Showing papers on "Deflection (engineering) published in 2007"

Simplified Model for Wall Deflection and Ground-Surface Settlement Caused by Braced Excavation in Clays

Abstract: Accurate prediction of ground-surface settlement adjacent to an excavation is often difficult to achieve without using accurate representation of small-strain nonlinearity in a soil model within finite-element analyses. In this paper a simplified semiempirical model is proposed for predicting maximum wall deflection, maximum surface settlement, and surface-settlement profile due to excavations in soft to medium clays. A large number of artificial data are generated through finite-element analyses using a well-calibrated, small-strain soil model. These data, consisting of wall displacements and ground-surface settlements in simulated excavations in soft to medium clays, provide the basis for developing the proposed semiempirical model. The proposed model is verified using case histories not used in the development of the model. The study shows that the developed model can accurately predict maximum wall deflection and ground-surface settlement caused by braced excavations in soft to medium clays.

Bridge deflection measurement using digital image correlation

Abstract: Digital image correlation technique is used for measuring vertical deflections of bridge girders during a bridge load testing. A bridge is loaded by a heavy cargo truck on the bridge road. Then, the deflection distribution is measured by digital image correlation. The applicability of digital image correlation to bridge deflection measurement is investigated by comparing the results obtained by digital image correlation with those obtained by displacement transducers. The effect of random pattern on an object surface is also investigated by measuring with and without random pattern. The results show that the deflection distributions of the bridge obtained by digital image correlation agree well with those obtained by the displacement transducers when the random pattern is attached on the bridge surface. In addition, it is found that the deflections can be measured even if the artificial random pattern is not applied to the surface of the bridge girder. It is emphasized that noncontact displacement measurement is possible by simple and easy procedure with digital image correlation for the structural evaluation of infrastructures.

Blast loading response of reinforced concrete panels reinforced with externally bonded GFRP laminates

Abstract: The behavior of reinforced concrete panels, or slabs, retrofitted with glass fiber reinforced polymer (GFRP) composite, and subjected to blast load is investigated. Eight 1000 × 1000 × 70 mm panels were made of 40 MPa concrete and reinforced with top and bottom steel meshes. Five of the panels were used as control while the remaining four were retrofitted with adhesively bonded 500 mm wide GFRP laminate strips on both faces, one in each direction parallel to the panel edges. The panels were subjected to blast loads generated by the detonation of either 22.4 kg or 33.4 kg ANFO explosive charge located at a 3-m standoff. Blast wave characteristics, including incident and reflected pressures and impulses, as well as panel central deflection and strain in steel and on concrete/FRP surfaces were measured. The post-blast damage and mode of failure of each panel was observed, and those panels that were not completely damaged by the blast were subsequently statically tested to find their residual strength. It was determined that overall the GFRP retrofitted panels performed better than the companion control panels while one retrofitted panel experienced severe damage and could not be tested statically after the blast. The latter finding is consistent with previous reports which have shown that at relatively close range the blast pressure due to nominally similar charges and standoff distance can vary significantly, thus producing different levels of damage.

Long-term and collapse tests on a timber-concrete composite beam with glued-in connection

Abstract: The paper reports the results of a comprehensive experimental test performed on a 6 m span timber-concrete composite beam with glued re-bar connection. The beam had first been subjected to sustained load in unsheltered outdoor conditions for 5 years. Eventually a ramp loading test up to failure was performed. The long-term test showed an increase in deflection mainly during the first two years, while the slip rose during the whole testing period. Thermo-hygrometric variations of environment caused an important fluctuation of all quantities on both yearly and daily scale. By comparing experimental and analytical results, it is highlighted that composite beams in outdoor conditions should be assigned to the 3rd service class according to the Eurocode 5 (EC5). Analytical predictions based on approximate formulae suggested by such regulation are found to be not conservative for the long-term behaviour and fairly accurate for the collapse behaviour. Since the simplified formulae proposed by the latest versions of the EC5-Parts 1.1 and 2 largely underestimate the actual connection stiffness and strength, it is recommended that realistic values of these properties, such as those obtained through push-out tests, be used when designing timber-concrete composite beams.

