• Computers and Concrete
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• v.19 no.1
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• pp.51-58
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• 2017

The paper presents the experimental investigations for studying the effect of ground granulated blast furnace slag (GGBFS) on the time-dependent deflection of reinforced concrete (RC) beams due to creep and shrinkage. The RC beams were reinforced with 2-10 mm bars at tension side and subjected to constant sustained two-point loading for the period of 150 days. The amount of cement replacement by GGBFS was varied from 0 to 60% with an increment of 20%. The total deflection was measured at different ages of up to 150 days under sustained loads. The experiments revealed that the time-dependent deflection of the reinforced concrete RC beams containing GGBFS was higher than that of plain concrete RC beams. At 150 days, the average creep and shrinkage deflection of RC beams containing 20%, 40% and 60% GGBFS was 1.25, 1.45 and 1.75 times higher than the plain concrete beams. A new model, which is an extension of authors' earlier model, is proposed to incorporate the effect of GGBFS content in predicting the long-term deflection of RC beams. Besides validating the new model with the current data with higher percentage of tension reinforcement, it was also used to predict the authors' earlier data containing lesser percentage of tension reinforcement with reasonable accuracy.

• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.531-546
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• 1999

The paper presents an experimental and theoretical study on the influence of steel fibers and longitudinal tension and compression reinforcements on immediate and long-term deflections of high-strength concrete beams of 85 MPa (12,300 psi) compressive, strength. Test results of eighteen beams subjected to sustained load for 180 days show that the deflection behavior depends on the longitudinal tension and compression reinforcement ratios and fiber content; excessive amount of compression reinforcement and fibers may have an unfavorable effect on the long-term deflections. The beams having the ACI Code's minimum longitudinal tension reinforcement showed much higher time-dependent deflection to immediate deflection ratio, when compared with that of the beams having about 50 percent of the balanced tension reinforcement. The results of theoretical analysis of tested beams and those of a parametric study show that the influence of steel fibers in increasing the moment of inertia of cracked transformed sections is most pronounced in beams having small amount of longitudinal tension reinforcement.

• Steel and Composite Structures
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• v.39 no.1
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• pp.21-33
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• 2021

This paper aims to improve the current state-of-the-art in long-term deflection prediction in steel-concrete composite beams. The efficiency of a time-dependent finite element model based on linear creep theory is verified with available experimental data. A parametric numerical study is then carried out, which focuses on the effects of concrete creep and/or shrinkage, ultimate shrinkage strain and reinforcing bars in the slab. The study shows that the long-term deformations in composite beams are dominated by concrete shrinkage and that a higher area of reinforcing bars leads to lower long-term deformations and steel stresses. The AISC model appears to overestimate the shrinkage-induced deflection. A modified ACI equation is proposed to quantify time-dependent deflections in composite beams. In particular, a modified reduction factor reflecting the influence of reinforcing bars and a coefficient reflecting the influence of ultimate shrinkage are introduced in the proposed equation. The long-term deflections predicted by this equation and the results of extensive numerical analyses are found to be in good agreement.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.157-169
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• 2011

In this paper the time-dependent closed-form static solution of the suspended pre-stressed biconcave and biconvex cable trusses with unmovable, movable and elastic or viscoelastic yielding supports subjected to various types of vertical load is presented. Irvine's forms of the deflections and the cable equations are modified because the effects of the rheological behaviour needed to be incorporated in them. The concrete cable equations in the form of the explicit relations are derived and presented. From a solution of a vertical equilibrium equation for a loaded cable truss with rheological properties, the additional vertical deflection as a time-function is determined. The time-dependent closed-form model serves to determine the time-dependent response, i.e., horizontal components of cable forces and deflection of the cable truss due to applied loading at the investigated time considering effects of elastic deformations, creep strains, temperature changes and elastic supports. Results obtained by the present closed-form solution are compared with those obtained by FEM. The derived time-dependent closed-form computational model is used for a time-dependent simulation-based reliability assessment of cable trusses as is described in the second part of this paper.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.11a
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• pp.647-650
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• 2003

Under sustained loads, the deformation of a structure gradually increase with time and eventually may be much greater than its instantaneous value, This inelastic and time-dependent deformation causes increase in deflection and curvature, redistribution of stress and internal action, In this paper, time-dependent analysis with creep and shrinkage of uncracked and cracked partially prestressed concrete flexural members is presented.

• Computers and Concrete
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• v.14 no.4
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• pp.419-444
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• 2014

In this study experimental result of a total of eight SCC and FRSCC slabs with the same cross-section were monitored for up to 240 days to measure the time-dependent development of cracking and deformations under service loads are presented. For this purpose, four SCC mixes are considered in the test program. This study aimed to compare SCC and FRSCC experimental results with conventional concrete experimental results. The steel strains within the high moment regions, the concrete surface strains at the tensile steel level, deflection at the mid-span, crack widths and crack spacing were recorded throughout the testing period. Experimental results show that hybrid fibre reinforced SCC slabs demonstrated minimum instantaneous and time-dependent crack widths and steel fibre reinforced SCC slabs presented minimum final deflection.

