Deflection Criteria Research Articles

Stochastic aspects of crack deflection and crack path prediction in short fiber reinforced polymer matrix composites

Owing to the production process, short fiber reinforced composites exhibit a pronounced anisotropy of both elastic properties and crack growth resistance. In particular the latter issue has a major impact on crack deflection and inevitably has to be taken into account for the sake of an accurate prediction of crack paths. The perpendicular axes of transverse isotropy are associated with the fiber orientations, whereupon a crack in transverse direction encounters the largest fracture toughness. While the local mean fiber orientations in polymer matrix composites are determined by the injection molding process, their statistical fluctuations can approximately be described in terms of Gaussian random field models. Furthermore, statistical variations of the volume fraction of fibers and the fiber–matrix adhesion give rise to stochasticity of the local ratio of fracture toughness anisotropy. Influencing factors of prediction regions of crack paths obtained from finite element simulations with an adapted J-integral deflection criterion are investigated, just as stochastic aspects of bifurcation phenomena of crack deflection observed under mode-I loading.

Rare earth monosilicates as oxidation resistant interphase for SiCf/SiC CMC: Investigation of SiCf/Yb2SiO5 model composites

Model composites consisting of SiC fiber and Yb2SiO5 were processed by the spark plasma sintering (SPS) method. The mechanical compatibility and chemical stability between Yb2SiO5 and SiC fiber were studied to evaluate the potential application of Yb monosilicate as the interphase of silicon carbide fiber reinforced silicon carbide ceramic matrix composite (SiCf/SiC CMC). Two kinds of interfaces, namely mechanical and chemical bonding interfaces, were achieved by adjusting sintering temperature. SiCf/Yb2SiO5 interfaces prepared at 1450 and 1500 °C exhibit high interface strength and debond energy, which do not satisfy the crack deflection criteria based on He-Hutchison diagram. Raman spectrum analyzation indicates that the thermal expansion mismatch between Yb2SiO5 and SiC contributes to high compressive thermal stress at interface, and leads to high interfacial parameters. Amorphous layer at interface in model composite sintered at 1550 °C is related to the diffusion promoted by high temperature and DC electric filed during SPS. It is inspired that the interfacial parameters could be adjusted by introducing Yb2Si2O7−Yb2SiO5 interphase with controlled composition to optimize the mechanical fuse mechanism in SiCf/SiC CMC.

Comparative Study on Slab Deflections

Slabs are one of the most common structural components in RC-framed structures, usually analysed under transverse loading. In the analysis, the thickness of the slab generally governs the serviceability requirement for deflection. The thickness of the slab controls the weight of the building since its contribution is nearly 50% of the total weight of the building. In order to minimize the weight of the building, proper analysis of the slab ensures minimum thickness satisfying deflection criteria. For a given loading, span, and assumed thickness of the slab, analysis will be performed using the material properties such as modulus of elasticity and Poisson’s ratio. Several theories, including the Rankine-Grashoff theory, Timoshenko’s plate theory, Marcus, and other methods have been proposed over the years using the same concept. These methods do not consider the participation of reinforcement in deflection estimation. IS code 456 – 2016 specifies limiting span to depth ratios with suitable modification factors based on percentage of tension reinforcement and stress level in steel for satisfactory serviceability criteria of deflection. In the present study, an attempt was made to compare the slab deflections analytically and experimentally with and without reinforcement contribution for the exactness of proposed theories. It concludes that, in one-way simply supported slabs, theoretical values differ by 45% from experimental values in reinforced concrete (RC) slabs. In two-way simply supported plain concrete (PC) slabs, the Rankine-Grashoff theory is in good agreement with the experimental values. Theoretical values of the two-way slabs when compared with experimental (RC slab) values are in good agreement with plate theory.

Characteristics of Cracking Failure in Microbump Joints for 3D Chip-on-Chip Interconnections under Drop Impact.