Assessing micromechanical properties of cells with atomic force microscopy: importance of the contact point.

Abstract: Mechanical properties are obtainable from atomic force microscopy (AFM) indentation force-depth curves, which are calculated from relationships between tip deflection and cantilever position, i.e. deflection curves. Indentation depth is the difference between tip deflections on a rigid and a soft material for the same amount of cantilever advancement, after contact is made. Since the contact point cannot be unequivocally identified from experimental data, there is some uncertainty in estimating material properties. Using simulations, this study examines some important issues related to the influence of contact point identification on estimated material properties. Simulations for linear materials using a typical stiffness for an AFM cantilever demonstrate that certain portions of the post-contact region of deflection curves for soft and very stiff materials can be approximated by quadratic and linear functions, respectively. Based on these findings, we first develop and verify an objective, automatic method to identify the contact point for materials with linear properties. We then assess the effect of misidentifying the contact point, with and without noise. If the contact point is missed by 100 nm, however, the true material properties cannot be estimated accurately. Noise adds to uncertainty in material properties at small indentations but the combined effect of missing the contact point and noise is dominated by the former. Even though the algorithm was developed for linear materials, it is also suitable for certain nonlinear materials making it more generally applicable.

Minimization of needle deflection in robot‐assisted percutaneous therapy

Abstract: Background Needle deflection and tissue deformation are two problems encountered during needle insertion into soft, non-homogeneous tissue. They affect the accuracy of needle placement, which in turn affects the effectiveness of needle-based therapies and biopsies. Methods In this study, a needle is inserted using a robot with two degrees of freedom. The needle is modelled as a flexible beam with clamped support at one end, and its deflection is estimated using online force/moment measurements at the needle base. To compensate for the needle deflection, the needle is axially rotated through 180° . The needle deflection estimation data is used to find the insertion depths at which needle rotations are to be performed. Results A bevelled-tip needle was inserted into animal tissue. The needle deflection at the target was reduced by about 90%. It was observed that minimization of needle deflection reduced tissue deformation. The proposed method reduced needle deflection more than when needle insertion was performed with constant rotation. Conclusions Estimating needle tip position using online force/moment measurement improves the accuracy of robot-assisted percutaneous procedures when imaging feedback is not available. Copyright © 2007 John Wiley & Sons, Ltd.

Snap-Through and Pull-In Instabilities of an Arch-Shaped Beam Under an Electrostatic Loading

Abstract: The snap-through and pull-in instabilities of the micromachined arch-shaped beams under an electrostatic loading are studied both theoretically and experimentally. The pull-in instability that results in a system collision with an electrode substrate may lead to a system failure and, thus, limits the system maximum displacement. The beam/plate structure with a flat initial configuration under an electrostatic loading can only experience the pull-in instability. With the different arch configurations, the structure may experience either only the pull-in instability or the snap-through and pull-in instabilities together. As shown in our computation and experiment, those arch-shaped beams with the snap-through instability have the larger maximum displacement compared with the arch-shaped beams with only the pull-in stability and those with the flat initial configuration. The snap-through occurs by exerting a fixed load, and the structure experiences a discontinuous displacement jump without consuming power. Furthermore, after the snap-through jump, the structures are demonstrated to have the capacity to withstand further electrostatic loading without pull-in. Those properties of consuming no power and increasing the structure deflection range without pull-in is very useful in microelectromechanical systems design, which can offer better sensitivity and tuning range.

Effective Moment of Inertia for Calculating Deflections of Concrete Members Containing Steel Reinforcement and Fiber-Reinforced Polymer Reinforcement

Abstract: This study reevaluates the effective moment of inertia expression that was first proposed by Branson in 1963 and currently is incorporated in the ACI Code. Effective moment curvature relationships are compared. The flexural behavior at service load levels and application to beams with fiber-reinforced polymer (FRP) reinforcement are examined. It is found that Branson’s expression is valid for members with steel reinforcement ratios greater than 1%. However, this expression overestimates member stiffness at lower reinforcement ratios and gives a member deflection less than expected, as demonstrated by comparison with test results. Branson’s approach also underestimates deflection of slender walls with a central layer of reinforcement, as well as deflection of FRP-reinforced concrete beams. The author presents an alternative formulation of the effective moment of inertia that is applicable to all ranges of reinforcement ratio for both steel and FRP reinforcement without the need to apply correction factors.

Deflection Calculation of FRP Reinforced Concrete Beams Based on Modifications to the Existing Branson Equation

Abstract: Fundamental concepts of tension stiffening are used to explain why Branson’s equation for the effective moment of inertia Ie does not predict deflection well for fiber reinforced polymer (FRP) reinforced concrete beams. The tension stiffening component in Branson’s equation is shown to depend on the ratio of gross-to-cracked moment of inertia ( Ig ∕ Icr ) , and gives too much tension stiffening for beams with an Ig ∕ Icr ratio greater than 3. FRP beams typically have an Ig ∕ Icr ratio greater than 5, leading to a much stiffer response and underprediction of computed deflections as observed by others in the past. One common approach to computing deflection of FRP reinforced concrete beams has been to use a modified form of the Branson equation. This paper presents a rational development of appropriate modification factors needed to reduce the tension stiffening component in Branson’s original expression to realistic levels. Computed deflections using this approach give reasonable results with the right mod...

Euler-Bernoulli beams with multiple singularities in the flexural stiffness

Abstract: Euler–Bernoulli beams under static loads in presence of discontinuities in the curvature and in the slope functions are the object of this study. Both types of discontinuities are modelled as singularities, superimposed to a uniform flexural stiffness, by making use of distributions such as unit step and Dirac's delta functions. A non-trivial generalisation to multiple different singularities of an integration procedure recently proposed by the authors for a single singularity is presented in this paper. The proposed integration procedure leads to closed form solutions, dependent on boundary conditions only, which do not require enforcement of continuity conditions along the beam span. It is however shown how, from the solution of the clamped-clamped beam, by considering suitable singularities at boundaries in the flexural stiffness model, responses concerning several boundary conditions can be recovered. Furthermore, solutions in terms of deflection of the beam are obtained for imposed displacements at boundaries providing the so called shape functions. The above mentioned shape functions can be adopted to insert beams with singularities as frame elements in a finite element discretisation of a frame structure. Explicit expressions of the element stiffness matrix are provided for beam elements with multiple singularities and the reduction of degrees of freedom with respect to classical finite element procedures is shown. Extension of the proposed procedure to beams with axial displacement and vertical deflection discontinuities is also presented.

Deformation and fracture modes of sandwich structures subjected to underwater impulsive loads

Abstract: Sandwich panel structures with thin front faces and low relative density cores offer significant impulse mitigation possibilities provided panel fracture is avoided. Here steel square honeycomb and pyramidal truss core sandwich panels with core relative densities of 4% were made from a ductile stainless steel and tested under impulsive loads simulating underwater blasts. Fluid-structure interaction experiments were performed to (i) demonstrate the benefits of sandwich structures with respect to solid plates of equal weight per unit area, (ii) identify failure modes of such structures, and (iii) assess the accuracy of finite element models for simulating the dynamic structural response. Both sandwich structures showed a 30% reduction in the maximum panel deflection compared with a monolithic plate of identical mass per unit area. The failure modes consisted of core crushing, core node imprinting/punch through/tearing and stretching of the front face sheet for the pyramidal truss core panels. Finite element analyses, based on an orthotropic homogenized constitutive model, predict the overall structural response and in particular the maximum panel displacement.

