• Computational Structural Engineering
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• v.7 no.4
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• pp.10-16
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• 1994

근본적으로 터널을 정확히 해석하려면 3차원 해석이 필요하다. 그러나 3차원 해석은 다루어야 할 자료가 방대하고 또한 시공 단계를 고려하는 3차원 소성해석을 정확히 하기 위해서는 슈퍼컴퓨터와 같은 컴퓨터 파워가 요구된다. 따라서 터널의 해석에서는 대개 하중분배율법을 사용하여 2차원 해석을 수행하고 있는 실정이다. 그러나 하중분배율법에 의한 2차원 해석의 결과는 선택한 하중분배율법에 의존함으로 정확한 하중분배율을 아는 것이 중요하다. 2차원 터널해석을 정확히 하기 위해서는 본문에 기술한 요건을 갖춘 프로그램의 확보, 하중분배율에 대한 정확한 평가, 측압 계수의 신중한 선택, 주위 지반의 물성에 대한 신중한 평가가 필요하다.

• Journal of the Korea Concrete Institute
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• v.28 no.3
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• pp.257-265
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• 2016

The failure behavior of reinforced concrete beams is governed by the mechanical relationships between the shear span-to-effective depth ratio, flexural reinforcement ratio, load and support conditions, and material properties. In this study, two simple indeterminate strut-tie models which can reflect all characteristics of the failure behavior of reinforced concrete beams were proposed. The proposed models are effective for the beams with shear span-to-effective depth ratio of less than 3. For each model, a load distribution ratio, defined as the fraction of load transferred by a truss mechanism, is also proposed to help structural designers perform the rational design of the beams by using the strut-tie model approaches of current design codes. In the determination of the load distribution ratios, the effect of the primary design variables including shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete was reflected through numerous material nonlinear analysis of the proposed indeterminate strut-tie models. In the companion paper, the validity of the proposed models and load distribution ratios was examined by applying them to the evaluation of the failure strength of 335 reinforced concrete beams tested to failure by others.

• Geotechnical Engineering
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• v.14 no.5
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• pp.5-16
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• 1998

2-D numerical methods have been applied to analyze the stability of tunnels because of computation efficiency, though the ground around the tunnel under construction shows 3-D reformational behaviour due to the transverse and longitudinal arching effects. Load distribution factors are introduced to the 2-D analysis for the consideration of the effects of the tunnel advance in three dimensions. The load distribution factors influence significantly the ground deformation and the load of primary supports like shotcrete and rockbolts. According to the previous studies for 3-D numerical studies. it was shown that load distribution factors were heavily dependent on the ground deformational properties, tunnel size and the advance length of a tunnel. However, as the quantitative methods evaluating the factors have not been presented yet, constant values have been assigned to the factors for 2-D analysis even if the conditions for tunnel design are different. Accordingly, this paper presents the method to evaluate quantitatively the load distribution factors through the regression analysis of 3-D analysis data on 72 design cases. Also, new modification to the load distribution factors are suggested for the ring-cut excavation method because the conventional 2-D analysis is not able to consider the support effects of the core left on the tunnel face.

• Tunnel and Underground Space
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• v.21 no.3
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• pp.192-204
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• 2011

In this study, 3-D analyses were conducted while taking every construction stage into account. Then 2-D analyses were conducted which yield the same results with the 3-D results. The crown settlement normalized by the ultimate value was compared during the process to overcome the discrepancy caused by different dimensions. When a bench or a core is left uncut to give extra support to the face and eventually the whole excavation boundary, this extra supporting effect also has to be included in the analysis. In this study, this effect is also implemented in terms of the load distribution factor. When the length of the bench is very short compared to the diameter of the tunnel in such cases as in short bench cut or in mini-bench cut, the supporting effect of the face does not disappear even after the bench is completely excavated and supported since the face is still too close to the point of interest. The 4th load distribution factor was defined to stand for the advance of the face after the completion of the excavation cycle. The 4th load distribution factor turned out to be very useful in determining the load distribution factors when a tunnel is excavated by bench cut with various bench lengths under different initial conditions.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.7
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• pp.2702-2707
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• 2010

The load distribution factor (LDF) values of new composite I-beam panel bridges that were subjected to dead load were investigated using three-dimensional finite element analyses with the computer program ABAQUS(2007). This study considered some design parameters such as the slab thickness, the steel-plate thickness, and the span length for design of new composite bridges. The distribution values that were obtained from these analyses were compared with those from the AASHTO Standard, AASHTO LRFD, and the equations presented by Tarhini and Frederick, and Back and Shin. For the simple application of the design, bridge engineers can use the LDF of 0.67 for the exterior girder and of 0.340 for the interior girder.

