Load Reduction Factor Research Articles

Study on interaction of Viscoelastic and Mechano-sorptive creep and effect of Fibre Reinforcement on creep of Timber beams

Timber is a sustainable material widely used in structural elements. Its viscoelastic nature, in which the stress-strain relation varies with time, poses significant challenge to the durability of timber structures. Creep of timber under constant loading depends on various factors like stress level, moisture content, load-to-grain angle, temperature, relative humidity etc. Among these, relative humidity and moisture content in timber are the most crucial. Drastically varying moisture content causes mechano-sorptive creep. However, the interaction and contribution of various factors causing creep is still a matter of research. Various codes provide generalized creep coefficient for long term deflection and load reduction factors. A detailed rheological model was proposed by Toratti which addresses mechano-sorptive creep explicitly, incorporating both recoverable and irrecoverable part in creep. This paper aims to review the study on interaction between viscoelastic creep and Mechano-sorptive creep in various environmental conditions. Effect of reinforcing timber beams, on the long term deflection due to creep is also made a subject of study to identify a possible solution to the accelerated deflection by Mechano-sorptive creep, which will be unavoidable in tropical areas with extreme climactic changes. A comparative study between the various standard codes with Indian Standard Codes for timber with respect to creep, is also made, to identify the gaps in IS codes.

Fracture investigation at 300oC on carbon-steel and austenitic stainless-steel pipes of NPPs under cyclic loads

The Leak-Before-Break (LBB) of high enthalpy piping of Indian NPPs require fracture stability demonstration of pipelines with postulated cracks under design basis earthquake loads. Earlier large number of cyclic fracture and corresponding monotonic fracture tests on large sized pipe components were conducted at room temperature. In current program, monotonic/cyclic fracture experiments are extended to reactor operating temperature (300 oC). The aim of this study is to demonstrate the structural integrity of SA333Gr6 piping and Stainless Steel (SS) 304LN welds under monotonic/cyclic loading which simulates extreme earthquake events and operating temperatures. Total six pipes/pipe welds of carbon steel (8-inch NB ~219 mm outer diameter and 19 mm thick) and SS304LN (12-inch NB~324 mm and outer diameter ~25 mm thick) with through-wall cracks have been tested under four-point bending. Two monotonic fracture tests have been conducted at 300 oC under monotonic loadings. Different experimental results like LLD (Load Line Displacement), Total Load, CMOD (crack mouth opening displacement), Crack Growth values have been obtained. Based on this data the load carrying capacity are obtained for both 8-inch and 12-inch cracked pipes. The cyclic fracture tests have also been conducted at 300 oC under fully reversing cyclic loading on four pipes. Three 8-inch SA333Gr6 pipes have been tested under different magnitude of peak load values. Similarly, one 12-inch SS pipe is also tested under cyclic loading. For carbon steel pipes, the reduction in load capacity is slightly higher under cyclic loadings at 300 oC compared to that at room temperature. However, for stainless steel pipes the load reduction factor at 300 oC is in good agreement with that at room temperature.

Eccentric compression capacity of circular CFST columns under random pitting corrosion

This study explores how random pitting corrosion affects the ultimate eccentric load-carrying capacity of corroded CFST columns at various corrosion levels. The research examines how the load-carrying capacity of circular steel tube concrete columns changes under eccentric loading conditions due to variations in the quality loss rate of the external steel tube caused by corrosion. The established finite element model is validated using existing experimental data, showing a high degree of accuracy. Additionally, the study investigates influencing factors, including corrosion thickness (tc/t), both constant and random corrosion (tc/t), eccentricity (e), corrosion pit diameter (Dc), material strength, and component dimensions. The findings reveal how these parameters affect the reduction of eccentric compressive load-carrying capacity. To visually illustrate this effect, the concepts of load reduction factors Rcs′ and Rc′ are introduced, representing the ratio of load-carrying capacity before and after corrosion. Based on extensive random finite element analyses, we propose a load-carrying capacity calculation formula for the eccentric load reduction factor applicable to corroded circular CFST columns. The study also demonstrates that axial compression can be considered a special case of eccentric loading with an eccentricity of 0. Consequently, by incorporating stability and eccentricity reduction factors, adjustments are made to existing axial load-carrying capacity prediction formulas, resulting in the calculation formula for the reduction factor Rc′. By measuring the local quality loss rate of the external steel tube of corroded circular CFST columns, it is possible to predict both axial and eccentric load-carrying capacities.