Micromechanical Analysis of Composite Corrugated-Core Sandwich Panels for Integral Thermal Protection Systems

Abstract: termsA44 andA55 werecalculatedusinganenergyapproach.Usingtheshear-deformableplatetheory,aclosed-form solution of the plate response was derived. The variation of plate stiffness and maximum plate deflection due to changing the web angle are discussed. The calculated results, which require significantly less computational effort and time, agree well with the three-dimensional finite element analysis. This study indicates that panels with rectangular webs resulted in a weak extensional, bending, and A55 stiffness and that the center plate deflection was minimum for a triangular corrugated core. The micromechanical analysis procedures developed in this study were used to determine the stresses in each component of the sandwich panel (face and web) due to a uniform pressure load.

Analytical investigation and numerical verification of Casimir effect on electrostatic nano-cantilevers

Abstract: In this paper, the two-point boundary value problem (BVP) of the nano-cantilever deflection subjected to Casimir and electrostatic forces is investigated using analytical and numerical methods to obtain the instability point of the nano-beam. In the analytical treatment of the BVP, the nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. Then, closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the beam are computed under the combined effects of electrostatic and Casimir forces. Electrostatic microactuators and freestanding nanoactuators are considered as special cases of our study. The detachment length and the minimum initial gap of freestanding nanocantilevers, which are the basic design parameters for NEMS switches, are determined. The results of the analytical study are verified by numerical solution of the BVP. The centerline of the beam under the effect of electrostatic and Casimir forces at small deflections and at the point of instability is obtained numerically to test the validity of the shape function assumed for the beam deflection in the analytical investigation. Finally, the large deformation theory is applied in numerical simulations to study the effect of the finite kinematics on the pull-in parameters of nano-canilevers.

Thermo elastic analysis of a functionally graded rotating disk with small and large deflections

Abstract: A functionally graded (FG) rotating disk with axisymmetric bending and steady-state thermal loading is studied. The material properties of the disk are assumed to be graded in the direction of the thickness by a power law distribution of volume fractions of the constituents. First-order shear deformation Mindlin plate and von Karman theories are employed. New set of equilibrium equations with small and large deflections are developed. Using small deflection theory an exact solution for displacement field is given. Solutions are obtained in series form in case of large deflection. Mechanical responses are compared small deflection versus large deflection as well as homogeneous versus FG disks. It is observed that for particular values of the grading index n of material properties mechanical responses in FG disk can be smaller than in a homogeneous disk. It is seen that given the non-dimensional maximum vertical displacement wmax/h close to 0.4 for a homogeneous (full-ceramic in this study) disk greater errors in the mechanical responses for FG disks would be introduced if one uses small deflection theory.

Influence of Skew Angle on Reinforced Concrete Slab Bridges

Abstract: The effect of a skew angle on simple-span reinforced concrete bridges is presented in this paper using the finite-element method. The parameters investigated in this analytical study were the span length, slab width, and skew angle. The finite-element analysis (FEA) results for skewed bridges were compared to the reference straight bridges as well as the American Association for State Highway and Transportation Officials (AASHTO) Standard Specifications and LRFD procedures. A total of 96 case study bridges were analyzed and subjected to AASHTO HS-20 design trucks positioned close to one edge on each bridge to produce maximum bending in the slab. The AASHTO Standard Specifications procedure gave similar results to the FEA maximum longitudinal bending moment for a skew angle less than or equal to 20°. As the skew angle increased, AASHTO Standard Specifications overestimated the maximum moment by 20% for 30°, 50% for 40°, and 100% for 50°. The AASHTO LRFD Design Specifications procedure overestimated the FEA maximum longitudinal bending moment. This overestimate increased with the increase in the skew angle, and decreased when the number of lanes increased; AASHTO LRFD overestimated the longitudinal bending moment by up to 40% for skew angles less than 30° and reaching 50% for 50°. The ratio between the three-dimensional FEA longitudinal moments for skewed and straight bridges was almost one for bridges with skew angle less than 20°. This ratio decreased to 0.75 for bridges with skew angles between 30 and 40°, and further decreased to 0.5 as the skew angle of the bridge increased to 50°. This decrease in the longitudinal moment ratio is offset by an increase of up to 75% in the maximum transverse moment ratio as the skew angle increases from 0 to 50°. The ratio between the FEA maximum live-load deflection for skewed bridges and straight bridges decreases in a pattern consistent with that of the longitudinal moment. This ratio decreased from one for skew angles less than 10° to 0.6 for skew angles between 40 and 50°.