• Journal of the Korea Concrete Institute
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• v.28 no.3
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• pp.267-278
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• 2016

In this study, the ultimate strength of 335 simply supported reinforced concrete beams with shear span-to-effective depth ratio of less than 3 was evaluated by the ACI 318-14's strut-tie model approach implemented with the indeterminate strut-tie models and load distribution ratios of the companion paper. The ultimate strength of the beams was also estimated by using the experimental shear strength models, the theoretical shear strength models, and the current strut-tie model design codes. The validity of the proposed strut-tie models and load distribution ratios was examined by comparing the strength analysis results classified according to the prime design variables of the shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete.

• Journal of the Korea Concrete Institute
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• v.23 no.1
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• pp.3-12
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• 2011

The structural behavior of continuous reinforced concrete deep beams is mainly controlled by the mechanical relationships associated with the shear span-to-effective depth ratio, flexural reinforcement ratio, load and support conditions, and material properties. In this study, a simple indeterminate strut-tie model which reflects characteristics of the complicated structural behavior of the continuous deep beams is presented. In addition, the reaction and load distribution ratios defined as the fraction of load carried by an exterior support of continuous deep beam and the fraction of load transferred by a vertical truss mechanism, respectively, are proposed to help structural designers for the analysis and design of continuous reinforced concrete deep beams by using the strut-tie model approaches of current design codes. In the determination of the load distribution ratio, a concept of balanced shear reinforcement ratio requiring a simultaneous failure of inclined concrete strut and vertical steel tie is introduced to ensure a ductile shear failure of reinforced concrete deep beams, and the primary design variables including the shear span-to-effective depth ratio, flexural reinforcement ratio, and concrete compressive strength are implemented after thorough parametric numerical analyses. In the companion paper, the validity of the presented model and load distribution ratio was examined by applying them in the evaluation of the ultimate strength of multiple continuous reinforced concrete deep beams, which were tested to failure.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.4
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• pp.1065-1079
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• 2014

The ultimate behavior of reinforced concrete corbel is complicated due to the primary design variables including the shear span-to-effective depth ratio a/d, flexural reinforcement ratio, load condition, and material properties. In this study, a simple indeterminate strut-tie model reflecting all characteristics of the ultimate strength and complicated structural behavior is proposed for the design of the reinforced concrete corbels with shear span-to-effective depth ratio of $a/d{\leq}1$. A load distribution ratio, defined as the fraction of applied load transferred by horizontal truss mechanism, is also proposed to help structural designers perform the design of reinforced concrete corbels by using the strut-tie model approaches of current design codes. For the development of the load distribution ratio, numerous material nonlinear finite element analyses of the proposed indeterminate strut-tie model were conducted by changing primary design variables. The ultimate strengths of reinforced concrete corbels tested to failure were evaluated by incorporating the proposed strut-tie model and load distribution ratio into the ACI 318-11's strut-tie model method. The validity of the proposed model and load distribution ratio was examined by comparing the strength analysis results with those by the ACI 318-11's conventional design method and strut-tie model methods of current design codes.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.2A
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• pp.259-267
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• 2008

The ultimate strengths of reinforced concrete deep beams are governed by the capacity of the shear resistance mechanism composed of concrete and shear reinforcing bars, and the structural behaviors of the beams are mainly controlled by the mechanical relationships according to the shear span-to-effective depth ratio, flexural reinforcement ratio, load and support conditions, and material properties. In this study, a simple indeterminate strut-tie model reflecting all characteristics of the ultimate strengths and complicated structural behaviors is presented for the design of simply supported reinforced concrete deep beams. In addition, a load distribution ratio, defined as a magnitude of load transferred by a vertical truss mechanism, is proposed to help structural designers perform the design of simply supported reinforced concrete deep beams by using the strut-tie model approaches of current design codes. In the determination of a load distribution ratio, a concept of balanced shear reinforcement ratio requiring a simultaneous failure of inclined concrete strut and vertical steel tie is introduced to ensure the ductile shear failure of reinforced concrete deep beams, and the prime design variables including the shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete influencing the ultimate strength and behavior are reflected upon based on various and numerous numerical analysis results. In the companion paper, the validity of presented model and load distribution ratio was examined by employing them to the evaluation of the ultimate strengths of various simply supported reinforced concrete deep beams tested to failure.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.2A
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• pp.269-279
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• 2008

In this study, the ultimate strengths of 229 simply supported reinforced concrete deep beams tested to shear failure were evaluated by the ACI 318-05's strut-tie model approach implemented with the presented indeterminate strut-tie model and its load distribution ratio. The ultimate strengths of the deep beams were also estimated by the experimental shear equations, design codes that were based on experimental and theoretical shear strength models, and current strut-tie model design codes. The validity of the present strut-tie model and its load distribution ratio was examined through the comparison of the strength analysis results classified according to the prime design variables of the shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete.