Contraflexure Research Articles

Strength requirements of single cold-formed channels connected back-to-back

Tests to determine the failure modes and capacity of the eaves region of steel portal frames are presented. This was part of a major research project to establish the overall behaviour of steel portal frames, constructed from single channels and bolted back-to-back at the eaves joint. Variables in the 4 tests include the number of bolts in the connection, the points of contraflexure, the width of the channel flanges and the strength of the channels. Three modes of failure were observed, namely: local buckling of the compression zone of the flange and web of the channels, lateral torsional buckling of the channels between points of lateral support, and bolts in bearing. The final failure mode in all structures was local buckling of the compression flange and web. Local buckling was made more critical by stress concentrations, shear lag and bearing deformations caused by back-to-back bolted connections. It is proposed to apply a factor of 0.8 to the yield moment and the buckling moment of resistance to account for stress concentrations, shear lag and bearing deformations.

Debonding of steel plates adhesively bonded to the compression faces of RC beams

Reinforced concrete beams in buildings and bridges are increasingly being retrofitted by adhesively bonding steel or FRP plates to their tension faces. However, tests have shown that tension face plates are prone to premature debonding. One way of preventing or inhibiting debonding of tension face plates in continuous beams is to extend the plate-ends past the points of contraflexure into the compression faces. In this paper: it is shown that compression face plates are less likely to debond than tension face plates; results of thirteen tests on debonding due to vertical shear forces (critical diagonal crack debonding) and curvature (flexural end plate debonding) are described; and critical diagonal crack and flexural end plate debonding models are developed for compression face plates that can be used to ensure that beams with tension face plates that are extended into the compression faces do not debond prematurely.

An Analytical Solution to the Lateral Buckling of an Elastica with Self-Contact

An exact solution to the lateral buckling of an elastic column with self-contact is obtained. By assuming that a counter force exists to maintain the horizontal coordinate at the contact point at the same value as the highest point of the bent beam, we can prevent the shape of the solution from overlapping itself. As the simplest case, we obtain elliptical integral solutions of a laterally post-buckled shape of a linear elastic inextensible column under a concentrated load. For this case, the slope's angle at the contra-flexure point remains constant regardless of the value of the load parameter beyond the minimum critical value. The counter force and several other parameters are expressed in terms of the critical slope angle at the contra-flexure point. Finally, numerical algorithms are suggested for solving the problem, which enable a solution for a nonlinear material or a combined loading case.

Nonlinear influence of contraflexure migration on near-curtailment stresses in hyperstatic FRP-laminated steel members

The flexural characteristics of hyperstatic steel members with adhesively bonded Fibre reinforced polymer (FRP) laminates are considered. It is shown that, during elasto-plastic activity, the migration of the points of contraflexure along such members has two nonlinear effects on the stresses in both the laminate and the adhesive. First, the lengths of laminate traversed by these migrating points undergo reversal of axial stress from tension to compression, which exposes the laminate to potential buckling. Second, the bond stresses in the adhesive near laminate curtailment increase dramatically, and so may initiate brittle failure near curtailment by separation of the laminate from the steel member. Nonlinear finite element (FE) analyses are used to illustrate both these effects. The FE model is verified by comparison with published data, and is then used to analyse an isostatic and a hyperstatic FRP-laminated steel member. The results show that the above nonlinear influences are pronounced in the hyperstatic member, but are absent from the isostatic member. Tapering of both the laminate and adhesive profiles near curtailment of the laminate is investigated as a potential means of reducing these effects in the hyperstatic member. Finally, the implications of the above effects for the performance of hyperstatic FRP-laminated steel members in practice, are discussed.

Interaction between Flexure and Shear on the Debonding of RC Beams Retrofitted with Compression Face Plates

Steel and FRP plating reinforced concrete structures is increasingly being used for retrofitting. Plates can be bonded to any surface of a beam or slab, although it is common practice to adhesively bond plates to the tension faces. The addition of these tension face plates reduces the sectional ductility of the beam. Furthermore, these tension face plates are prone to premature debonding because the stress concentrations induced by these plates overlap with those induced by the tension reinforcing bars adjacent to the plate. Solutions to these two problems, which are the subject of this paper, consist of: adhesively bonding plates to the compression faces to counterbalance the tension face plates and, hence, improve the beam sectional ductility; and to extend the tension face plates, in continuous beams, past the points of contraflexure so that they terminate in a compression face. In this paper, eleven new tests on 340 mm deep beams are presented that show that compression face plates are less prone to debonding than tension face plates.

Composite Action in Steel Girder Bridge Superstructures Subjected to Transverse Earthquake Loading

Experiments are being performed on a 0.4 scale model of a steel girder bridge superstructure with a reinforced concrete deck to investigate means of improving the seismic performance of typical slab and girder bridges. During the early stages of experimentation, the need to understand the influence of composite action became apparent. Accordingly, an analytical study was undertaken. The first of several finite element analyses on a typical continuous four-span, four-girder bridge model assumed shear studs along the entire length of the bridge to provide full composite action. A second model omitted the shear connectors in the negative moment regions, a common design practice to avoid fatigue concerns in the top flange. It was found that the shear connectors in the fully composite model were sufficient to ensure composite action when subjected to transverse loading and provided an adequate load path through the superstructure and into the substructure. However, the lack of shear connectors in the negative moment regions caused the load to be transferred into the steel girders at the points of contraflexure, resulting in damage to these girders and inadequate formation of the ultimate limit state in the columns. The lack of composite action was also found to change the distribution of transverse shear forces in the cross frames, which is important for design of the end cross frames. Making the top chord of the cross frames composite with the deck, at the column bent locations, proved effective in minimizing damage to the superstructure.

Experimental Behavior of Jacketed Reinforced Concrete Beams

Repair and strengthening of reinforced concrete beams is commonly carried out by “jacketing.” Jacketing is the addition of concrete and steel reinforcement (both longitudinal and transverse) to an existing beam. This paper describes an experimental investigation into the behavior of reinforced concrete beams strengthened by jacketing. Static and dynamic load tests to failure were carried out on 61 slant shear prisms and 13 jacketed reinforced concrete T-beams. The concrete used in the jacket was preplaced aggregate concrete. The strength of the bond between preplaced aggregate concrete and plain concrete was assessed by slant shear tests and a Mohr-Coulomb-type failure envelope was derived. Static failure of the beam specimens was related to this failure envelope. The beam experimental results demonstrated the importance of adequate reinforcement detailing (i.e., that full anchorage of the additional steel at simple supports and points of contraflexure and anchorage of the additional links at the top of t...

On the accuracy of the continuum method for analysis of coupled shear walls of unequal width

The continuous medium technique has been widely used in the preliminary analysis and design of coupled shear walls in tall buildings by practising engineers for many years. One of the basic assumptions made when using this approximate method is that the coupling beams deform with points of contraflexure at mid-span. However, when there is a non-negligible difference between the stiffness's of the structural walls connected by the coupling beams, the points of contraflexure of the beams can move off-centre, and hence noticeable error in the analysis may occur. This paper presents a study on the accuracy of the continuous medium technique for the preliminary analysis of concrete coupled structural walls with unequal width. Comparison of the analytical results between the method and the wide-column analogy has been made. Recommendations for using the continuum method to analyse coupled shear walls are presented.

On the accuracy of the continuum method for analysis of coupled shear walls of unequal width

The continuous medium technique has been widely used in the preliminary analysis and design of coupled shear walls in tall buildings by practising engineers for many years. One of the basic assumptions made when using this approximate method is that the coupling beams deform with points of contraflexure at mid-span. However, when there is a non-negligible difference between the stiffness's of the structural walls connected by the coupling beams, the points of contraflexure of the beams can move off-centre, and hence noticeable error in the analysis may occur. This paper presents a study on the accuracy of the continuous medium technique for the preliminary analysis of concrete coupled structural walls with unequal width. Comparison of the analytical results between the method and the wide-column analogy has been made. Recommendations for using the continuum method to analyse coupled shear walls are presented.

Application of the compressive-force path concept in the design of reinforced concrete indeterminate structures: A pilot study

In the past, physical models have been proposed, in compliance with the concept of the compressive-force path, for the realistic design of various statically determinate structural concrete members. The present work extends these models so as to encompass indeterminate RC structural forms. Pilot tests conducted on continuous beams and fixed-ended portal frames have revealed that designing such members to present-day concepts may lead to brittle types of failure. On the other hand, similar members designed on the basis of the proposed physical models attained very ductile failures. It appears that, unlike current design approaches, the compressive-force path concept is capable of identifying those areas where failure is most likely to be triggered, and ensures better load redistribution, thus improving ductility. The beneficial effect of proper detailing at the point of contraflexure in an indeterminate RC member is to be noted.

Ultimate Strength Analysis of Stub Girders

This paper is on the determination of the ultimate load-carrying capacity of stub girders. Two different methods are presented for this purpose. In the first method, the stub girder is modeled as a vierendeel truss girder. Based on an assumed collapse mechanism, shear force distribution between the top and bottom chords proportioned according to the shear and flexural stiffnesses and point of contraflexure at the midlength of opening, an explicit expression to calculate the ultimate load is derived. The second method uses the finiteelement software package ABAQUS for the nonlinear analyses of idealized two-dimensional stub girder models. The methods furnish results that are in reasonable agreement with experimental results, for girders in which the premature failure of shear connectors, local buckling of stubs and the main girder, and the longitudinal shear failure are prevented.

Rotation capacity of structural concrete members

A plastic rotation capacity expression based on a realistic non-linear analysis model is derived for structural concrete members. Effects of section shape, compression reinforcement and bending moment distribution are considered. A set of diagrams enables the plastic rotation capacity of rectangular, T and I structural concrete members under linear, sagging, and hogging bending moments to be determined. Use of these diagrams enables the compatibility requirement of critical sections of structural concrete continuous beams under either concentrated or distributed loads to be checked. Comparison with available plastic rotation formulations shows that neglecting the influences of the loading distribution and of ratios between contraflexure point distance and the section depth may lead to non-conservative results. It is found that for lightly reinforced sections (steel failure) plastic rotation capacities increase, while for highly reinforced sections (concrete failure) plastic rotation capacities decrease, with increasing reinforcement index values.

鉄骨構造露出形式柱脚部の耐荷機構に関する実験的研究

The purpose of this paper is to grasp the load carrying mechanism of exposed type of steel column bases. From the test results of steel column-bases subjected to axial force, bending moment and shear force by changing the height of point of contraflexure, conclusions are obtained as following. The dowel action of tension side anchor bolts and the frictional action of base plates are very important elements for the load carrying mechanism of steel column bases. And they are ensured by the top of concrete footing reinforced with steel bars. The dowel action of compressin side anchor bolts is injurious for the frictional action of base plates because their shear resistance is very small.

Effects of water adsorption on Kaolin clay during shear : Glenn, G R Transp Res Rec N675, 1978, P20–23

Stress-controlled direct shear tests were made on laboratory-desiccated specimens of kaolin clay (W sub D approximately - 1.5 percent). The standard apparatus was modified to permit progressive adsorption of water through the bottom porous plate. Various levels of constant shearing stress pi and a vertical stress of 24 kPa (3.5 lbf/sq in.) were applied, and shearing deformation measurements to failure were taken. When the deformation rate accelerated markedly, failure was defined for that particular pi and water content w. Failure surface w determinations were confirmed by an independent study of time versus wetting rate. Deceleration in wetting rate with increasing water content indicated decreasing negative pore pressure or soil water suction. Suction increases shearing resistance by its reinforcement of effective normal stress between soil solids; it is greater at lower w and reduces most at w greater than 23 percent--the point of contraflexure in the wetting rate versus w curve--which is followed by swelling. Higher constant stress levsls produced initial deformations at lower w and at higher deformation rates. The approximately linear relation between applied pi and w at initial deformation indicates that increases in w account for decreases in interparticle shearing resistance and corresponding losses of strength. This is confirmed by qualitative analysis of test results in relation to the Coulomb equation and the principle of effective stress. Because the maximum strength of specimens at W sub D was greater than maximum strengths between 1.5 and 23 percent, stress-controlled tests were replaced by strain-controlled tests; therefore, peak and residual strengths were obtained on desiccated specimens rewet to w in this range and held constant during stress application. These tests were extended to W sub E (equilibrium W approximately 35 percent) for comparison with stress-controlled test results. /Author/