With the rapid development of microelectronics packaging and integration, the failure risk of micro-solder joints in packaging structure caused by impact load has been increasingly concerning. However, the failure mechanism and reliability performance of a Cu-pillar-based microbump joint can use little of the existing research on board-level solder joints as reference, due to the downscaling and joint structure evolution. In this study, to investigate the cracking behavior of microbump joints targeted at chip-on-chip (CoC) stacked interconnections, the CoC test samples were subjected to repeated drop tests to reveal the crack morphology. It was found that the crack causing the microbump failure first initiated at the interface between the intermetallic compound (IMC) layer and the solder, propagated along the interface for a certain length, and then deflected into the solder matrix. To further explore the crack propagation mechanism, stress intensity factor (SIF) of the crack tip at the interface between IMC and solder was calculated by contour integral method, and the effects of solder thickness and crack length were also quantitatively analyzed and combined with the crack deflection criterion. By combining the SIF with the fracture toughness of the solder–Ni interface and the solder matrix, a criterion for crack deflecting from the original propagating path was established, which can be used for prediction of critical crack length and deflection angle for the initiation of crack deflection. Finally, the relationship between solder thickness and critical deflection length and deflection angle of main crack was verified by a board level drop test, and the influence of grain structure in solder matrix on actual failure lifetime was briefly discussed.

ВЕРОЯТНОСТНАЯ ОЦЕНКА НАДЕЖНОСТИ СТАЛЬНЫХ ФЕРМ ПО КРИТЕРИЮ ПРОГИБА НА ОСНОВЕ Р-БЛОКО

The article describes algorithms for probabilistic evaluation of steel trusses’ reliability by the deflection criterion using p-boxes as models of random variables. The p-boxes are an area formed by the boundary cumulative distribution functions (CDFs). There is a real probability distribution function of a random variable inside the p-box area. Based on the presented approaches, it is possible to design trusses on a given reliability index or probability of non-failure. P-boxes as random variable models take into account aleatory and epistemological uncertainties at the same time. Such models are relevance for snow loads as one of the main factors affecting the stress-strain state of trusses. Information about the reliability level of steel trusses according to the deflection criterion is necessary for a system assessment of the reliability of a truss. An approach of structural reliability analysis is also proposed for existing trusses, where the ultimate deflection is limited by the condition of buckling of the selected truss bar.

Design of tool employed in dissimilar micro-friction stir welding

Friction Stir Welding is a unique way of welding similar or dissimilar materials, utilizing the friction created between the spinning tool and workpiece. This work focus on improving the weld quality obtained from micro-FSW of dissimilar materials. The tool profile used is vital in generating the frictional heat, and its failure degrades the actual process. So, the need for selecting or designing a best tool for the process is important. Design methodology is used to make this process more efficient. Several design concepts have been utilized; including Mind Map, Morphological chart, and the best tool profile was assessed using a Pugh matrix. Finite Element Analysis (FEA) was carried out using different tool profile subjected to heat generation. Based on the temperature distribution and minimum deflection criteria, the best tool design is selected and compared with the tool profile obtained based on design methodology. The best conceivable concept has been the tool pin with a triangular profile. Based on the study High Carbon High Chromium tool steel is selected as tool material, considering the mechanical properties and cost of tooling.

Multivariate Side-Informed Gaussian Embedding Minimizing Statistical Detectability

Steganography schemes based on a deflection criterion for embedding posses a clear advantage against schemes based on heuristics as they provide a direct link between theoretical detectability and empirical performance. However, this advantage depends on the accuracy of the cover and stego model underlying the embedding scheme. In this work we propose an original steganography scheme based on a realistic model of sensor noise, taking into account the camera model, the ISO setting and the processing pipeline. Exploiting this statistical model allows us to take correlations between DCT coefficients into account. Several types of dependency models are presented, including a very general lattice model which accurately models dependencies introduced by a large class of processing pipelines of interest. We show in particular that the stego signal which minimizes the KL divergence under this model has a covariance proportional to the cover noise covariance. The resulting embedding scheme achieves state-of-the-art performances which go well beyond the current standards in side-informed JPEG steganography.

