of spike per square meter and the number of grain in each spike. In the study, 3 mega environments were formed. G19 in the first mega environment, G13 in the second mega environment and G21, G22 in the third mega environment came to the fore. G9, G13 and G19 were seen as hopeful lines in the grain yield. Also, E5 was the ideal environment and, G19 had the highest adaptability and grain yield. It has been concluded that G19 may be a candidate for variety because genotypes that are stable in different environmental conditions are preferred by the producers.

Estratégias de seleção de linhagens de feijão-comum quanto à produtividade e à qualidade comercial de grãos

Abstract The objective of this work was to evaluate common bean lines for yield and commercial grain quality in multi-environments, and to maximize the efficiency of selection using complementary methods. Over three crop years, 79 trials using carioca common bean lines were carried out in the dry, winter, and rainy crop seasons, in the Southern, Southeastern, Midwestern, and Northeastern regions of Brazil. The experimental design was a randomized complete block with three replicates and 17 genotypes. The evaluated traits were: grain yield (GY), grain appearance (GA), sieve yield (SY), and 100-seed weight (100SW). Adaptability and stability analyses were carried out using models that consider the genotype effect as fixed or as random, in a mixed-model perspective. A significant interaction between genotypes and environments was observed for all traits evaluated. The CNFC 15086 line presented the highest GY and 100SW, besides a high adaptability and stability. The most prominent line for GA was CNFC 15038. The CNFC 15097 line is recommended as a cultivar (BRS FC406) because it shows, simultaneously, favorable performances for GY, GA, SY, and 100SW, as well as for adaptability and stability.

Post punching shear pattern and progressive collapse of flat slab building

Abstract The possibility of the occurrence of a second punching shear failure and of a Progressive Collapse after a punching shear failure had occurred in one flat slab column connection is investigated in two building structures, using Eberick and SAP2000 softwares and the Yield Line Method, and codes ACI318:2019, EUROCODE2:2004 and NBR6118:2014. It is shown that slab column connections should be designed and detailed to prevent Progressive Collapse and that Integrity Reinforcement should always be present, and that the remaining capacity of floors after punching failures depends on the i) post-punching resistance of the connection being punched; ii) post-punching resistance of the neighbors’ connections; iii) flexural resistance of the slabs, and that the flexural resistance of the slab’s floors can be evaluated by the Yield Line Method.

Flexural Capacity of Cross-Shaped Concrete-Filled Steel Tubular Column–Steel Beam Joints with Side-Plate Connections

The application of connection joints between a cross-shaped concrete filled steel tubular column and a steel beam can improve the seismic performance, which also provides an effective way for saving building space. In this paper, models and flexural capacity of the connection joint with and without side plates were designed and evaluated, respectively. A refined mechanical analysis model of a joint subjected to low-cycle reciprocating loading was established using the finite element software ABAQUS. The failure characteristics of the joints with and without side plates were compared. The influence of axial compression ratio, side plate height, and side plate thickness on the flexural capacity of joints with side plates was studied. Moreover, the failure mode and force transfer mechanisms of these joints were analyzed. Based on the results of the finite element analysis (FEA), the ultimate tensile capacity of the steel tube column flange to the steel beam was calculated according to the yield line theory; the tension transmitted by the side plate was simplified for calculation via the static equilibrium method. Subsequently, the formula for calculating the flexural capacity of the joint with side plates is established. The results show that the ultimate bearing capacity of the joint was increased by 41.5% due to side plates effect, which decreased with an increasing axial compression ratio. Moreover, the ultimate bearing capacity of the joints increase slightly with an increase of height and thickness of the side plate, and the maximum increase was only 6.2%. In addition, the calculated results obtained by the proposed formula of ultimate flexural capacity are consistent with the results of the FEA.

