Showing papers on "Bending moment published in 1994"

Drying creep of concrete: constitutive model and new experiments separating its mechanisms

Abstract: A new experimental method which allows the direct separation of the components of drying creep due to microcracking and stress-induced shrinkage is developed, demonstrated and validated. The basic idea is to compare the curvature creep of beams subjected to the same bending moment but very different axial forces. The results confirm that drying creep has two different sources: microcracking and stress-induced shrinkage. The latter increases continuously, whereas the former first increases and then decreases. The test results are fitted using a finite element model. The results validate the present model for drying creep. The microcracking is described by an established model, and the free (unrestrained) shrinkage of a material element is shown to depend approximately linearly on the humidity drop.

Passive stiffness of the lumbar torso in flexion, extension, lateral bending, and axial rotation : effect of belt wearing and breath holding

Abstract: This work investigated the passive bending properties of the intact human torso about its three principal axes of flexion: extension, lateral bending, and axial rotation. Additionally, the effects of wearing an abdominal belt and holding the breath (full inhalation) on trunk stiffness was investigated. The torsos of 22 males and 15 females were subjected to bending moments while "floating" in a frictionless jig with isolated torso bending measured with a magnetic device. Belts and breath holding appear to stiffen the torso about the lateral bending and axial rotation axes but not in flexion or extension. Torsos are stiffer in lateral bending and capable of storing greater elastic energy. Regression equations were formulated to define stiffness and energy stored for input to biomechanical models that examine low back function and for bioengineers designing hardware for stabilization and bracing or investigation of traumatic events such as automobile collision.

Lateral load analysis of single piles and drilled shafts

Abstract: The p‐y method of analysis models nonlinear behavior, and is an effective method of designing deep foundations subjected to, lateral loads Deflections and bending moments calculated using p‐y analyses have usually been found to be in good agreement with field measurements This paper describes a method of analysis, the characteristic load method (CLM) that is simpler than p‐y analyses, but that closely approximates p‐y analysis results The method uses dimensional analysis to characterize the nonlinear behavior of laterally loaded piles and drilled shafts by means of relationships among dimensionless variables The new method is simple enough for use by manual calculation, and it can also be adapted for computer use Lateral deflections and maximum bending moments calculated using CLM have been found to be in good agreement with values measured in field load tests

An active flexible wing multi-disciplinary design optimization method

Abstract: This paper discusses Active Flexible Wing (AFW) technology and describes how it differs from conventional wing design. The benefits of AFW are briefly described. Two design procedures which aid in the design and optimization of an AFW wing are described in detail. The first procedure is for the design of an AFW control system on an existing wing. This procedure optimizes control surface positions to maximize air vehicle maneuverability, without exceeding structural limits. The second procedure is for the design of a new wing using AFW technology. This procedure simultaneously couples aerodynamic, structural, and external load designs. The process optimizes a wing structure and control surface positions for minimum weight and drag, while satisfying structural constraints. = buckling constraints = bending moment = drag of case i = hinge moment = roll moment of load case i = lift of load case i = pitching moment of load case i = roll rate = torsion moment = twist and camber variables (e.g., wing jig shape design) = structural design variables = flutter constraints = structural weight = control surface positions and air vehicle flight angle design variables = roll axis inertia = roll acceleration = stress constraints of load case i {a} = vector of rigid aerodynamic panel deflections {!} = lift vector on aerodynamic panels * Project Engineer, Advanced Aircraft Member AIAA [ A ] = aerodynamic panel lift due to alpha influence coefficient matrix [ B ] = aerodynamic to structural transformation matrix [ K ] = global stiffness matrix [ d ~ / dtk] = derivative of the global structural stiffness matrix with respect to structural design variables [ S I ] =structural flexibility matrix (in units of deflection per force) on aerodynamic model [ S A ] = structural flexibility matrix (in units of rotation per force) on aerodynamic model

Schaum's Outline of Theory and Problems of Strength of Materials

Abstract: Tension and compression statically indeterminate force systems - tension and compression thin-walled pressure vessels direct shear stresses torsion shearing force and bending moment centroids, moments of inertia and products of inertia of plane areas stresses in beams elastic deflection of beams - double-integration method elastic deflection of beams - method of singularity functions statically indeterminate elastic beams special topics in elastic beam theory plastic deformation of beams columns strain energy methods combined stresses members subject to combined loadings - theories of failure.