Long-Term Behavior of Wood-Concrete Composite Floor/Deck Systems with Shear Key Connection Detail

Abstract: The paper investigates the long-term behavior of wood-concrete composite beams with notched connection detail. The experimental program comprised the characterization of the component materials (wood, concrete, and connection detail) and long-term tests on beam specimens. The beam specimens were monitored during the construction process, and for an overall period of 133 days after the application of the service load. The experimental results have then been extended to the entire service life of the structure using a one-dimensional finite-element model. It was found that the increase in moisture content due to the bleeding of the fresh concrete is not an issue for the durability of the wood deck, and the type of construction (shored or unshored) does not significantly affect the structural performance. The rheological phenomena experienced by the component materials lead to quite large deflections over the entire service life, whereas the variation in stress is not significant. If the limitation of the deflection is required for serviceability considerations, the use of concrete with reduced shrinkage and the precambering of the wood deck are to be recommended. A simplified approach based on closed form solutions for composite beams with smeared flexible connectors is finally proposed for the prediction of the long-term behavior.

The stiffness of laser stake welded T-joints in web-core sandwich structures

Abstract: The purpose of this paper is to describe experiments carried out on laser stake welded T-joints of web-core steel sandwich structures. A special test setup was developed to measure the shear-induced rotation at the T-joint. The ratio of the shear force to rotation angle gave the joint stiffness. This stiffness was measured for specimens with two different face-plate thicknesses. The influence of weld thickness, root gap and occurrence of contact were further investigated with finite element simulations. Finally, the shear stiffness of the sandwich structure transverse to the web plate direction was determined using the experimentally obtained average joint stiffness value. The validation of the shear stiffness was carried out by considering a beam in four-point bending. The agreement between calculated deflection and stress and experimental results was found to be good.

Rational model for calculating deflection of reinforced concrete beams and slabs

Abstract: Deflection control is an important performance criterion that needs to be satisfied to ensure serviceability of the structure for its intended use. The extent of cracking and amount of reinforcemen...

Magnetically-assisted remote control (MARC) steering of endovascular catheters for interventional MRI: a model for deflection and design implications.

Abstract: Current applied to wire coils wound at the tip of an endovascular catheter can be used to remotely steer a catheter under magnetic resonance imaging guidance. In this study, we derive and validate an equation that characterizes the relationship between deflection and a number of physical factors: θ ∕ sin ( γ − θ ) = n I A B L ∕ E I A , where θ is the deflection angle, n is the number of solenoidal turns, I is the current, A is the cross-sectional area of the catheter tip, B is the magnetic resonance(MR)scanner main magnetic field, L is the unconstrained catheter length, E is Young’s Modulus for the catheter material, and I A is the area moment of inertia, and γ is the initial angle between the catheter tip and B . Solenoids of 50, 100, or 150 turns were wound on 1.8 F and 5 F catheters. Varying currents were applied remotely using a DC power supply in the MRI control room. The distal catheter tip was suspended within a phantom at varying lengths. Images were obtained with a 1.5 T or a 3 T MRscanner using “real-time” MR pulse sequences. Deflection angles were measured on acquired images. Catheter bending stiffess was determined using a tensile testing apparatus and a stereomicroscope. Predicted relationships between deflection and various physical factors were observed ( R 2 = 0.98 − 0.99 ) . The derived equation provides a framework for modeling of the behavior of the specialized catheter tip. Each physical factor studied has implications for catheter design and device implementation.