Development of Moment Coefficients For Two Adjacent Side Supported Slab By Using Yield Line Theory

The slab is a key and generally used structural component. The shape, arrangement, and stiffness of the supporting beams all have a significant role in the slab's performance.IS 456:2000 coefficients are only applicable to rectangular slabs with four non-yielding side supports. But due to architectural requirements, structural engineers are now confronted with a variety of complications, such as slabs supported on two adjacent sides. In the past analytical model was suggested for slab supported over two adjacent edges carrying uniformly distributed area load but design aids were not prepared. The analytical model presented herein to analyze two adjacent edges supported slab carrying uniformly distributed area load on its top edge using yield line analysis. It is also validated with well-established literature. Design aids are also prepared and validated with FE nonlinear analysis in software ATENA and the results are in favour.

The Impact of Seeding Rate and Locations on Some Grass Pea (Lathyrus sativus) Lines for Growth, Forage and Seed Yield in Sulaimani Region

This study was carried out at two locations in Sulaimani governorate, Qlyasan and Kanipanka, during the winter season of 2017-2018 to evaluate the response of four lines of Grass pea Lathyrus sativus (IF 003, IF 133, IF 102, IF 067) lines and four seeding rates (80kg/h, 100kg/h, 120kg/h, 140kg/h). The experiment was conducted at (December 5th /2018) in Kanipanka and (December 6th /2018) at Qlyasan. The design of factorial experiment RCBD with three replications was conducted. Means comparison was carried out by the least significant difference (L.S.D) at a significant level of 5%. The results confirmed that the grass pea lines, as the average of both locations there were highly significant differences among lines due to plant height, days to %50 flowering, leaf dry weight, and number of bacterial nodules/plant, but significant differences were observed for the character stem dry weight... It was noticed that the effect of locations on growth and forage characters for grass pea was highly significant for the days to maturity, leaf dry weight, stem dry weight, leaf stem ratio and number of bacterial nodules/plant, while it was significant for the character plant height. It was indicated that the second location recorded the highest value for plant height, leaf dry weight, stem dry weight, leaf stem ratio and number of bacterial nodules/plant with 60.080cm, 1.970g, 1.850g, 2.600 and 16.390 respectively. At the average of both locations there were differences highly significant among lines due to days to maturity, leaf dry weight, stem dry weight, leaf stem ratio and number of bacterial nodules/plant. Line number IF067 produced the highest value for days to maturity and stem dry weight and number of bacterial nodules/plant with 155.6 days, 4.990 g and 14.27 respectively. The effect of seeding rate on seed yield and it is components for grass pea at the average of both locations and there was highly significant for the number of pod/plant, seed yield, biological yield, and harvest index significant for 100 seed weight. As the average of both locations using 140 kg/h seeds produced maximum values for the most characters.

Design of steel transmission pole base plates using yield line method

Steel transmission poles are widely used for their strength, ease of construction, small footprint, and aesthetic appearance. These poles can be either directly embedded into their foundations or supported on based plates which are connected to the reinforced concrete footings via group of anchor bolts.There are few available published methods for the analysis and design of this type of base plate connection. These methods are not widely used in the industry as they are either complex, lack solid theoretical background, or yield results that are not consistent with manufacturer's time-tested proprietary design methods. Therefore, there is a need for an accurate method suitable for technical or design office for designing these connections when subjected to axial loads, bending moments or the combined effect of both.This paper presents a numerical study performed on the base plates of polygonal steel poles that are supported directly on anchor bolts with levelling nuts and subjected to bending moment and axial load. The Finite Element (FE) analysis part of the work is carried out using ADINA software and the results obtained from the analyses are compared with published experimental results from which it is concluded that the finite element model can accurately predict the behaviour of these connections.Parametric investigation is then conducted to gain more insight into the behaviour of these base plate connections and to use the obtained data the validation of the proposed design method. The parametric investigation covered the behaviour of these connections under pure axial load and pure bending moment while the varying parameters considered included number of shaft sides, base plate thickness, number of anchor bolts and anchor bolt diameter.Design formulae based on the yield line theory are then proposed and a comparison between the yield loads calculated using the proposed expressions and finite element results is presented. The yield loads resulting from using the proposed design method agreed with the finite element results with a maximum calculated difference of 13%.

