Design Bending Moment Research Articles

RC wall building structures: Comparison of first and second generation Eurocode 8 seismic design and detailing strategies

This study provides a thorough comparative analysis of structural design strategies across different ductility classes and seismic action levels, as outlined in Eurocode 8 provisions. The analysis is carried out for 5- and 10-storey building examples. The research highlights key findings regarding base shear demand, storey displacements, sensitivity coefficients, and other crucial structural performance parameters. Those findings indicate that while buildings designed for DCM and DC3 ductility classes generally exhibit similar base shear values and roof displacements, exceptions arise, particularly in the lower-storey buildings where DC2 demonstrates significantly lower roof displacements. The influence of strut inclination on design bending moments is also noted, underscoring its significance in structural behaviour. Moreover, the study delves into interstorey drift ratio (IDR) demands from analysis, revealing consistent displacement patterns across various structures with notable implications for deflection and stability. Additionally, insights into chord rotation control, sensitivity coefficients, and reinforcement quantities shed light on their behaviour under diverse seismic conditions, aiding in optimising structural design strategies.

Minimum design bending moment for systems of equivalent stiffness

In this article, the minimum design bending moment of concrete slender columns is studied by assuming a system of equivalent stiffness. For concrete structural parts such as slender columns, their stiffness is dependent on the loading, originated from lumped and distributed masses, and the rheological behavior of the material. The latter alters the concrete’s modulus of elasticity, introducing changes over time. Basically, the desired transformation is from a one-dimensional non-prismatic system to another prismatic one which exhibits an equivalent bending stiffness. As the bending stiffness changes due to the change of the problem’s independent variables, the geometric characteristics of the transformed system reflect the same dependence as the original system. This implies changes in the minimum design moment since it is linked to the dimensions of the equivalent section. To assess the hypothesis proposed, a numerical simulation is conducted over a real structural system using a vertical loading ranging from zero up to the critical buckling force, taking into account the change in the modulus of deformation of concrete and assuming a certain level of cracking of the material. The results obtained showed that the strategy of using a system of equivalent stiffness simplifies the analysis of non-prismatic elements because the problem is reduced to a prismatic element of equivalent properties. Besides that, due to the incorporation of the concrete creep in the problem, the maximum moment obtained in the equivalent system needs to be multiplied by a factor of 2.94 in order to equal the maximum moment occurring in the original system.

Damage analysis of hybrid carbon/Glass-Epoxy pipe elbows under bending and pressure loading

Given their many advantages, composite materials have always proven their effectiveness. As in aeronautical structures where reinforcement techniques are used, their application is widened in various fields. Analyzing these composite structures or proposing new concepts for reinforcements remains an interest of several researchers. This work opts for the use of a hybrid composite of a tubular structure of an elbow attached by straight parts. The structural composite is twill. The aim of the elbow damage study is to evaluate the proposed reinforcement concept. The stiffness and damage parameters of the plies are introduced at the size of the fiber and according to the thickness per row of finite elements, hence the use of an adequate meshing technique. The linear behavior follows the equivalent stress flow theory of Von Mises. The results presented as moment-rotation curves were evaluated under design effect and bending moment mode. Depending on the loading conditions, the proposed concept of the hybrid composite showed an overcapacity of resistance where the location of the fiber qualities played the optimization of this capacity. The structure has shown even more resistance for certain locations of the folds which are reinforced in thickness. Depending on the bending moment mode applied, the results show that the damage is caused at very low deformations by ovalization of the elbow and in fiber tension.

A Soil-Structure Interaction Study using Sustainable Structural Fill below Foundations

Structural fill is utilized to improve the bearing capacity and reduce settlement below foundations supported on weak soils or when foundations are supported on filled up soil. The present study evaluates the potential application of municipal solid waste finer fraction (MSW-FF) as a sustainable structural fill material. The finer fraction constitutes significant proportion of old landfill waste in cities, and do not easily find applications as compared to the other fraction of old waste. The present work determines the engineering properties of MSW-FF. A detailed assessment has also been carried out to evaluate the bearing capacity, settlement and modulus of subgrade reaction for the shallow foundation of different sizes and shapes resting on (a) soil with low subgrade modulus and (b) soil improved with a layer of MSW-FF as structural fill. A soil-structure interaction analysis has also been carried out by utilizing STAAD Pro. software, to understand the effect of soil and foundation stiffness on the foundation design parameters, viz., base pressure, settlement, bending moment and shear stress in shallow foundations for both cases (natural soil and with MSW-FF as structural fill). The comparison of different foundation systems resting on soil improved with MSW-FF structural fill layer and soil with low subgrade modulus has been presented to demonstrate the efficacy of MSW-FF as a suitable structural fill material. From the soil-structure interaction analysis, it is observed that the effect of soil subgrade modulus on foundation base pressure and settlement is prominent, while having a negligible effect of bending moment and shear stress in the foundation. Further, the relative stiffness of foundation and soil has a significant effect on the foundation design parameters. The study results are quite encouraging with respect to the potential of utilizing MSW-FF as a sustainable structural fill and put forward a new and promising alternate material for application in different infrastructure projects.