Large deflection of beams under moment gradient

Abstract: Two different approaches are presented for the large-deflection analysis of an inextensible elastic beam under moment gradient. One end of the beam is hinged and at a fixed distance away from this end is a frictionless support where the beam can slide freely. In the first approach, the differential equation based on elastica theory is formulated and solved by using elliptic integrals; which yield a closed-form solution. In the second approach, the governing differential equations are solved numerically by the shooting-optimization technique in which the fourth- order Runge-Kutta algorithm and an optimization algorithm are employed. Comparison studies of the results obtained from the two methods are made and the results are found to be in very good agreement.

Effect of pile driving on adjacent piles in clay

Abstract: When a pile is driven into clay, horizontal and vertical movements are developed in the soil surrounding the pile. These movements will tend to develop axial forces and bending moments in adjacent piles that have already been installed. Possible consequences for these piles are (i) structural damage or cracking (of concrete piles) arising from the induced bending moments, (ii) tensile failure of the piles due to the induced axial forces, and (iii) lifting-off of the pile tip from the bearing stratum due to the axial induced movements. This paper describes the results of a theoretical analysis of the bending moments and axial forces developed in a pile due to driving of an adjacent pile in clay. The analysis uses approximate distributions of horizontal and vertical soil movements caused by pile driving, developed from a "strain-path" analysis, together with inferences from model pile test data. An examination is made of various factors that may influence the induced bending moments and forces, including pi...

Numerical analysis of punching failure in reinforced concrete structures

Abstract: Reinforced concrete slabs supported on columns fail by punching when a conical plug of concrete perforates the slab above the column. This failure has been mostly investigated experimentally, so what can numerical simulation contribute to understand this phenomenon? To answer this question, a computational simulation tool based on the finite element method is developed. This numerical model is implemented into a computer code in applying the object-oriented programming concept. The requirements that the numerical model should fulfill are derived from a review of the experimental results published in the literature and obtained in our laboratory. The numerical model reproduces the non-linear material behavior characterizing reinforced concrete structures by decoupling the actions of steel reinforcement and concrete. The steel reinforcement is represented by uniaxial truss elements which follow a bi-linear stress-strain response. The concrete is modeled with continuum elements which are described at the constitutive level within the framework of the incremental flow theory of plasticity. The concrete triaxial strength is delimitated with a new failure criterion. A plastic flow rule is derived so as to reproduce the evolution of the plastic strain observed experimentally. Cracking induces strain-softening which refers to a gradual decrease in tensile strength with increasing deformations. The reduction of the tensile strength is controlled by an isotropic decohesion process which is monitored by constant fracture energy. The stiffness degradation due to cracking is reproduced with an isotropic elastic damage model. A perfect bond between concrete and steel is assumed. The capabilities of the numerical model are illustrated by simulating the localized shear failure in soil under a footing, the uniaxial tensile, and the confined compressive tests in plain and reinforced concrete specimens. The simulation of punching failure is investigated for three circular reinforced concrete slabs. The comparison with experimental results indicates that: (1) the punching failure mechanism –characterized by a localized inclined punching crack– is generated, (2) the value of the punching load is predicted, (3) the cracking sequence is reproduced, (4) the global response is slightly too stiff. For slabs with orthogonal reinforcement, the perfect bond hypothesis does not allow to capture the punching failure mechanism and the numerical model is improved by relaxing this hypothesis. The developed computational simulation tool reproduces the punching failure observed experimentally and is consequently used to investigate the failure mechanism. First, it is shown that the punching crack results from a crack coalescence phenomenon at the top of the slab followed by a crack propagation in the direction of the corner slab-column. Second, a condition for punching failure to occur is determined. Third, it is illustrated that the size-effect observed experimentally is reproduced and is reflected by a modification of the tensile stress distribution along the punching crack. Finally, a parametric study of the punching failure is performed revealing that punching failure is governed by the tensile strength of concrete. It is also shown that increasing the percentage of reinforcement raises the punching load and reduces the ductility of failure. Lastly, the computational simulation tool allows to demonstrate that in a circular slab, the applied bending moment is not determinant for the value of the punching load.

Mechanics of Solids: An Introduction

Abstract: 1: Introduction to Stress and Strain 2: Uniaxial Loading and Deformation 3: Torsion of Circular Shafts 4: Shear Forces and Bending Moments in Beams 5: Stresses due to Bending 6: Deflections of Statically Determinate Beams 7: Deflections of Statically Indeterminate Beams 8: Stress and Strain 9: Analysis of Combined States of Stress 10: Buckling and Stability. Appendix: solutions to selected problems.

Lateral load analysis of groups of piles and drilled shafts

Abstract: Current procedures for designing groups of piles for lateral loading require the use of a computer or extensive manual computations. This paper presents a simple method (the group amplification procedure) for estimating pile group deflections and maximum bending moments based on the theories of Poulos, and Focht and Koch. The method is applicable to groups of drilled shafts as well as groups of piles. Group lateral deflections and the maximum bending moment in the most severely loaded pile in the group are estimated by multiplying the values for single piles by amplification factors (which have values larger than unity). Lateral deflections and maximum bending moments calculated using the group amplification procedure have been found to be in good agreement with values measured in field load tests.

High‐Order Bending of Sandwich Beams with Transversely Flexible Core and Nonparallel Skins

Abstract: The bending behavior of a general tapered sandwich beam with a flexible core in the vertical direction and a piecewise uniform sandwich beam with tapered transition zones between the uniform regions is analytically investigated. The structure is modeled as a combination of a core that is assumed to be a two- dimensional elastic medium, in the longitudinal and transverse directions, and skins considered as one-dimensional inclined beams. Thus the effects of the flexibility of the core in the vertical direction and that of the vertical component of the longitudinal and the shear forces in the inclined skins on the local and the overall behavior are considered. The field equations and the boundary and the continuity conditions are rigorously derived using variational principles. The proposed analysis accounts for higher-order effects due to the flexibility of the core in the form of nonlinear displacements fields through its height that comprises a parabolic distri- bution of the vertical deformation, which changes the distance between the skins, as well as the height of the core and a cubic variation of the longitudinal displace- ment. These high-order effects are especially pronounced in the vicinity of con- centrated or localized distributed loads or supports as well as at the ends of tapered transition zones and are usually associated with stress concentration in the form of high peeling and shear stresses at the skin-core interfaces and high bending stresses in the skins. These effects also exist at the ends of taper transition zones of a piecewise uniform beam due to the concentrated resultant of the shear and lon- gitudinal internal forces of the skins even in the case of a distributed load. The characteristic behavior of a tapered sandwich beam and a piecewise uniform beam with a tapered transition region are studied in terms of deflections, shear forces and bending moments in the skins, normal transverse and shear stresses in the core, and shear and peeling stresses at the interfaces between the core and the skins. Numerical results of stress concentration effects for some typical cases are presented and discussed.

Seismic shear demand of ductile cantilever walls - a canadian code perspective

Abstract: During severe earthquakes, ductile flexural walls are expected to exhibit inelastic flexural behaviour while other brittle deformation mechanisms, such as shear, should remain elastic. The philosophy of the Canadian seismic provisions for flexural walls is based on the assumption that the force reduction factor is applicable to both flexure and shear. If the bending moments are limited because of the flexural strength of a wall, then the shear forces are considered to be limited by the same ratio. Recent case studies have not confirmed this philosophy. Brittle shear failures in walls are still possible even if their shear strengths are established by the Canadian standards. This paper presents an analytical investigation on the shear demand of ductile flexural walls designed for three different seismic zones in Canada. For each zone, an ensemble of code compatible historical earthquake ground motions is identified. The shear demand of each structure, under each earthquake record, is obtained by nonlinear ...