A study on scantling formulae of plate members due to lateral pressure under the effect of axial loads

Existing rule scantling formulae of plate members are based on conventional plastic design theory, and do not necessarily reflect complicated plate bending phenomena under axial loads. In this study, we first formulated the effect of axial load on the fully plastic moment based on the von Mises yield criterion for longitudinally stiffened plate in addition to the well-known formula for transversely stiffened plate. In addition, we derived a theoretical formulation of the lateral pressure corresponding to 2-point hinge and 3-point hinge formation taking account of the effect of the additional lateral force due to the axial loads on the deflected plating, using a simple plate strip bending model assuming a long plate with a large aspect ratio.Then, a series of elastic-plastic FE analyses was carried out to verify the structural behavior and the effect of axial load on the plate plastic bending strength. The plate strength was evaluated based on the residual deflection criteria of two cases (0.26 mm and 4.0 mm), and the results were compared with the theoretical derivation. As a result, it was found that assumption of linear strength reduction to the axial stress can cover the transversely stiffened plate under compressive axial stress conservatively. As to the transversely stiffened plate under tensile axial stress and the longitudinally stiffened plate, the strength reduction was in accordance with the reduction in the fully plastic moment based on the von Mises yield criterion in the conservative side. Finally, based on the findings, the required plate thickness coefficients were proposed on an empirical basis both for transversely and longitudinally stiffened plate under compressive and tensile axial loads.

Mechanical Properties of novel hardened cement paste reinforced with Multi-Walled Carbon Nano-Tubes (MWCNTs) and Glass Fibers Nano material

To improve the mechanical and durability properties of ordinary Portland cement (OPC) mortar and paste, the incorporation of multi walled Carbon nanotubes (MWCNTs) and their dispersion procedures, functionalization, and ultra sonication have been intensively implemented. Most of the studies showed significant enhancements in the mechanical properties of OPC mortar or paste; however, others showed impairments. The recent studies regarding the implementation of MWCNTs and Glass Fibres on the mechanical properties of OPC paste and mortar were reviewed and these properties include compressive, tensile, flexural strengths, and elastic modulus. A statistical study was conducted to evaluate the mechanical properties of concrete by dispersion of MWCNT’s and Glass Fibres in the cement paste. In these composites, the percentage of MWCNTs was fixed at 0.75% by weight of cement, while the percentage of Glass Fibers was fixed at 0.25% by weight of cement. The samples were cured in tap water for 28 days at 25 + 2?C.Composite specimens were tested for compression and flexure in order to evaluate their mechanical properties such as compressive strength, flexural strength, toughness and ductility and compared with the results of plain cement control beams. The maximum deflection was found to be 0.5mm with a maximum load of 500N. The flexural strength was observed to be 1250.50 N/mm2 as per ASTM D 790 which is 20% more than the flexural strength obtained with Plain Cement+MWCNT’s and 60 to 70% more than that obtained with Plain Cement + Glass Fibres. The flexural modulus as per deflection criteria is 535.94 N/mm2 which is 10 to 20% more than that obtained of Plain Cement+MWCNT’s and Plain Cement+ Glass Fibres. The compressive strength of Plain Cement+0.75% MWCNT’s+0.25% Glass fibres was found to be 65 N/mm2 which is greater than Plain cement and Plain cement+MWCNT’s. Surface morphology by Scanning Electron microscopy of the specimens infers the clustering of glass fibres and demonstr

Reducing the Structural Mass of Large Direct Drive Wind Turbine Generators through Triply Periodic Minimal Surfaces Enabled by Hybrid Additive Manufacturing