Dynamics of bouldery debris flow impacting onto rigid barrier by a coupled SPH-DEM-FEM method

Boulders entrained in debris flows can often generate destructive impact forces and cause damages to rigid barriers. In this study, a large-scale numerical flume model based on the smoothed particle hydrodynamics (SPH), the discrete element method (DEM) and the finite element method (FEM) is established to investigate the impact of bouldery debris flow onto a rigid barrier. The numerical model is first validated with the reported experimental data, in terms of the impact force, the displacement of boulder and flow front. The numerical model is then used to investigate the dynamic interaction between bouldery debris flow and rigid barrier, the energy dissipation of the boulder and the mechanism of buffering effect of debris flow. The numerical results show that the debris slurry can provide a buffering effect to the boulder by reducing the boulder kinetic energy. The buffering effect decreases with the channel slope. Based on the numerical results, a load reduction factor is recommended to consider the buffering effect. The findings of this study can provide some references for the design of rigid barrier.

Failure Mechanisms and Parameters of Elastoplastic Deformations of Anchorage in a Damaged Concrete Base under Seismic Loading

The article addresses mechanisms of anchorage failure in a concrete base studied within the framework of physical experiments. The authors investigated the most frequently used types of anchors, such as the cast-in-place and post-installed ones. The anchorages were studied under static and dynamic loading, similar to the seismic type. During the experiments, the post-earthquake condition of a concrete base was simulated. Within the framework of the study, the authors modified the values of such parameters, such as the anchor embedment depth, anchor steel strength, base concrete class, and base crack width. As a result of the experimental studies, the authors identified all possible failure mechanisms for versatile types of anchorages, including steel and concrete cone failures, anchor slippage at the interface with the base concrete (two types of failure mechanisms were identified), as well as the failure involving the slippage of the adhesive composition at the interface with the concrete of the anchor embedment area. The data obtained by the authors encompasses total displacements in the elastic and plastic phases of deformation, values of the bearing capacity for each type of anchorage, values of the bearing capacity reduction, and displacements following multi-cyclic loading compared to static loading. As a result of the research, the authors identified two types of patterns that anchorages follow approaching the limit state: elastic-brittle and elastoplastic mechanisms. The findings of the experimental research allowed the authors to determine the plasticity coefficients for the studied types of anchors and different failure mechanisms. The research findings can be used to justify seismic load reduction factors to be further used in the seismic design of anchorages.

A study on earthquake performances of reinforced concrete buildings with various number of stories

Seismic codes generally require that the Equivalent Seismic Load Method or the Modal Response Spectrum Method is adopted in the design of buildings. In the equivalent seismic load method, the equivalent seismic static force applied to the building is determined depending on the seismicity of the region where the building is located, the usage class of the building, the fundamental period of the building and the building mass. Later, this equivalent seismic load is reduced by the seismic load reduction factor to take into account the increase in the capacity of the system and the decrease in the seismic demand due to the nonlinear and inelastic behavior of the system, i.e., by accepting limited inelastic deformations in the building subjected to the design earthquake. Then, structural system of the building is analyzed under the reduced seismic forces in addition to the vertical loads by using the load combinations given in the design codes. The process is completed by designing the sections and the structural elements of the building. Similar processes can be implemented by using the modal response spectrum method. The difference between these two methods is consideration of the higher modes of the building instead of the first mode only and the use of the modal masses of the building for each mode, instead of the total mass of the building. In the latter method, the contributions of the higher mode are combined by using specific superposition rules. The codes assume that the structural systems designed in this way will exhibit the almost same level of inelastic deformation, i.e., the controlled damage state, regardless of the building parameters, such as the number of stories. In this study, an attempt is made to investigate the validity of this implicit acceptance. For this purpose, the buildings with a various number of stories are designed by satisfying the bare minimum requirements of the code only, as much as possible. The seismic behavior and the lateral load capacity of these buildings are examined by the static and dynamic nonlinear analyses. The ratio of the nonlinear load capacity to the reduced equivalent seismic load is evaluated depending on the number of the stories of the buildings. The results which are presented in detail yield that the buildings with a low number of stories have relatively larger nonlinear lateral load capacity-to-the reduced elastic seismic load ratio, which is not compatible with the general implicit assumption made in the seismic codes.