Interlaminar Stresses in Composite Laminates Under Out-of-Plane Shear/Bending

Abstract: An approximate method is developed to investigate the interlaminar stresses near the free edges of beam-typecomposite laminate structures subjected to out-of-plane shear/bending. The method is based upon admissiblefunction representations for in-plane stresses that contain a linear variation in the longitudinal direction.Closed-form solutions of all stress components are sought by minimizing the complementary energy with respectto the unknown functions. The resulting solutions satisfy the stress equilibrium, compatibility, and all of theboundary conditions. Numerical examples are given for both cross-ply and angle-ply laminates. It is found thatinterlaminar stresses under the shear/bending, particularly those for angle-ply laminates, may exhibit substan-tially different characteristics than under uniaxial loading or under pure bending.

Large dynamic plastic deflection of a simply supported beam subjected to rectangular pressure pulse

Abstract: This paper concerns the dynamic behaviour of rigid, perfectly plastic simply supported beams with finite deflections by considering both bending moments and axial forces. In the case of rectangular pressure pulse loading, approximate rigid-plastic theoretical solutions are obtained for both medium load and high load; to this end a parabolic law between bending moment and axial force as yield condition is approximated by a circumscribing or an inscribing rectangle. The concept of Saturation Impulse is put forward for the dynamic response of rigid, perfectly plastic structures with finite deflections subjected to rectangular pressure pulse. The value of dimensionless saturation impulse for both simply supported and fully clamped beams are given.

Rectangular thick plate with free edges on pasternak foundation

Abstract: In this paper the work on the thick‐plate equations and their solution for the problem concerning the bending of a rectangular plate with four free edges resting on the Pasternak foundation are described. The basic equations are those obtained from Reissner's 1945 theory, and are modified to include the Pasternak foundation. The solutions of the basic equations are arrived at by superposing the solutions of three elemental plates, one with four guided support edges; the other two with two guided support edges and two free edges acted upon by an unknown bending moment. Finally, numerical examples are also presented to examine the solution for convergence and validation. It shows that the presented solution can be used as a good mechanical model for the analysis of the plate structures supported by elastic foundation, where the transverse shear deformation and the local effects in the plates and the transverse connection in the foundation must be considered.

Injection moulding machine

Abstract: Injection moulding machine with a machine frame (2, 3, 13) and a fixed and hydraulically or electromechanically movable die platen (5). In order to compensate to a large extent for the bending moment arising during closure of the mould, which distorts the machine frame (2, 3, 13), the machine has, in addition to an actuatable force member (9) that operates the die platen, preferably a hydraulic jack, a further drivable power member (10) whose force is applied symmetrically to that of the first, and which is simultaneously actuated by a force that corresponds to or is proportional to the closing force produced by the first power element (9).

Procedure and device for testing the attachment and bending strength of poles

Abstract: A description is given of a method for testing the stability and bending strength of poles (1) which are anchored upright, in which in each case the pole to be tested is subjected to a variable bending moment, as well as of a device for carrying out the method. The device comprises a force unit (2), which with an increasing force (F) can be introduced into the pole (1) above its anchorage and the pole can be loaded with a bending moment, as well as a force sensor (4) to measure this force, whose level and variation can be evaluated to determine the stability of the pole. In this arrangement, provision is made of a distance sensor (5), which can be brought into contact against the pole above the pole anchorage, to measure the lateral deflection (S) of the pole occurring because of the bending moment, and the measured values generated by the force and distance sensor can be simultaneously processed in an evaluation circuit (6.1, 6.2) and can be displayed with reference to their mutual dependence. A linear variation of this dependence up to a desired testing force shows in this arrangement that the pole (1) and its anchorage are in order. If, before reaching the desired testing load, a transition of the relationship between loading and deflection value from a linear into a non-linear variation is indicated, a plastic deformation of the tested pole is present, that is to say a pole is present which is damaged.