As the power output of direct drive generators increases, they become prohibitively large with much of this material structural support. In this work, implicit modeling was coupled to finite element analysis through a genetic algorithm variant to automate lattice optimization for the rotor of a 5 MW permanent magnet direct drive generator for mass reduction. Three triply periodic minimal surfaces (TPMS) were chosen: Diamond, Schwartz Primitive, and Gyroid. Parameter and functionally graded lattice optimization were employed to reduce mass within deflection criteria. Inactive mass for the 5 MW Diamond, Schwartz Primitive, and Gyroid optimized designs was 10,043, 10,858, and 10,990 kg, respectively. The Schwartz Primitive rotor resulted in a 34% reduction in inactive mass compared to a 5 MW baseline design. Radial and axial deflections were below the critical limit of 0.65 and 32.17 mm, respectively. The lowest torsional deflection was seen in the Schwartz Primitive TPMS lattice at 3.89 mm. Based on these designs, hybrid additive manufacturing with investment casting was used to validate manufacturability in metal. A fused deposition modeling (FDM) TPMS topology was printed for validation of the FEA results. Comparison between digital image correlation of the FDM printed design and FEA design resulted in a 6.7% deformation difference for equivalent loading conditions.

Detectability-Based JPEG Steganography Modeling the Processing Pipeline: The Noise-Content Trade-off

The current art of steganography shows that schemes using a deflection criterion (such as MiPOD) for JPEG steganography are usually subpar with respect to distortion-based schemes. We link this lack of performance to a poor estimation of the variance of the model of the noise on the cover image. However, this statistically-based method provides a better assessment of the detectability of hidden data as well as theoretical guarantees under a given model. In this paper, we propose a method to obtain better estimates of the variances of DCT coefficients by taking into account the dependencies introduced by development pipeline on pixels. A second method, which is a side-informed extension of Gaussian Embedding in the JPEG domain using quantization error as side-information, is also formulated and shown to achieve state-of-the-art performances. Eventually, the trade-off between noise and content complexity in steganography is thoroughly analyzed through the lenses of these two new methods using a wide range of numerical experiments.

Experimental Investigation on the Propagation of Hydraulic Fractures through Coal‐Rock Interfaces

Although hydraulic fracturing has been one of the primary stimulation methods for coal‐bed methane (CBM) exploration, it is difficult to be applied in soft and low‐permeability coal seams due to the instability of wells in such geological structures. In order to solve the problem, an idea of indirect fracturing is proposed, that is, fractures are initiated in stable and hard rocks and then propagated to coal seams in which crack networks can be formed. To verify the feasibility of such an approach, the true triaxial hydraulic fracturing experiments were conducted using two‐dimensional and three‐dimensional coal‐rock combination samples, respectively. This study investigates the fracture patterns, pressure variation, and fracture morphology. The results show that in the process of fracture propagation from sandy mudstones to coals, the strain energy release rate in the sandy mudstones is 10.69∼25.53 times greater than that in the coal. When the fracture has a tendency to deflect toward the lower strength coal strata, under the condition of large K2/K1, the deflection criterion will be met first and the fracture will deflect and grow into the coal strata. In addition, the complex crack network can be generated when the hydrofracture intersects the coal‐rock interface and the fracture pattern is analyzed.

Allowable wall deflection of braced excavation adjacent to pile-supported buildings

To protect adjacent buildings is a major concern for the construction of excavation in urban areas. In practice, the impacts on neighboring pile-supported buildings are normally minimized by limiting the deflection of earth retaining wall. Existing deflection criteria, however, are often empirical. In this work, we employ an analytical model to relate the wall deflection of braced excavation to the response of adjacent pile-supported buildings and thus forming a theoretical tool for determining the allowable deformation of excavation support structures based on the tolerance of buildings to distortion. The model combines closed-form excavation-induced free-field soil movements with elastic continuum solution that explicitly accounts for the interactions between raft, piles, and soils. Following validation against field model test and finite element simulation, the model is utilized to reveal the correspondence between the angular distortion of pile-supported buildings and the maximum retaining wall deflection under different combinations of excavation geometry, soil properties, and parameters of pile foundation potentially encountered in practice. A dimensionless factor composed of these influencing variables is proposed, and its correlation with the ratio of the building angular distortion over the maximum retaining wall deflection provides a rational way to determine the serviceability limit states of braced excavation.