Tsunami wave run-up load reduction inside a building array

The influence of a building array on tsunami-driven run-up loads is studied through laboratory experiments and Computational Fluid Dynamics (CFD) simulations. Results show that the number of rows of buildings providing shelter is an explanatory variable for the maximum wave run-up load reduction. Load Reduction Factors (LRF) are defined, with values monotonically decreasing as the number of rows providing shelter increases. The effect of the building array on maximum inundation levels, maximum cross-shore velocity, and maximum momentum flux is studied, finding that these hydrodynamics properties have larger magnitudes when compared to bare earth values. A brief discussion about the effect of the cross-shore distance between rows, the width of the structures in the frontmost row, and the offset between rows is presented. Under the wave conditions and the geometry tested, maximum wave loading is decreased up to about 4 times when 4 or more rows are providing shelter, with most of the load reduction taking place in the first 4 rows. When more than 4 rows are providing shelter to a structure of interest, Load Reduction Factors decrease weakly with the number of rows providing shelter. Although the present analysis has limitations in terms of geometry and wave conditions and more tests have to be conducted to draw conclusions for a wider range of conditions, it shows experimental and numerical evidence that maximum wave loading on structures can be strongly affected when they are part of a building array.

Behaviour of concrete beams reinforced using basalt and steel bars under fire exposure

Basalt bars for concrete reinforcement, known as basalt fiber-reinforced polymers (BFRPs), are new natural inorganic materials with distinct mechanical properties that have been used recently in the construction field. Generally, the FRPs bars have no yield before the brittle failure as steel bars and their behavior, when exposed to fire, is still under investigation, this paper presents an experimental and theoretical study to get more knowledge about the characteristics and the fire resistance of a concrete beam reinforced using BFRPs and BFRPs mixed with steel bars. Eight half-scale concrete beams were constructed and tested up to failure at room temperature and under direct fire at 500 °C for 2 h. The basalt-to-steel percentage is the main parameter of this study. The BFRP-to-main-steel-bar replacement percentages are 100%, 67%, and 33% as three tension reinforcement bars were used. The results are discussed in terms of load capacity, cracking behaviour, and failure modes. Moreover, the experimental results are compared with theoretical calculations according to the ACI code and with numerical results obtained using the ANSYS finite element program. The results show that the beams with both steel and basalt reinforcement showed a better shear strength, enhanced crack stiffness, and lower degree of brittleness at failure. Our results also showed that the BFRPs beams yielded a better degradation resistance when the beams were exposed to fire as the failure load reduction factor for the BFRPs beam was 6.17% compared with that of steel beam which was 22.32%. More studies are needed to justify our observations in details and determine their applicabilities under different conditions.

Study on live load reduction factors of train for long span multitrack railway suspension bridges

The reduction factor of live load of train for design of long span multitrack railway bridge is investigated as a parallel research program of design of the Wufengshan Yangtze River suspension bridge in China. Firstly, to simplify the calculation of cable force of the suspension bridge with higher geometry non-linearity, the force history curves of typical suspenders are developed in the simulation of random trains running on the railway on bridge. Secondly, the probabilities of the trains running on the multitrack railway crossing on the bridge are analyzed and the probability models of the force of key suspender is established by Monte-Carlo simulation based on the established suspender force history curves. Finally, the suspender force reduction factors for bridge with multitrack railway on it are determined in the sense of the same exceeding probability. The results indicate that the probability is small for the trains on different tracks crossing on bridge at the same time. The probability distribution of the maximum force of the key suspender within the design working life can be described by a combination of a weighted lognormal and a weighted normal distribution. For the two-, three- and four-tracks railway suspension bridge, the derived reduction factors of the suspender force or the live load of the trains are 0.90, 0.75 and 0.65, respectively. Comparing these factors with those specified in the China railway bridge design code reveals that the reduction factor for two-tracks railway bridge is the same, and somewhat smaller for the three- and four-tracks railway bridge.

