Shear Moment Research Articles

Comparison of Seismic Behaviors of Interior Joints in PT and RC Flat Plate Systems

The purpose of this study is to compare the seismic behaviors of interior post-tensioned (PT) and reinforced concrete (RC) flat plate slab-column connections designed to resist only gravity loads. In general, flat plate systems have been used to support gravity loads, which should be constructed with lateral system such as shear walls or moment frames. Flat plate systems should retain the ability to undergo the lateral drift associated with the lateral system without loss of gravity load carrying capacity. Although these systems are common, relatively little experimental study has been conducted to assess actual behavior under lateral loads. Therefore, this study was undertaken to assess the seismic performance of two PT and one RC slab-column interior connection under high gravity loads. This study observed that PT connections had a better seismic performance than corresponding RC connections in terms strength, deformability, energy absorption.

Power spectrum shape from peculiar velocity data

We constrain the velocity power spectrum shape parameter Γ in linear theory using the nine bulk flow and shear moments estimated from four recent peculiar velocity surveys. For each survey, a likelihood function for Γ was found after marginalizing over the power spectrum amplitude σ8Ω0.6m using constraints obtained from comparisons between redshift surveys and peculiar velocity data. In order to maximize the accuracy of our analyses, the velocity noise σ* was estimated directly for each survey. A statistical analysis of the differences between the values of the moments estimated from different surveys showed consistency with theoretical predictions, suggesting that all the surveys investigated reflect the same large-scale flows. The peculiar velocity surveys were combined into a composite survey yielding the constraint Γ= 0.13+0.09−0.05. This value is lower than, but consistent with, values obtained using redshift surveys and cosmic microwave background data.

The effect of camera viewing angle on posture assessment repeatability and cumulative spinal loading

Video-based task analysis in the workplace is often limited by equipment location and production line arrangement, therefore making it difficult to capture the motion in a single plane. The purpose of this study was to investigate the effects of camera placement on an observer's ability to accurately assess working postures in three dimensions and the resultant influence on the reliability and repeatability of calculated cumulative loading variables. Four video cameras were placed at viewing angles of 0°, 45°, 60° and 90° to the frontal plane, enabling the simultaneous collection of views of four lifting tasks (two symmetric and two asymmetric). A total of 11 participants were trained in the use of the 3DMatch 3-D posture matching software package (developed at the University of Waterloo) and were required to analyse 16 lifting trials. Four of the participants were randomly selected to return within 72 h and repeat the analysis protocol to test intra-observer repeatability. Posture matching agreement between camera views was higher when the body segments had a minimal range of motion during the task. There was no significant participant main effect; however, there was a significant (p < 0.05) task main effect. Intraclass correlation coefficients (ICC) were calculated to assess the between day reliability. Compression, reaction anterior shear and extension moment were all found to have excellent reliability (ICC > 0.75). Joint anterior shear and joint posterior shear both provided fair to good reliability (0.4 > ICC < 0.75). Overall, the impact of the camera viewing angle on an observer's ability to match working postural exposure was found to be small.

Experimental and theoretical analysis of the moment–rotation behaviour of stiffened extended end-plate connections

A new theoretical model to evaluate the moment–rotation ( M – ϕ ) relationship for stiffened and extended steel beam–column end-plate connections has been derived in this paper. Based on a specific definition of the end-plate connection rotation, the end-plate connection is decomposed into several components, including the panel zone, bolt, end-plate and column flange. The complete loading–deformation process of each component is then analysed. Finally the loading–deformation process for the whole connection is obtained by superimposing the behaviour of each component. In addition, 5 joint tests have been conducted to verify the proposed analytical model. By comparing it with the test results, it has been concluded that this analytical model can evaluate the rotational behaviour of end-plate connections, as well as the moment–rotation ( M – ϕ ) curve and the initial rotational stiffness accurately. Furthermore, it can analyse every contribution to the joint’s rotational deformation, such as the shear deformation of the panel zone, the bolt extension, the bending deformation of the end-plate and column flange, etc. This analytical model also provides moment–shear rotation ( M – ϕ s ) and moment–gap rotation ( M – ϕ ep ) curves, which establish a reliable foundation for analysing the detailed rotational behaviour of end-plate connections.

Transverse shear and pressurization effects in the bending of plates with reinforced cracks

The authors develop an eigth-order model for bending of transversally isotropic plates and use integral transforms and a collocation method to form a line-spring model for a cracked plate. The eigth-order model allows satisfaction of the three standard plate bending boundary conditions; the normal moment, twisting moment, and transverse shear force, and an additional shear stress resultant that allows analysis of transverse normal stresses near the crack tip. The line-spring model is used to develop geometry correction factors for bending of finite-thickness plates, accounting for transverse shear deformation and pressurization of the plate near the crack tip. The line-spring model is then applied to the problem of a plate with a reinforced crack, and the results are used to validate an interpolation solution based on an energy method. While not explicitly analysed, the models are applicable to many problems, including bending of bonded repairs, fracture and fatigue of composite and layered materials, surface cracks, crack tip plasticity and crack closure or crack face interaction.

Load and resistance data for precast stringer highway bridges

Statistical parameters for the load effects and resistances of precast "type G" stringer bridges erected in Alberta since the late 1950s are presented to assist practicing engineers assessing similar bridges using the mean load method. The load effect data include unit weight data for normal weight and two lightweight concretes; traffic volumes, gross vehicle weights, and single, tandem, and tridem axle weights observed on primary, secondary, and local roads; and dynamic load allowances for shear and bending moment on short span bridges. Extreme annual traffic loads are derived. The resistance data include compressive and tensile strengths of normal weight and two lightweight concretes and yield strengths for corroded and uncorroded reinforcing steel. Additional statistical parameters are presented to account for other readily discerned bridge-specific idealization factors that affect the reliability indices. Professional factors for flexural and shear resistance are derived using experimental data reported from past investigations of type G stringers by others.Key words: concrete, core tests, corrosion, dynamic load allowance, material properties, single axles, tandem axles, tridem axles, reliability.

Assessment of precast stringer highway bridges using mean load method

The mean load method of the Canadian Highway Bridge Design Code is used to evaluate the shear and bending moment reliability of existing precast "type G" stringer bridges in Alberta that date from the late 1950s. The overall stringer population is categorized into distinct subpopulations using bridge-specific factors, including the degree of deterioration and approach span condition, which are readily identified during a brief field visit or from inspection reports. Critical sections to be investigated for reliability resisting shear forces or bending moments are determined. The reliability indices decrease if the reinforcement is corroded or the bridge approach is not smooth, and the reduction of the maximum axle loads permitted by legislation due to these factors is quantified. For bridge subpopulations where the actual reliability index is less than the target value for current legal axle loads, the critical axle load for moment is less than that for shear. Therefore, if flexural distress is not noted during inspection of such structures, they are likely adequate for the actual loading they are subjected to.Key words: corrosion, deterioration, dynamic load allowance, mean load method, reliability, visual inspection.

A 4-node co-rotational ANS shell element for laminated composite structures

The formulation of a non-linear composite 4-node co-rotational resultant shell element is presented for the solution of bending, free vibration, critical buckling and postbuckling analysis of composite plates and shells. Using the ANS (assumed natural strain) method the present shell element generates shear locking behavior, and such element performs very well as much as shells get thin. The formulation of the geometrical stiffness presented here is exactly defined on the mid-surface and is efficient for analyzing stability problems of thin and thick laminated plates, and shells by incorporating bending moment and transverse shear resultant forces. The transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The adoption of a second-order co-rotational formulation makes it computationally efficient compared to the most existing composite shell elements. The proposed formulation is computationally efficient and the test results showed good agreement.

BEM based on discontinuous solutions in the theory of Kirchhoff plates on an elastic foundation

We examine the construction of discontinuous solutions for Kirchhoff plates on a generalized elastic foundation. By discontinuous solutions we mean solutions which, when crossing certain lines, have discontinuities of the first type. In the theory of Kirchhoff plates, there may be jumps of the transverse deflection, slope angle, bending moment and equivalent shear force. Initially we construct the solutions due to concentrated jumps. Using them as Green functions, we express discontinuous solutions that are the base for the indirect method of boundary integral equations.

Design Charts for Helicoidal Stair Slabs with Landing at Midspan

Helicoidal staircases are quite popular among architects for aesthetic reasons. While design charts for simple helicoidal stair slabs are available in design handbooks, no such aid is available for fixed ended helicoidal slabs with landings at midspan. This paper attempts to propose such a design tool for the practicing engineer. Because of the symmetric nature of the slab, four of the six stress resultants at midspan become zero. Thus if the two redundants at midspan can be determined, the rest of the analysis becomes a statically determinate problem. Strain energy method has been used to analyze the structure and determine these two redundants at midspan. Based on this analytical framework, charts have been proposed to quickly determine these midspan redundants. Different geometric parameters have been considered and nondimensional parameters have been used to derive the charts. Finally, the effect of a landing on the stress resultants has been investigated through a limited parametric study. It has been found that the presence of landing significantly affects the maximum vertical moment and torsion. Landing span also considerably influences the distribution of vertical moment, torsion, and vertical shear along the span.

Simplified Structural Analysis of Retaining Walls on Stepped Footings

Stepped footings are often required for earth retaining structures to suit grade changes in the site. The behavior of walls supported on stepped footings is not well understood due to the presence of reentrant corners and double curvature. In this study, a large number of reinforced concrete retaining walls with different geometry are analyzed using the finite element method. The bending moments throughout the wall and shear forces at the support are determined and presented in a tabular format that is easy to use by practicing structural engineers. The results of the analysis showed that positive and negative bending moments can possibly exist in a retaining wall supported on stepped footing; hence both faces of the wall should be reinforced for flexure. Further, very high stresses due to shear and bending moment occur at the reentrant corner of the stepped footing. These forces, however, cannot realistically exist in thin reinforced concrete structures due to postcracking deformations. Therefore, structural design at such a location should be based on values of shear force and bending moment just off the reentrant corner, provided that proper detailing with diagonal steel reinforcement is utilized at the tip of the step.

Dynamic Wave Loads On a High Speed Catamaran Ferry Fitted With T-Foils and Stern Tabs

Measurements of unsteady stress have been made on an INCAT wave-piercing catamaran during an extended period of passenger operations under varying sea conditions, vessel speed and heading relative to the sea. It has been found that the stress fluctuations are consistent with unsteady bending of the hull cross section. The measured results are compared with the predictions of a time domain, spatially fixed, strip theory method suitable for computation at high Froude number. It is found that there is a progressive nonlinear reduction of global bending moment and sectional shear fluctuations relative to wave height as the wave height increases. The intensity of the observed stress fluctuations is shown to be consistent with the loading predictions of the time domain method. © 2005: Royal Institution of Naval Architects.

Bond Performance of Interior Beam-Column Joints with High-Strength Reinforcement

Reinforced concrete structures function by ensuring that the forces can be transferred between the concrete and reinforcement. One place this occurs is at the bond between the concrete and the reinforcement. This article considers the bond performance of interior beam-column joints, where reinforcement must transition from being at yield in tension on one side of the joint to being close to yield in compression on the other side. The authors report on a study of four beam-column joints, undertaken to assess the accuracy of New Zealand design rules relating to bond strength in beam-column joints when applied to large diameter, high-strength reinforcement. In their samples, the ratio of longitudinal beam reinforcement diameter to column depth intentionally did not meet the requirements of the New Zealand design standard for any of the units. The units were subjected to cyclic displacements up to interstory drift angles of 5%. Bond failure occurred in two of the four test units, at drift levels exceeding those allowed by international codes. The authors conclude that the unexpectedly good bond strength was caused by the large quantity of column longitudinal reinforcement included in these units. The reinforcement gave the columns a large excess of moment and vertical joint shear capacity over that required. This reduced damage (particularly the formation of splitting cracks) in the joint zone concrete as testing progressed, thus improving bond conditions.