Static and sustained loading behavior of a basalt FRP shell–concrete composite bridge deck: An experimental and numerical study

The fiber reinforced polymer (FRP)-concrete composite bridge deck is expected to be a competitive alternative to the reinforced concrete bridge deck owing to its great durability, low weight, and high loading efficacy. Based on previous studies, an optimized basalt FRP shell (BFRP)–concrete composite bridge deck was investigated experimentally and numerically in this study. Through the construction simulation test, the optimized BFRP shell was proved to be a qualified formwork with a 30.9% lower midspan deflection than the BFRP shell of previous studies and was lower than 1/800 of the net span. In the static test, the load capacities of deck specimens with depths of 200 mm and 180 mm reached 470 kN and 340 kN, respectively, with residual deflections lower than 7 mm. Meanwhile, the deck showed decent collaborative behavior, without visible interfacial debonding or slippage during the static test. Compared with the previously studied bridge deck, the bridge deck of the current study can achieve a higher short-term cost performance. After 175 days of three-point flexural sustained loading, the additional midspan deflections were 0.3 mm, 0.37 mm, and 0.46 mm, for load levels of 0.2, 0.25, and 0.3, respectively, which were less than 7% of their instantaneous elastic deflections. The finite element (FE) model was established using the Bailey-Norton model for the creep of the FRP and Bazant’s B-3 model for the creep of the concrete. The FE results were in good agreement with the experimental results, both in short- and long-term scenarios. Using numerical simulation with a load duration of 50 years, the allowable load level of this bridge deck reached 0.4, which meets the criteria for creep deflection in the ACI standard.

Optimization of composite wing spars for an unmanned aerial vehicle

In this paper, the weight optimizing of an unmanned aerial vehicle wing spar was designed by using composite material. The optimization parameters were considered, respectively: the wing mass, the location of the spars and ribs, and the spars mass. Determined the selecting of wing spars locations for optimizing spars design based on the minimum weight of the wing. Layer optimizing was used to reduce the weight of composite wing spars. The thickness of front spar and rear spar element such as web and flange were optimized by criterion of allowable normal stress and deflection. The analysis of stress-strain state for all variants were carried out in the FEMAP software package. As the result of analysis, the total weights of composite wing spars reduced 18.17% than the original spars.

Active Damping of Nonstationary Vibrations of a Three-Layer Electro-Viscoelastic Composite Plate

A method for constructing nonstationary vibration equations for electro-viscoelastic composite plates with their active damping is described. The problem is solved in an integral Fourier transform frequency space. To construct a multilayer plate model, a discrete structural approach was used, i.e., the plate is divided through the thickness into computational layers, within which the displacements and electric potentials are approximated by means of quadratic Lagrange polynomials. At the edges of the plate, the Navier conditions are met. The semi-analytical nonstationary vibration equations are derived by means of the variational convolutional Lagrange equation. To represent them in a frequency space, a direct integral Fourier transform is used, which makes it possible to use experimentally determined frequency-dependent complex characteristics directly in calculations of nonstationary vibrations of plates without additional transformations of integral physical relations. Solutions of the problem of active damping of nonstationary vibrations for the frequency images of displacements and electric potentials have been found, their convergence is analyzed. The procedure has been evaluated by analyzing the active damping of nonstationary vibrations of a three-layer edge-hinged square plate under the action of a blast wave impulse. The middle layer is made of a composite material, and the outer electro-viscoelastic layers act as a sensor and an actuator. The active damping of vibrations is provided by connecting these layers of the plate into a negative feedback circuit with the proportional-differential control law. The viscoelastic and electro-viscoelastic characteristics of the materials are taken into account by means of complex elastic, dielectric and piezoelectric moduli. The results of analyzing the active damping of nonstationary vibrations of a plate are presented. The values of the proportional and differential components of the controller as characteristics of this damping were chosen taking into account the permissible electric field strength of the actuator. The research results for the case of passive damping of vibrations are also given for comparison. The dependences of the decrement of plate vibrations on the differential component of the controller and of the maximum plate deflection on the reinforcement angle of the middle layer material have been established. The optimum reinforcement angle according to the minimum plate deflection criterion has been determined, which provides an increase in the efficiency of active damping of nonstationary vibrations of the plate owing to an increase in the differential component of the controller.

