• Steel and Composite Structures
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• v.6 no.1
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• pp.15-31
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• 2006

Beams with web openings are an attractive system for multi-storey buildings where it is always desirable to have long spans. The openings in the web of steel beams enable building services to be integrated within the constructional depth of a floor, thus reducing the total floor depth. At the same time, the increased beam depth can give high bending moment capacity, thus allowing long spans. However, almost all of the research studies on web openings have been concentrated on beam behaviour at ambient temperature. In this paper, a preliminary numerical analysis using ABAQUS is conducted to develop a general understanding of the effect of the presence of web opening on the behaviour of steel beams at elevated temperatures. It is concluded that the presence of web openings will have substantial influence on the failure temperatures of axially unrestrained beams and the opening size at the critical position in the beam is the most important factor. For axially restrained beams, the effect of web openings on the beam's large deflection behaviour and catenary force is smaller and it is the maximum opening size that will affect the beam's response at very high temperatures. However, it is possible that catenary action develops in beams with web openings at temperatures much lower than the failure temperatures of the same beam without axial restraint that are often used as the basis of current design.

• Structural Engineering and Mechanics
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• v.76 no.3
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• pp.395-412
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• 2020

In this article, the values of internal force and deformation of a curved beam under any action with the firm or elastic supports are determined by using structural matrices. The article presents the general differential formulation of a curved beam in global coordinates, which is solved in an orderly manner using simple integrals, thus obtaining the transfer matrix expression. The matrix expression of rigidity is obtained through reordering operations on the transfer notation. The support conditions, firm or elastic, provide twelve equations. The objective of this article is the construction of the algebraic system of order twenty-four, twelve transfer equations and twelve support equations, which relates the values of internal force and deformation associated with the two ends of the directrix of the curved beam. This final algebraic system, expressed in matrix form, is divided into two subsystems: twelve algebraic equations of internal force and twelve algebraic equations of deformation. The internal force and deformation values for any point in the curved beam directrix are determined from these values in the initial position. The five examples presented show how to apply the matrix procedures developed in this article, whether they are curved beams with the firm or elastic support.

• Structural Engineering and Mechanics
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• v.59 no.5
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• pp.933-950
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• 2016

Decks, interior beams, edge beams and girders are the parts of a steel floor system. If the deck is optimized without considering beam optimization, finding best result is simple. However, a deck with higher cost may increase the composite action of the beams and decrease the beam cost reducing the total cost. Also different number of floor divisions can improve the total floor cost. Increasing beam capacity by using castellated beams is other efficient method to save the costs. In this study, floor optimization is performed and these three issues are discussed. Floor division number and deck sections are some of the variables. Also for each beam, profile section of the beam, beam cutting depth, cutting angle, spacing between holes and number of filled holes at the ends of castellated beams are other variables. Constraints include the application of stress, stability, deflection and vibration limitations according to the load and resistance factor (LRFD) design. Objective function is the total cost of the floor consisting of the steel profile cost, cutting and welding cost, concrete cost, steel deck cost, shear stud cost and construction costs. Optimization is performed by enhanced colliding body optimization (ECBO), Results show that using castellated beams, selecting a deck with higher price and considering different number of floor divisions can decrease the total cost of the floor.

• Steel and Composite Structures
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• v.8 no.3
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• pp.217-230
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• 2008

The increasing use of performance-based approaches in structural fire engineering design of multi-storey composite buildings has prompted the development of various tools to help quantify the influence of tensile membrane action in composite slabs at elevated temperatures. One simplified method which has emerged is the Bailey-BRE membrane action method. This method predicts slab capacities in fire by analysing rectangular slab panels supported on edges which resist vertical deflection. The task of providing the necessary vertical support, in practice, requires protecting a panel's perimeter beams to achieve temperatures of no more than $620^{\circ}C$ at the required fire resistance time. Hence, the integrity of this support becomes critical as the slab and the attached beams deflect, and large deflections of the perimeter beams may lead to a catastrophic failure of the structure. This paper presents a finite element investigation into the effects of vertical support along slab panel boundaries on the slab behaviour in fire. It examines the development of the membrane mechanism for various degrees of edge-beam protection, and makes comparisons with predictions of the membrane action design method and various acceptance criteria.