Primjena metode konačnih elemenata za 2D i 3D analize slijeganja izazvanih izgradnjom tunela

Results of a series of 3D and 2D analyses of open-face tunnelling in marly-clayey deposits are presented in the paper. A parametric study was performed to investigate the influence of initial stress state, soil deformability, shear strength parameters, and soil anisotropy, on settlement prediction. Comparison of 2D and 3D results shows that the settlement trough predicted by 2D analysis agrees well with 3D results when an appropriate amount of unloading prior to lining installation is adopted. It is demonstrated that the load reduction factor significantly depends on shear strength parameters of soil.

2018 Türkiye Bina Deprem Yönetmeliği Yığma Yapılar Bölümü Üzerine Bir Değerlendirme ve Donatısız Yığma Bina Örnekleri için Karşılaştırmalı Analiz

Türkiye Bina Deprem Yönetmeliği (TBDY-2018), yığma yapıların analizi ve tasarımını konu alan bölümde oldukça kapsamlı değişikliklerle yayımlanmış ve 2019 yılı başında yürürlüğe girmiştir. İlgili bölüme, donatı içeren üç yeni yığma yapı türü eklenmiş, kesit hesabında emniyet gerilmesi yerine taşıma gücü yöntemine geçilmiş ve spektral ivme katsayısı, deprem yükü azaltma faktörü gibi önemli bazı parametrelerde değişikliklere gidilmiştir. Bu çalışmada, TBDY-2018’in ilgili hükümleri değerlendirilmiş ve bir önceki yönetmeliğe göre tasarlanan ve değerlendirilen yığma bina örnekleri için hesaplar TBDY-2018 ile tekrarlanmıştır. Değerlendirme sonucunda, TBDY-2018 yönetmelik kurallarına göre ivme değeri 0.10g düzeyi üzerindeki deprem kuvvetleri altında donatısız yığma bina tasarımı yapmanın, duvar kesitleri büyütülse bile, mümkün olmadığı görülmüştür. Ayrıca, 2007 yönetmeliğine göre tasarlanan mevcut donatısız yığma binalar TBDY-2018 hükümlerine göre kesme kuvveti güvenliğini sağlayamamaktadır.

Second-order effects in URM walls subjected to compression and out-of-plane bending: From numerical evaluation to proposal of design procedures

Although the load-bearing capacity of masonry walls has been receiving researchers’ attention since the 1950s both analytically and experimentally, in the scientific and technical community there is still heated debate on the actual methodology to adopt for the verification of URM walls subjected to eccentrically loaded walls, considering second-order effects. Moreover, it is still not well recognised that safety checks on structural walls subjected to significant lateral (e.g. seismic) actions require to be verified in terms of lateral flexural capacity and that buckling effects also need to be properly considered in these cases. To date, possible design procedures for evaluating second-order effects in strength verification of walls are based on axial load and moment capacity reduction factors, here respectively called ϕm and ϕM. This paper offers a refinement of the numerical calculations of ϕm and ϕM, leading to polynomial-type models and analytical formulations that improve accuracy in evaluating both factors. Moreover, it has analytically and numerically been demonstrated that there is a one-to-one correspondence between the two reduction factors ϕ, since they represent two ways of characterising the same effect. The results on the reduction factors are finally compared with those from past experimental campaigns and from some standards and can serve as reference for codified procedures.

Bridge assessment reduction factors based on Monte Carlo routine with copulas

The issue of assessment of existing bridges has become important over the last decades among structural engineers and authorities. Due to factors like deterioration of materials, increasing traffic loads and intensity of traffic, it is necessary to evaluate the performance of existing bridges. It is widely accepted that current design codes are not suitable for the assessment of bridges. This study is aimed at finding correlations between load effects and easily obtainable traffic descriptors such as average daily truck traffic and percentage of long vehicles that are used to modify the design traffic load model. First objective of the paper is to develop a robust Monte Carlo simulation technique by using bivariate copula functions. Such routine enables the generation of all the traffic flows necessary to assess the influence of traffic characteristics on the extrapolated load effects and as a second objective to establish design load reduction factors. The results exhibit that an assessment traffic load model based on basic traffic descriptors can be potentially used to evaluate existing bridges.