Successive sustained loading effect on the long-term deflection of flat slab

The research work presents the experimental long-term behaviour of reinforced concrete (RC) flat slab specimens at 1:2 scale, subjected to uniformly distributed sustained load in successive phases up to 90 days. The sustained load was applied in two stages, in the first stage, it was 3 kN/m2 for 30 days, whereas in the second stage, it was increased from 3 kN/m2 to 6 kN/m2 for the next 60 days. Age-dependent strength of cement mortar and concrete as used in RC flat slabs has been determined using the method as per the Indian code of practice. The contribution of creep and shrinkage deflection in total deflection for the column strip, middle strip, and cantilever portion has been observed in the range of 34% to 42% at the end of 90 days. After the first 30 days, the mid panel deflection of the flat slabs was larger as compared to column strip and cantilever deflection. At 90 days, the cantilever portion experienced the highest deflection as compared to middle strip and column strip deflection. The measured deflection has also been compared with the IS code procedure and it is found that the code underestimates the long-term deflection of the flat slab. Further, the finite element modelling using ABAQUS has also been carried out on the RC flat slab to validate the experimental results of the same slab within the elastic range. The present study gives an idea to the designer for fixing the thickness of the slab by considering the long-term deflection criteria in the design of the RC flat slab based on its behaviour under sustained loading.

Computation of Static Modulus of Elasticity and Poisson's Ratio of M20 Grade Self-Curing Concrete with Peg-400 as a Self Curing Agent Using is Code and Astm Standard

The concrete does not attain its original shape after unloading as it is not an elastic material. It is a non-linear material as depicted by its stress-strain curve. Hence, the elastic constants like modulus and Poisson’s ratio are not strictly applicable to such a complex, heterogeneous and nonlinear construction material. However, an elastic behaviour is assumed for the analysis and design of concrete structures by making use of these constants. The modulus of elasticity of concrete is its inherent property of undergoing an elastic deformation. Higher value of modulus leads to an enhanced stiffness of the structural elements. Curing is one of the important parameters influencing the modulus value. Curing caters to maintaining the required temperature, preventing water loss and shrinkage associated with it. The Shrinkage Reducing Admixture (SRA) in the form of Polyethylene Glycol 400 (PEG 400) liquid, added as a self-curing agent, plays an important role of reducing the water evaporation from the concrete mass, resulting into an improved water retention capacity of the concrete. PEG 400 is hydrophilic in nature. It plays a dual role of controlling evaporation and attracting moisture from the atmosphere. Self-curing leads to uninterrupted and effective curing by retaining the required quantity of water for an adequate cement hydration and maintaining the high relative humidity (RH), thereby resulting in to hard and dense concrete, with reduced thermal and shrinkage cracks. To provide a practical solution for the nonavailability of better quality water or lack of proper curing due to negligence, producing a self-curing concrete is a sustainable option. Generally, self-curing is advocated for the High Strength Concrete (HSC) having low water-cement ratio (w/c), because of chemical shrinkage associated with Portland cement hydration and low permeability of these materials. Moreover, it is an effective way to reduce the self-desiccation, autogenous shrinkage, plastic shrinkage cracking, drying shrinkage cracking and water absorption. Though the structural elements like Reinforced Cement Concrete (RCC) slabs are cast using lower grade concrete like M20, generally with higher w/c ratio, they are directly exposed to the harsh environment while concreting and a considerable period after concreting. To add to this, many times, the curing is not sufficient on the construction site. This leads to the undesirable situation of concrete properties not getting developed to their full potential values; the vital parameters being strength and modulus. Modulus of elasticity of concrete is known to be a function of its compressive strength. Development of required modulus of elasticity, for a structural element with a particular concrete grade, makes it adequately stiff thereby satisfying the limit state of serviceability for deflection. Excessive deflection of any structural element is highly undesirable phenomenon; moreover, it is well established fact in RCC theory that the slab depth is governed by the deflection criterion. This paper discusses an experimental investigation of short term static modulus of elasticity and Poisson’s ratio of M20 grade of self curing concrete using PEG 400 as a self curing agent. Three different dosages of 1%, 1.5% and 2% of PEG 400, expressed as percentage of weight of cement, were used. The conventional cylindrical specimens were subjected to water curing for 28 days, whereas self cured cylinders were exposed to air curing in an open shaded area for 28 days. Indian Standard: IS 516- 1959 and American Society for Testing and Materials (ASTM) standard: C469/C469M-2014 were followed for testing conventional as well as self cured specimens. The laboratory investigation was aimed at comparing the values of the two elastic constants obtained for the self cured concrete with that for the conventional mix, by both the methods. Though conventional concrete had highest values of density and compressive strength, it was observed that concrete with 1.5% PEG 400 exhibited greatest values of modulus of elasticity, by both the methods. Dosages of 1.5% and 2% of PEG 400 resulted in to higher values of Poisson’s ratio in comparison with that for conventional mix and 1% PEG 400 mix.