Shear strength of horizontally curved steel I-girders — finite element analysis studies

This paper presents the results of finite element analysis (FEA) studies of four curved steel I-girder shear components tested experimentally in previous research, as well as parametric extensions of these tests. These studies focus on the influence of horizontal curvature on the maximum strength of transversely stiffened members with web slenderness D / t w approximately equal to the largest value permitted in AASHTO [AASHTO LRFD bridge design specifications. 3rd ed. In: 2005 Interim Provisions, Washington (DC): American Association of State and Highway Transportation Officials; 2004], and with panel aspect ratios of d o / D = 1.5 and 3.0. These ratios are larger than previously considered in experimental tests of curved I-girders with similar or larger slenderness. The girders studied have subtended angles between their bracing locations of L b / R = 0.05 and 0.10, and web panel d o / R values ranging from 0.03 to 0.10. The FEA models incorporate the measured material stress–strain relationships and section dimensions from the physical tests, detailed modeling of the test boundary conditions, residual stresses due to flame cutting and welding, and initial geometric imperfections in the form of buckling mode shapes. The load transfer mechanisms of the test girders are investigated via elastic buckling and full nonlinear analyses. The parametric studies are performed to investigate the effects of residual stresses and geometric imperfections, the behavior of equivalent straight girders, and the influence of reduced flange size on the peak shear capacity and moment–shear interaction.

Bending Moment–Shear Force Interaction Domains for Prestressed Concrete Beams

The performance of a prestressed concrete beam, subjected to bending moment M together with shear force V, has been the object of many studies and is an important aspect to take into account in the design. Some models, proposed by researchers and international codes, evaluate the shear strength of prestressed beams by modifying the truss model by Morsch, so as to account for the different slope of stress fields in the web due to the prestressing action. More recent approaches add a strut-and-tie model to the traditional truss model. This paper generalizes a model that was previously proposed for box and I-shaped reinforced concrete cross sections of structural elements. The model, that now includes the effect of prestressing tendons, considers variable-depth stress fields applied to the cross section, subdivided into layers, and allows evaluation of normalized m-v design domains depending both on the web and flange reinforcement and on the slope of the prestressing steel tendons. The reliability of the method has been validated by comparing its numerical results to the strength provided by tests on reinforced concrete beams and on thin-webbed prestressed concrete beams, referred to in the literature. Finally, it has been used in the design of a pretensioned bridge beam to evaluate the additional reinforcement necessary in the flanges, as a function of the reinforcement provided to the web.

A variational principle based study of KPP minimal front speeds in random shears

The variational principle for Kolmogorov–Petrovsky–Piskunov (KPP) minimal front speeds provides an efficient tool for statistical speed analysis, as well as a fast and accurate method for speed computation. A variational principle based analysis is carried out on the ensemble of KPP speeds through spatially stationary random shear flows inside infinite channel domains. In the regime of small root mean square (rms) shear amplitude, the enhancement of the ensemble averaged KPP front speeds is proved to obey the quadratic law under certain shear moment conditions. Similarly, in the large rms amplitude regime, the enhancement follows the linear law. In particular, both laws hold for the Ornstein–Uhlenbeck (O–U) process in the case of two-dimensional channels. An asymptotic ensemble averaged speed formula is derived in the small rms regime and is explicit in the case of the O–U process of the shear. The variational principle based computation agrees with these analytical findings, and allows further study of the speed enhancement distributions as well as the dependence of the enhancement on the shear covariance. Direct simulations in the small rms regime suggest a quadratic speed enhancement law for non-KPP nonlinearities.