Wind loads and their reduction on mesh fabrics

The presented contribution deals with evaluation of wind loads on various layouts of plastic and steel mesh fabric. To obtain real wind effects and loads, the experimental measurement in the Boundary Layer Wind Tunnel (BLWT) in Bratislava has been prepared. The goal of an investigation is the determination of wind loads on permeable materials – plastic and steel fabric, using wind load reduction factor k. The mean wind pressure on the permeable material is obtained by multiplying the wind pressure to the impermeable surface by the reduction factor k depending on the Reynolds number. The experimentally determined reduction factor can be applied for design of the safety mesh fabric. Wind loads were obtained from measurement of wind velocity by Hot-Wire anemometry (HWA).

The role of overstrength on the seismic performance of asymmetric‐plan structures

SummaryUneven distribution of seismic demand in asymmetric‐plan structures is a critical concern in earthquake‐resistant design. Contemporary seismic design strategies that are based on linear elastic response, single load reduction factor, and uniform ductility demand throughout an asymmetric system generally lead to unsatisfactory performance in terms of realized ductilities and nonuniform damage distribution due to strong torsional coupling associated with asymmetric‐plan systems. In many cases, actual nonlinear behavior of the structure displays significant deviation from what is estimated by a linear elastic, force‐based seismic design approach. This study investigates the prediction of seismic demand distribution among structural members of a single‐story, torsionally stiff asymmetric‐plan system. The focus is on the effect of inherent unbalanced overstrength, resulting from current force‐based design practices, on the seismic response of code‐designed single‐story asymmetric structures. The results obtained are utilized to compile unsymmetrical response spectra and uniform ductility spectra, which are proposed as assessment and preliminary design tools for estimating the seismic performance of multistory asymmetric structures. A simple design strategy is further suggested for improving the inelastic torsional performance of asymmetric systems. Providing additional strength to stiff edge members over their nominal design strength demands leads to a more balanced ductility distribution. Finally, seismic responses of several asymmetric case study structures designed with the aid of the proposed strategy are assessed for validating their improved performance.

Buckling Analysis of Orthotropic Thick Cylindrical Shells Considering Geometrical Imperfection Using Differential Quadrature Method (DQM)

Abstract This paper presented a three dimensional analysis for the buckling behavior of an imperfect orthotropic thick cylindrical shells under pure axial or external pressure loading. Critical loads are computed for different imperfection parameter. Both ends of the shell have simply supported conditions. Governing differential equations are driven based on the second Piola–Kirchhoff stress tensor and are reduced to a homogenous linear system of equations using differential quadrature method. Buckling loads reduction factor is computed for different imperfection parameters and geometrical properties of orthotropic shells. The sensitivity is established through tables of buckling load reduction factors versus imperfection amplitude. It is shown that imperfections have higher effects on the buckling load of thin shells than thick ones. Results show that the presented method is very accurate and can capture the various geometrical imperfections observed during the manufacturing process or transportation.

Changes and Driving Forces of the Water-Sediment Relationship in the Middle Reaches of the Hanjiang River

Riverine sediment transport plays an important role in the global geochemical cycle. With a growing interest in global riverine environmental changes, a better understanding of water-sediment relationship dynamics and their driving forces is crucial for basin management, which is particularly associated with cascade dam construction. In this contribution, a simple and effective sediment load reduction factor analysis is used to attribute the changes in river sediment load to different drivers. The Mann–Kendall (MK) trend test and the double-mass curve (DMC) method were combined to reveal the trends and causes of change in the water-sediment relationship from 1965 to 2015 in the middle reaches of the Hanjiang River. We found that sediment load trend decreased significantly, which was caused by a decrease in water yield (5.05%), and the relative contributions of precipitation decrease (1.66%). Furthermore, only one mutation could be identified in 1974 at Huangzhuang station. Evapotranspiration and vegetation coverage had slight decreasing effects on sediment load. The impact of human activities on the water-sediment relationship has intensified over the past 15 years. We therefore propose the establishment of an integrated basin-wide ecosystem and optimized reservoir operation rule for sustainable water use and sediment regulation.