Experimental investigation of transient bending moment of piles during seismic liquefaction

The purpose of this paper is to study the behavior of pile-supported structures in liquefiable soils, specifically when the soil surrounding the pile transits from no-liquefaction to full-liquefaction. A series of shaking table tests were performed on four pile-supported structures subjected to different input motions and, as a result, with different times to reach full-liquefaction. The bending moment of the piles during the transient phase is compared with those predicted in pre- and post-liquefaction stages. The experimental results showed that the maximum bending moment may occur during the transient phase (i.e. during the development of excess pore pressure before the soil is fully liquefied). Arguably, the observed amplification in bending moment is caused by the the tuning effect between the predominant frequency of the input motion and the frequency of the pile-supported structure, which is progressively decreasing during the liquefaction process. Results are presented using a non-dimensional framework whose parameters are derived from the governing mechanics. A new parameter TAF (Transient Amplification Factor) is defined to predict the design bending moment during the transient phase. It is shown that the transient bending moment can be obtained from the newly introduced parameter TAF, and the values of maximum bending moments in the pre- and post-liquefaction stages. It is found that TAF is a function of two easily obtainable parameters: (a) time taken to reach full liquefaction, this can be obtained through site response analysis; (b) elongation of natural period of vibration, expressed as ratio of the time period of the structure at full liquefaction to the time period at zero-liquefaction. Finally, practical implications of the main findings are discussed.

A closed-form solution for the failure interaction diagrams of pile groups subjected to inclined eccentric load

The work at hand proposes a method for assessing, under reasonable hypotheses from an engineering perspective, the failure envelope of a pile group subjected to generalized loading conditions involving a vertical and a lateral force along with a moment. Following different assumptions of increasing complexity, a simple closed-form expression, which is however capable of considering also the strong dependence of sectional yielding moment on the axial force, is derived. The use of such formula, which allows a practical hand calculation of the interaction diagrams at failure, returns conservative yet very accurate results. As a follow up, with reference to reinforced concrete piles, design considerations involving both structural and geotechnical failure under lateral load are reported. It is found that for most cases, if steel reinforcement is established to resist the design bending moment, the geotechnical Ultimate Limit State checks are automatically satisfied.

Determination of optimal cross-section values of precast roof beams under changing design bending moments and in terms of different concrete strengths

Determination of optimal cross-section values of precast roof beams under changing design bending moments and in terms of different concrete strengths

Simple Span Bridge Loading Based on Weight in Motion Data

Over Dimension Over Load (ODOL) vehicle is claimed to be the cause of a number of fatal accidents and damage to road infrastructure in Indonesia and has become a serious issue for roads and bridges maintenance. Over loaded vehicles can result in damage to the bridge, reduced bridge capacity and can even result in collapse of the bridge. Therefore the characteristics of the actual vehicle load need to be known and compared to the bridge design load according to the bridge design code and standard. In this paper, an analysis is carried out on the actual traffic load data obtained from the measurement results using Weight in Motion (WIM) in Kaligawe, Semarang, Indonesia. Monte Carlo simulation is used to simulate the arrival of the vehicle. The results of vehicle load simulation are then applied to a simple span bridge with a span of 30, 40, 50 m. The bending moment and shear force obtained due to actual load compared to the magnitude of the bending moment and shear by applying Indonesia Bridge Loading Standard. The results show that 43 percent of vehicles are overloaded. The bending moment and shear force caused by actual load is less than the design bending moment and shear force for 30 m, 40 m and 50 m bridge span.