Minimum Averaged Compliance Density Based Topology Optimization of Structures

Usually, an optimal topology is obtained by optimizing the material distribution within a prescribed domain; for example, a rectangular domain with a specified length and width for a plane problem. However, the dimensions (i.e. aspect ratio) of a rectangular design domain have significant influence on the resultant optimal topology. In this paper, a minimum Averaged Compliance Density (ACD) based method for topology optimization of structures is proposed. Unlike the conventional topology optimization method, the ACD is taken as the objective function, and the topology and domain dimensions of the structure are optimized simultaneously. As an example, the topology of a cantilever beam with large aspect ratio will be optimized, which is often difficult for traditional topology optimization algorithms. Through optimizing the topology and the dimensions of the design domain, a base structure is obtained, which is repeated to yield the whole, assembled beam. The influence of the relative values of shear force and moment is analyzed numerically. Results show that as the value of the bending moment increases relative to the shear force, the optimal topology changes from a truss‐like structure to a vertically stiffened box‐like structure.

Assessment and Risk Ranking of Conventionally Reinforced Concrete Bridges for Shear

Large numbers of conventionally reinforced concrete bridges remaining in service are lightly reinforced for shear. State-of-the-art assessment of these bridges for shear requires consideration of shear and moment interaction. An assessment and risk-ranking methodology is proposed that incorporates moment–shear interaction. From analyses of vehicle loads on indeterminate bridge models, maximum moment and maximum shear are not coincident at intermediate support locations. Determining the critical combination of shear and moment requires evaluation of envelope values from shear–moment load histories for comparison with capacity curves. Capacity of the sections is determined by using AASHTO modified compression field theory, and statistical understrength is based on experimental test results. Comparison of the load effects and capacity is demonstrated for an in-service bridge to determine the reliability index (measure of relative risk) at sections along a girder. The reliability index can be used to establish rational load restrictions on the basis of a target reliability index for the inventory. The index can also be used for comparison between components and populations of conventionally reinforced concrete bridges for risk ranking. Ranking based on relative reliability indexes permits bridge engineers and managers to prioritize the bridges for repair or replacement.

Assessment and Risk Ranking of Conventionally Reinforced Concrete Bridges for Shear

Large numbers of conventionally reinforced concrete bridges remaining in service are lightly reinforced for shear. State-of-the-art assessment of these bridges for shear requires consideration of shear and moment interaction. An assessment and risk-ranking methodology is proposed that incorporates moment-shear interaction. From analyses of vehicle loads on indeterminate bridge models, maximum moment and maximum shear are not coincident at intermediate support locations. Determining the critical combination of shear and moment requires evaluation of envelope values from shear-moment load histories for comparison with capacity curves. Capacity of the sections is determined by using AASHTO modified compression field theory, and statistical understrength is based on experimental test results. Comparison of the load effects and capacity is demonstrated for an in-service bridge to determine the reliability index (measure of relative risk) at sections along a girder. The reliability index can be used to establis...

Effectiveness of the head and neck support (HANS1) device in frontal impacts of CART cars: a CAE analysis

Results of a CAE (Madymo) analysis probing effectiveness of the HANS device in reducing injuries to open-wheel racecar drivers in frontal impacts are presented. The model utilised a typical impact pulse used in sled tests. Results show that the HANS device significantly reduces upper-neck shear, tension, and extension moment. These results agree with published test data. Upper-neck loads remain lower than the no-HANS case for a wide range of tether stiffness. The same is true for upper-neck shear and tension for increasing tether slack. Results are more sensitive to changes in slack than stiffness. The predicted head injury criterion is higher for drivers with the HANS device. This is attributable to tether forces at the time of engagement, the magnitude and duration of which depend on contact-interaction between head and helmet-inside. Further tests are needed to better estimate this interaction. Results also show that lowering friction on HANS surfaces reduces head-neck injury potential.