Optimizing the Design of Tall Buildings Using the Principle of Virtual Work: The Effect of Semi Rigid Connections

The Virtual Work Optimization Method (VWOM) is used to optimize tall buildings with semi rigid connections. The VWOM is an automated method that minimizes the mass of a structure with a given geometry, deflection criteria and load cases, while adhering to building code requirements. Members are selected from a user defined database to meet strength and stiffness criteria. The rotational stiffness of connections can be specified and varied, from rigid to pinned. The method is explained using an example of a two storey one bay steel frame with six members. Four case studies are presented: (i) a six storey two bay frame, (ii) a ten storey one bay steel building, (iii) a fifteen storey three bay steel frame and (iv) a twenty four storey three bay building. The examples are compared to results found in the literature. Structures were optimized for a range of connection rotational stiffnesses. The VWOM obtained results up to 44.6% lighter than published work. Optimized results showed that in most cases the semi rigid connection produced the same results as the rigid connections. This is due to the rapid plateauing of the optimized mass as the connection stiffness increases. Thus, the typical definition of semi rigid and rigid rotational stiffnesses (for example Eurocode 3) are both found on this plateau. If some members are lightly loaded, broad semi rigid and rigid bands can be produced. The effect in these cases is that structures with rigid connections are lighter than those with semi rigid connections as no compensation in the member stiffness is required to meet deflection criteria.

Dynamic Reliability of Continuous Rigid-Frame Bridges under Stochastic Moving Vehicle Loads

The current volume of freight traffic has increased significantly during the past decades, impacted by the fast development of the national transportation market. As a result, the phenomena of truck overloading and traffic congestion emerge, which have resulted in numerous bridge collapse events or damage due to truck overloading. Thus, it is an urgent task to evaluate bridge safety under actual traffic loads. This study evaluated probabilistic dynamic load effects on rigid-frame bridges under highway traffic monitoring loads. The site-specific traffic monitoring data of a highway in China were utilized to establish stochastic traffic models. The dynamic effect was considered in a vehicle-bridge coupled vibration model, and the probability estimation was conducted based on the first-passage criterion of the girder deflection. The prototype bridge is a continuous rigid-frame bridge with a midspan length of 200 m and a pier height of 182 m. It is demonstrated that the dynamic traffic load effect follows Gaussian distribution, which can be treated as a stationary random process. The mean value and standard deviation of the deflections are 0.071 m and 0.088 m, respectively. The dynamic reliability index for the first passage of girder deflection is 6.45 for the current traffic condition. However, the reliability index decreases to 5.60 in the bridge lifetime, accounting for an average traffic volume growth ratio of 3.6%.