Optimization Study on Longitudinal Joints in Quasi-Rectangular Shield Tunnels

There are large bending moments in quasi-rectangular shield tunnels due to their deviation from the circular shape, and as for other types of shield tunnels, the longitudinal joints are the most critical parts in the lining structure. A new type of joint with ductile iron joint panels (DIJPs) was installed in quasi-rectangular tunnels to solve these problems. The distance from the bolts to the segment’s inner surface was improved for better performance under specific bending moment types. Both tests and finite element modeling (FEM) simulations were conducted to investigate the effect of the bolt position improvements. The resistances to crack appearance increased by 33.6% and 18.0% for positive and negative moment cases, respectively. The resistances to crack penetration increased by 13.8% and 18.4% for positive and negative cases. From the FEM approach, it was found that the behavior of the joint under the design bending moment range can be divided into three stages, whereby the bolts are only active from the second stage on. The effects of other optimizing methods, such as enhancement of concrete properties and increase of bolt diameters and numbers, are explored. Through comparison, it is believed that optimizing the joint section to increase the lever arm between bolts and the compression zone can improve the joint behavior most effectively. This optimization direction is recommended when designing a shield tunnel joint with DIJPs.

Comparison of the design of prestressed concrete hollow-core floor units with Eurocode 2 and ACI 318

A typical 1200 mm (48 in.) wide × 200 mm (8 in.) deep prestressed concrete hollow-core unit is analyzed and designed in order to make a comparison between Eurocode 2 and ACI 318-08. This includes calculations for serviceability limit state of stress and moment of resistance, ultimate moment of resistance, ultimate shear capacities, flexural stiffness (that is, for deflection), and cover to pretensioning tendons for conditions of environmental exposure and fire resistance. Concrete cylinder strength is 40 MPa (5.8 ksi), and concrete cube strength is 50 MPa (7.3 ksi). The hollow-core unit is pretensioned using seven-wire helical strands. Worked examples are presented in parallel formation according to Eurocode 2 and ACI 318. For uniformly distributed loads, the design criterion between the service moment to service moment of resistance (Ms/Msr for EC2 and Ms/Msn for ACI 318) and the ultimate design bending moment to ultimate moment of resistance (MEd/MRd for EC2 and Mu/φMn for ACI 318) is well balanced for this example. Usually the service moment is critical unless the amount of prestress is small. For EC2-1-1, flexurally uncracked shear capacity VRd,c is only limiting when the span-to-depth ratio in this example is less than about 35. For ACI 318, flexurally cracked shear capacity φVci is limiting when span-to-depth ratio is 42, showing that shear cracked in flexure will often be the governing criterion.

Исследование предельного состояния перекрытий корпуса судна из полимерных композиционных материалов

This paper presents the results of limit-state research for polymeric-composite grillages of hull under bending. Taking geometric non-linearity into account, it was possible to estimate supercritical straining of structural members and global buckling effect of certain beams upon overall hull stiffness. Numerical studies have shown that with given thicknesses and dimensions of principal members strength margin in terms of design bending moment is not less than 5, which means that these structural members could be further optimized towards lower material consumption.

Structural design of floodways under extreme flood loading

PurposeCurrent methods for floodway design are predominately based on hydrological and hydraulic design principles. The purpose of this paper is to investigate a finite element methods approach for the inclusion of a simplified structural design method into floodway design procedures.Design/methodology/approachThis research uses a three-dimensional finite element method to investigate numerically the different parameters, geometric configurations and loading combinations which cause floodway vulnerability during extreme flood events. The worst-case loading scenario is then used as the basis for design from which several structural design charts are deduced. These charts enable design bending moments and shear forces to be extracted and the cross-sectional area of steel and concrete to be designed in accordance with the relevant design codes for strength, serviceability and durability.FindingsIt was discovered that the analysed floodway structure is most vulnerable when impacted by a 4-tonne boulder, a 900 mm cut-off wall depth and with no downstream rock protection. Design charts were created, forming a simplified structural design process to strengthen the current hydraulic design approach provided in current floodway design guidelines. This developed procedure is demonstrated through application with an example floodway structural design.Originality/valueThe deduced structural design process will ensure floodway structures have adequate structural resilience, aiding in reduced maintenance and periods of unserviceability in the wake of extreme flood events.

Increasing the accuracy of definition torsional geometric properties for rolled and welded beams

The features of determining the torsional geometric properties of the cross-section of a steel beam, rolled or composed of three sheets of arbitrary thickness, are considered. When calculating warping properties, it is suggested to take into account the degree of torsional stiffness of the attached structures, that more accurately reflects the actual operation of the fixed beam in the composition of the decking. The differentiated account of rounding at the flange adjacent to the web leads in the rolled profiles to a significant structured increase in the value of the torsional constant. These factors characterize the special conditions of operation of the steel element with complex resistance, that allows determining more precisely the value of internal forces, namely the design bending moments in two planes and the bimoment, which are proportional to the distribution function of the angle of rotation of the rod along its length. It is noted that in fact the bimoment is not only determined by on the load, the elastic bending-torsional constant of the cross-section and the span of the beam, an eccentricity, as well as on the stiffness of the structure that attached to the beam.