Approximate Analysis of Multistory Multibay Frames

An approximate analysis of multistory, multibay elastic frames subjected to static lateral loads is developed. The approximation is made that the axial deformations of the columns have hyberbolic sine variation across the width of the building. Assuming points of contraflexure at the mid-heights of the columns and at the midspans of the connecting beams and using the energy approach permits the development of a set of two coupled differential equations. These can be reduced to one equation the solution of which can be written explicitly for each loading condition. Examples comparing results with those obtained by the exact stiffness matrix method show that the method yields acceptably accurate deflections, axial stresses, and column shears. Design curves for the rapid determination of these parameters are included.

Inelastic Analysis of R/C Frame Structures

An inelastic dynamic analysis method was developed for reinforced concrete frame structures. The analytical model was able to account for stiffness characteristics related to cracking of the concrete, yielding and strain hardening of the reinforcement, bond slip of tensile reinforcement in a joint core, and stiffness degradation due to load reversals. The location of point of contraflexure in a member was taken into consideration to account for the distribution of inelastic deformation. The analysis method was tested by comparing calculated response waveforms with observed response waveforms of a small-scale three-story one-bay reinforced concrete frame structure, which was subjected to an intense base motion on the University of Illinois Earthquake Simulator. The observed waveforms at large amplitudes were favorably simulated by the analytical model based on the material properties and geometry of the test structure.

Dynamic Analysis of Plane Coupled Shear Walls

The continuous method of analysis of coupled shear walls is reformulated in terms of deflection variables and used to study the dynamic behavior of plane coupled shear walls. The assumption that mid-points of the connecting beams are points of contraflexure is relaxed so that the resulting theory is applicable to the general case where the lateral loading on the piers can be arbitrarily distributed. The equations of motion with appropriate boundary conditions are given. The free vibration of coupled shear walls is studied and the fundamental frequency determined. Theoretical results are verified by dynamic testing on two models to show the theory is sufficiently accurate to provide information for dynamic analysis in seismic design.

Analysis of Pierced Shear Walls

The continuous connection method of analysis of coupled shear walls assumes that the discrete system of connections, formed by lintel beams or floor slabs, may be replaced by an equivalent continuous medium. By assuming that all cross-beams have a point of contraflexure at midspan, the behavior of the system may be expressed as a single second-order differential equation, enabling a general closed solution to the problem to be obtained. The writers have extended the technique to include shearing deformations of the walls. By comparing the theoretical values of both stresses and deflections with the results from a series of tests on model walls perforated with one or two bands of openings, it is shown that the influence of the shearing deformations in the walls is much less than that of the flexibility of the joints between the walls and connecting beams.

Analysis of Stepped-Column Mill Bents

The “moment-distribution” technique is applied to the analysis of stepped column mill bents, in this paper. Curves for obtaining the necessary distribution coefficients and the fixed-end moments are included. The method permits evaluating the relative resistance, to horizontal forces, of columns having different stiffnesses due to length, size, or other factors. Several examples of two-column and three-column bents are included to describe the method fully. Although this method will require more time than that of obtaining moments from an assumed point of contraflexure, the additional time would seem to be justified, because of the difficulty in estimating the location of such a point of contraflexure accurately for stepped columns.

EROSIONAL DEVELOPMENT OF STREAMS AND THEIR DRAINAGE BASINS; HYDROPHYSICAL APPROACH TO QUANTITATIVE MORPHOLOGY

EROSIONAL DEVELOPMENT OF STREAMS AND THEIR DRAINAGE BASINS; HYDROPHYSICAL APPROACH TO QUANTITATIVE MORPHOLOGY