Empirical equations to estimate non-linear collapse of medium-length cylindrical shells with circular cutouts

This paper examines the load bearing capacity of medium-length steel cylindrical shells with a circular cutout under the action of axial compression. Numerical simulations were performed for a radius-to-thickness ratio (R/t) ranging from 100 to 500, and an imperfection parameter (α) of between 1 and 4. Structural steel and the behavior of perfect plastic material were considered within the scope of the study. The investigation includes the influence of the cutout size and number, radius-to-thickness ratio. The paper also contains a comparison between theoretical predictions, ABAQUS® FE results and experimental data for axially compressed cylinders. A reasonable correlation was obtained between numerical predictions and experimental tests. Details relating to the experimental procedure and FE model are provided. A parametric study was conducted to propose empirical equations, estimating the limit load of cylindrical shells as a function of geometry (R/t, α and cutout number) and material properties (E, v and σy). Empirical formulas were produced, fitting a surface plot using the Least Square method, for both the perfect shell structure (reference shell load) and the limit load reduction factor (ϕ). All variables in the empirical formula were normalized. A stochastic error analysis was used as a tool to measure how the results of proposed equations approach the FE predictions. Finally, based on experimental and numerical results, formulas are presented to calculate the limit load of medium-length shells with and without circular cutouts having a discrepancy not exceeding ±10% regarding error analysis.

Large-scale successive boulder impacts on a rigid barrier shielded by gabions

Debris flows occur in multiple surges. Boulders entrained within the flow have been reported to incapacitate structures within its flow path. Single-layer cushions, such as gabions, are often installed to shield debris-resisting barriers from boulder impact. However, most relevant works only focus on single impact and the performance of gabions subjected to successive loading is still not well understood. A new large-scale pendulum facility was established to induce impact energy of up to 70 kJ on an instrumented rigid barrier shielded by 1 m thick gabions. The response of the gabions under six successive impacts was investigated. Results show that the peak boulder impact force given by the Hertz equation is at least four times the measured values. The recommended load-reduction factor (Kc) used in practice can be reduced by a factor of two. After six successive impacts at an energy level of 70 kJ, the transmitted force increases by up to 40%. Based on the Swiss guidelines, a 13% increase of gabion thickness is required when successive impacts are concerned. The results presented in this paper will be useful for practitioners designing rigid barriers.

Differential settlement effect on reliability of bridge superstructure and implementation in Load and Resistance Factor Design specification

Maximum deterministic differential settlement is used in current American Association of State Highway and Transportation Officials Load and Resistance Factor Design specification. However, the deterministic differential foundation settlement is quite different from the actual settlement due to the soil’s large variability. This article investigates the effects of the random differential foundation settlement on the reliability of bridge superstructure. A lognormal distribution with a coefficient of variation of 0.25 of random settlement is used in reliability analysis. Dead and live loads are modeled as random variables with normal and Gumbel Type I distributions, respectively. Then, the reliability of bridge superstructure considering random differential settlement effect is calculated using the first-order reliability method. Considering the regional traffic condition on Missouri roadways, the effect of a live load reduction factor on bridge reliability is investigated. The reliability indices of 14 existed bridges and 31 new designed multi-span girder bridges are calculated. It is demonstrated that small change in differential settlement can significantly reduce the reliability of the superstructure, depending upon the span length and rigidity of the girder. For the 31 new designed bridges without the settlement consideration in design can tolerate an extreme settlement of L/500 without reduced live loads and L/2500 with reduced live loads in the case of a bridge reliability index of 3.5. The reliability analysis results also indicate that without reduced live loads, current American Association of State Highway and Transportation Officials specification with a load factor of 1.0 for the differential settlement has enough safe margins within an allowable settlement of L/250. However, when live loads are reduced, the load factor for settlement has to be amplified. The calibrated load factor curve of differential settlement within allowable settlement L/250 is provided to achieve the target reliability index of 3.5.