EXPERIMENTAL STUDY ON BEARING CAPACITY OF DANGEROUS AND/OR OLD PRE-STRESSED CONCRETE BOX GIRDERS

In order to obtain the true bearing capacity of dangerous and old pre-stressed concrete box girder bridges, experiments on flexural and shear bearing capacity of full-scale dangerous and old pre-stressed concrete small box girders are conducted to study the mechanical degradation behavior of dangerous and old pre-stressed concrete box girders. Through the residual bearing capacity test of the full-scale prefabricated box girder, the load, deflection, strain and crack width of the test girders are measured and analyzed. The residual bending and shear ultimate capacity and stiffness of the small box girders are analyzed. The bending and shear behavior and failure mechanism of precast box girders in danger are obtained. The comparisons between the results of full-scale test and the calculated value of bearing capacity and also the design value of the internal force of I-Class highway are operated to analyze the actual performance of the small box girder made of dilapidated concrete. The damage reduction coefficient is introduced to establish the formula of ultimate bearing capacity of the girder. The test results stated that the structural damage affected the bearing performance of this box girder. The deflection of the test girder in the uncracked stage did not meet the proof stiffness requirements under the variable load of highway bridge. The calculated results of the flexural bearing capacity are basically identified with the result from full scale flexural test, which is 70% higher than the design bending moment by the internal force of the main girder. The results of full-scale shear tests are respectively 32% and 37% higher than the internal shear design values of the girder. The formulas with damage reduction coefficient for calculating the bending and shearing capacity of the concrete box girders is applicable to evaluate the bearing capacity of the dilapidated concrete girders with more accurate results, which can provide a reference for the evaluation and maintenance of massive existing small concrete box girders in China.

FE Modeling of Circular, Elliptic, and Triangular Isolated Slabs With a Continuous Damage Model

The nonlinear behaviour of reinforced concrete circular, elliptic and triangular isolated slabs was studied using computational mechanics. Concrete was modelled with a damage model which includes softening, while the behaviour of the reinforcing steel was modelled with a 1D bilinear plasticity model. The constitutive models and the finite element method were validated by comparing the computed numerical results with the experimental results of a rectangular slab reported in the scientific literature. The coefficient method is proposed for its simplicity to calculate design bending moments in slabs with circular, elliptic and triangular geometries. These coefficients were computed from the FE analysis. The layout of steel reinforcement is proposed, particularly lengths of zones for positive and negative moments, respectively. The crack paths are showed, which are depending on the boundary conditions, acting loads and geometry of the slabs.

Flexure Behaviour of Reinforced High Strength Concrete Elements Affected by Corrosion

Corrosion of the reinforcement is a constant vulnerability for reinforced concrete structures exposed to aggressive environments. High strength concrete is known to prevent corrosion of the reinforcement, in a non-cracked state, when exposed to aggressive environments. The purpose of this study is to assess the opportunity of using high strength concrete in cracked elements exposed to corrosion and compare them with non-exposed elements. A series of simply supported reinforced high strength concrete beams with concrete cover of 25 and 50 mm were pre-cracked, up to a service life crack of 0.1 mm, further exposed to accelerated corrosion through a process of electrolysis and finally tested to failure. A series of non-exposed witness specimens were also tested to failure. All elements were designed with the same bending capacity. The flexure behaviour was assessed by plotting experimental and theoretical ultimate limit state position of the neutral axis at midspan and the results show no significant differences in the overall behaviour, despite the affected reinforcement, between the corroded and non-corroded elements. Moreover, the design bending moments were approximately 40% lower than the experimental ones, even for corroded beams, which can be a significant strength reserve of the beams, useful in aggressive environments.