• Structural Engineering and Mechanics
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• v.22 no.2
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• pp.197-222
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• 2006

In this paper, the non-linear time-dependent closed-form, discrete and combined solutions for the post-elastic response of a geometrically and physically non-linear suspended cable to a uniformly distributed load considering the creep effects, are presented. The time-dependent closed-form method for the particularly straightforward determination of a vertical uniformly distributed load applied over the entire span of a cable and the accompanying deflection at time t corresponding to the elastic limit and/or to the elastic region, post-elastic and failure range of a suspended cable is described. The actual stress-strain properties of steel cables as well as creep of cables and their rheological characteristics are considered. In this solution, applying the Irvine's theory, the direct use of experimental data, such as the actual stress-strain and strain-time properties of high-strength steel cables, is implemented. The results obtained by the closed-form solution, i.e., a load corresponding to the elastic limit, post-elastic and failure range at time t, enable the direct use in the discrete non-linear time-dependent post-elastic analysis of a suspended cable. This initial value of load is necessary for the non-linear time-dependent elastic and post-elastic discrete analysis, concerning incremental and iterative solution strategies with tangent modulus concept. At each time step, the suspended cable is analyzed under the applied load and imposed deformations originated due to creep. This combined time-dependent approach, based on the closed-form solution and on the FEM, allows a prediction of the required load that occurs in the post-elastic region. The application of the described methods and derived equations is illustrated by numerical examples.

• Journal of the korean Society of Automotive Engineers
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• v.8 no.4
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• pp.66-72
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• 1986

Numerical analysis has been made on the dynamic behavior of a supporting structure subjected to a force of time dependent frequency. The effect of solid viscosity is studied when the frequency of external force passes through the first critical frequency of the simple beam for four times. Within the Euler-Bernoulli beam theory, the solutions are obtained by using finite Fourier and Laplace transformation methods with respect to space and time variables. The result shows that the maximum value of the dynamic deflection is considerably affected by the value of the solid viscosity as well as the frequency difference The maximum dynamic deflection is found to occur in the frequency lower limit C of 0.85-0.985 in the presence of the solid viscosity.

• Computers and Concrete
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• v.12 no.6
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• pp.739-754
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• 2013

Creep and shrinkage have pronounced effects on the long-term deflection of prestressed concrete members. Under repeated loading, the rate of creep in prestressed concrete members is often accelerated. In this paper, an iterative computational procedure based on the well known Model B3 for creep and shrinkage was developed to predict the time-dependent deflection of partially prestressed concrete members. The developed model was validated using the experimental observed deflection behavior of a simply supported partially prestressed concrete beam under repeated loading. The validated model was then employed to make predictions of the long-term deflection of the prestressed beams under a variety of conditions (e.g., water cement ratio, relatively humidity and time at drying). The simulation results demonstrate that ignoring creep and shrinkage could lead to significant underestimation of the long-term deflection of a prestressed concrete member. The model will prove useful in reducing the long-term deflection of the prestressed concrete members via the optimal selection of a concrete mix and prestressing forces.

• Journal of Biosystems Engineering
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• v.18 no.3
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• pp.262-269
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• 1993

Stress relaxation behaviors of the cucumber under bending moment were tested with UTM at three levels of loading rate and initial deflection ratio. Sample cucumber was selected from three cultivars of cucumber, Cheongjangmadi, Baekdadagi, and Gyeousalicheongjang, because these cultivars are the most popular grown cultivars in Korea. When the bending moment was applied to the cucumber sample, the effective span between simple supports was held a constant value of 116mm with consideration of the selected sample length. The objectives of this study were to develop the rheological models such as linear and nonlinear models of the stress relaxation for the cucumber samples, and to investigate the effects of loading rate and initial deflection ratio on the stress relaxation behavior of the cucumber. The results of this study may be summarized as follows : 1. Stress relaxation behavior of the cucumber could be well described by the generalized Maxwell model for each level of deflection ratio. But the stress relaxation behavior of the sample was found to be initial deflection ratio and time dependent, and it was represented the nonlinear viscoelastic model as a function of initial deflection ratio and time. 2. Stress relaxation behavior of the cucumber samples was very highly affected by the loading rate and the initial deflection ratio. The more loading rate and initial deflection ratio resulted in the more initial bending stress and after stress relaxation progressed more rapidly. 3. At the same test conditions, it was found that the stress relaxation rate of Cheongjangmadi was faster than that of other cultivars.