• Journal of the Korea Concrete Institute
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• v.18 no.5 s.95
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• pp.639-648
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• 2006

A shear experiment of one-way monotonic loading was carried out with the shear span ratio as the main experimental variable for reinforced concrete beam. Using the finite element analysis as the experimental analysis tool and the analysis method to compute the shear resistance of small shear span ratio, a new macro-model composed of crooked main strut and sub strut is proposed in consideration of the effect of bond action between re-bar and concrete based on the experimental result. The experimental finding affirmed the validity of the proposed macro-model when the shear span ratio was at or below 0.75 and confirmed that the experimental result was the most consistent with the computed analysis result when the effective factor of concrete compressive strength was set at 0.75.

• Steel and Composite Structures
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• v.8 no.1
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• pp.1-18
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• 2008

Observations from experiments and real fire indicate that restrained steel beams have better fire-resistant capability than isolated beams. Due to the effects of restraints, a steel beam in fire condition can undergo very large deflections and the run away damage may be avoided. In addition, axial forces will be induced with temperature increasing and play an important role on the behaviour of the restrained beam. The factors influencing the behavior of a restrained beam subjected to fire include the stiffness of axial and rotational restraints, the load type on the beam and the distribution of temperature in the cross-section of the beam, etc. In this paper, a simplified model is proposed to analyze the performance of restrained steel beams in fire condition. Based on an assumption of the deflection curve of the beam, the axial force, together with the strain and stress distributions in the beam, can be determined. By integrating the stress, the combined moment and force in the cross-section of the beam can be obtained. Then, through substituting the moment and axial force into the equilibrium equation, the behavior of the restrained beam in fire condition can be worked out. Furthermore, for the safety evaluation and repair after a fire, the behaviour of restrained beams during cooling should be understood. For a restrained beam experiencing very high temperatures, the strength of the steel will recover when temperature decreases, but the contraction force, which is produced by thermal contraction, will aggravate the tensile stresses in the beam. In this paper, the behaviour of the restrained beam in cooling phase is analyzed, and the effect of the contraction force is discussed.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.11a
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• pp.229-233
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• 2003

This paper describes a practical formulation of Non-Bernoulli-Compatibility Truss Model. Not only equilibrium conditions but also some approximations are employed to solve for the unknowns included in the proposed model. By assuming that the ratio of $V_a$ to V remains to be constant along the shear span, the relationship between $\alpha$ and z is mathematically established as an arch shape function. $V_m$ is also approximated to be an empirical value that is equal to the least membrane shear strength. The coefficient a is made utilizing a nonlinear finite element analysis. The adequacy of the model is examined by test results available in literatures, and the predicted values are shown to be in excellent agreement with the experimental results.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.11a
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• pp.275-278
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• 2005

This paper presents a model for evaluating the contribution by arch action and frame action to shear resistance in shear-critical reinforced concrete beams without stirrup. The rotating angle softened truss model is employed to calculate the shear deformation of the web and the relative axial displacement of the compression and tension chord by the shear flow are also calculated. From this shear compatibility condition in a beam, the shear contribution by the arch action is numerically decoupled. The transverse strain obtained from the proposed model is selected for shear failure criterion. Using the failure criterion, shear strength of RC slender beams without stirrup is predicted.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.677-697
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• 2010

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.1
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• pp.23-31
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• 2011

This study carried out shear experiment for concrete deep beam reinforced FRP(Fiber Reinforced Polymers) bar to investigate shear strength of deep beam. The test conducted for 15 specimens, and the variables were shear span-to-depth ratio, reinforcement ratio, effective depth, reinforcement components of shear strength. crack, deflection are investigated based on shear experimental. We compared shear strength using ACI 318-08 STM with proposed equations that considered arching action according to shear span-to-depth ratio. Consequently shear strength of deep beam reinforced FRP bar presented higher shear strength than steel bar. ACI STM's predictions are better accurate than other predicting equations.