Cyclic behavior and mechanical model of a novel endplate connection to double-skin composite wall with slip-critical blind bolts

This paper presents an assembled bolted endplate joint for connecting steel beams and double-skin composite walls (DSCWs). The slip-critical blind bolts (SCBBs) were utilized in this novel joint to decrease welding work on-site. In order to investigate the seismic performance of this novel joint, two full-scale beam-to-wall SCBB endplate connection specimens with different design parameters were tested under incremental cyclic loading. Two failure modes of the specimens, namely beam bucking (mode I) and column wall damage (mode II), were finally observed. Analyses of test results indicated that a properly designed SCBB endplate connection with failure mode I could exhibit stable load-bearing capacity and satisfactory energy dissipating capacity. On the contrary, failure mode II should be avoided in engineering due to its unacceptable performance. Finite element models (FEMs) were developed and validated subsequently to further investigate the interior stress and damage distribution. The parametric analysis was also conducted using the FEMs. Based on the experimental results and numerical analyses, an alternative mechanical model was proposed to predict the bending resistance capacity of the column wall. The segmentation method was adopted in the model to eliminate the dependency on a specific pattern of yield line without reducing the accuracy. The reliability of the strength-prediction model of the column wall was validated through the results of the parametric analysis. The design methods and specifications for the components of the joint were finally summarized to make the SCBB endplate connection effectively used in practical applications.

Torsional and compression loading of paperboard packages: Experimental and FE analysis

The present study investigates torsional and compressive loading of a paperboard package. Finite element (FE) analyses simulating the tests were performed to improve understanding of the stresses and deformations in the paperboard during loading. A simple experimental characterization of the necessary material properties could be performed to represent the multi‐ply paperboard as a single‐ply structure. The results from the single‐ply model were compared with a laminate model, and the differences between the models were small. Comparing experimental and FE simulations of box compression and torsion showed that the FE models could accurately predict the response curves. However, in the simulations, there was an overprediction of the maximum compressive force and maximum torque, which was expected since geometrical imperfections and the heterogeneous internal structure of the material were not accounted for in the material model or the FE model. Local yield lines formed at the onset of non‐linearities in the package load–displacement curves. Therefore, the strength of the paperboard affects the maximum compressive strength and maximum torque, and the bending stiffness of the paperboard only had a minor effect. When a first local maximum was reached, the number of FE that reached the failure stress increased exponentially. The simulations also showed that box compression was not an effect of package height, but higher packages had a lower maximum torque.

Flexural performance of weld-strengthened steel beam-square column joints subjected to axial column loading

This study proposes a novel strengthened joint with external rib plates for the H-shaped-beam square-column (HBSC) steel frame. The thermal effect of welding under load on the flexural performance of this joint was examined experimentally, numerically, and theoretically, both during and after the welding process. The following significant findings have been reported. The rib plates do not convey the axial pressure when welded to the column wall; consequently, the maximum thermal strain occurs on the column wall below the weld seams, reducing the column's stiffness and negatively contributing to the joint's flexural resistance. While the rib plates transmit force when they are welded to the angle steel, at this time, the rib plates experience the most significant thermal strain. The thermal effects of welding have been evaluated using a finite element model (FEM). Considering thermal effects, the FEM suggests a reduction factor of 0.90 for the load-bearing capacity. The yield strength of the strengthened joint is roughly double that of the unstrengthened joint, indicating that the reinforcement is effective. The initial stress ratio of the column must be kept below 0.7 to limit the rate at which the yield strength of the strengthened joint decreases as the compressive load increases. The stress distribution ratio between the vertical rib and the column wall has been determined using a simplified mechanical model. Based on the yield line principle, a formula for calculating the yield capacity of the strengthened joint has been derived.