Elastic-displacement-based multi-modal pushover analysis in high-rise core wall buildings

Higher mode effects play a major role in the seismic demands of high-rise buildings. Several recent studies have shown that seismic design demands such as design shear and bending moment in high-rise buildings cannot be predicted by the conventional code-based response spectrum analysis procedure. These can be determined by the more rigorous and accurate non-linear response history analysis procedure, but this procedure is computationally very extensive and time consuming. Yet a non-linear static pushover analysis cannot account for higher mode effects. Therefore, the applicability of a multi-modal pushover analysis (MMPA) procedure using elastic target displacement to cases of 20- 30- and 40-storey high-rise reinforced concrete core wall buildings is investigated in this study. The results obtained by the elastic displacement MMPA (EDMMPA) procedure are compared with those obtained from non-linear analysis. The comparison shows that EDMMPA can satisfactorily estimate the design shear force, bending moment and deformation demands with a variation of 10–20%. Thus, this computationally less demanding analysis can serve as a base line for preliminary design of high-rise reinforced concrete core wall buildings.

Seismic evaluation of the northbound N1/R300 bridge interchange

The design of the Stellenberg Interchange was finalised in 1982, with construction completed in 1986. The bridge was designed using a code of practice which did not include any requirements for seismic excitation. This code was superseded by the Code of Practice for the Design of Highway Bridges and Culverts, which provides detailed analysis guidelines for bridges located in seismic-prone areas. According to this code, the bridge is located in a seismic-prone area with an anticipated peak ground acceleration of 0.1 g. Current research suggests that this region could be exposed to a peak ground acceleration of approximately 0.2 g. Upon inspection of the bridge, it was noted that the bridge does not conform to modern-day best practice guidelines for bridges located in seismic-prone regions. These factors necessitated an exploratory investigation to determine whether the bridge can sustain earthquake magnitudes between 0.05 g and 0.2 g. The study was conducted by experimentally determining the natural frequencies with its corresponding mode shapes, which were used to calibrate a finite element model. The finite element model was subjected to different magnitude earthquakes to determine its structural integrity. The results show that, for an earthquake of 0.1 g, the bending moment at one of the column bases is exceeded, while two other column base moments are within 15% of its design capacity. For a 0.2 g magnitude earthquake, the design bending moments at five columns are significantly exceeded, while three other columns' design moments are close to being exceeded. The exceedance of the design moments could lead to significant damage, with the possibility of collapse of the bridge.

Influence of geometric imperfections on the ultimate strength of the double bottom of a Suezmax tanker

In this work, the influence of initial geometric imperfection modes on the ultimate strength of a ship’s hull is studied, with a focus on the buckling behavior of stiffened panels that initiates the structural hull failure. A numerical model of a cargo compartment at the midship of a Suezmax tanker is developed by using the finite element method and by considering both geometric and material nonlinearities. Analyses are conducted under hogging conditions to evaluate the double bottom stiffened panels experiencing axial compression by hull girder bending. Different imperfection modes on the bottom and inner bottom plates are considered in the model. Two cases are studied. In the first one, a half-wave imperfection mode is employed in the longitudinal and transversal directions. In the second case, the imperfection mode coincides with the main natural buckling mode of the plate between the stiffeners. Experimental tests were performed using small-scale models that are representative of the bottom panels, and the results are correlated with those from numerical simulations to define a proper mesh refinement to reproduce the buckling phenomenon. The ultimate strength of the ship hull, in full-scale, employed the same mesh refinement for the bottom panels, assuming the two proposed initial imperfections. The results from the ultimate strength are compared with the reference values for the design bending moment recommended by a classification society.

Selected aspects of designing deep excavations

Abstract This paper analyzes two approaches to serviceability limit state (SLS) verification for the deep excavation boundary value problem. The verification is carried out by means of the finite element (FE) method with the aid of the commercial program ZSoil v2014. In numerical simulations, deep excavation in non-cohesive soil is supported with a diaphragm wall. In the first approach, the diaphragm wall is modeled with the Hookean material assuming reduced average stiffness and possible concrete cracking. The second approach is divided into two stages. In the first stage, the wall is modeled by defining its stiffness with the highest nominal Young’s modulus. The modulus makes it possible to find design bending moments which are used to compute the minimal design cross-section reinforcement for the retaining structure. The computed reinforcement is then used in a non-linear structural analysis which is viewed as the “actual” SLS verification. In the second part, the paper examines the same boundary value problem assuming that the excavation takes place in quasi-impermeable cohesive soils, which are modeled with the Hardening Soil model. This example demonstrates the consequences of applying the steady-state type analysis for an intrinsically time-dependent problem. The results of this analysis are compared to the results from the consolidation-type analysis, which are considered as a reference. For both analysis types, the two-phase formulation for partially- saturated medium, after Aubry and Ozanam, is used to describe the interaction between the soil skeleton and pore water pressure.