End Restraint Effects Research Articles

Imperfect Columns with Biaxial Partial Restraints

An inelastic theoretical study of the effect of biaxial partial end restraints on the response of hollow rectangular steel nonsway columns with or without biaxial crookedness and residual stresses is presented. The partial end restraints considered have linear, elastic‐plastic, or trilinear moment‐rotation characteristics. The fundamental total equilibrium equations for the problem are derived. An algorithm is presented based on a coupling between an iterative tangent stiffness approach and a finite‐difference scheme for evaluating the spatial response of the materially nonlinear columns. The effect of partial end restraints, as well as the individual and combined influence of crookedness and residual stresses is also explained by means of load‐deflection, and bending stiffness degradation curves. Several interesting conclusions are drawn regarding the behavior of columns as affected by end restraints, imperfections and slenderness.

Effect of End Restraints and Forces on the State of Stress in Circular

ABSTRACT RESTRAINT of displacement and/or rotation of the wall at the base and roof of a silo along with forces and moments applied at the ends, may cause significant bending and shear stresses at the end regions of the silo. Since it is not easy to evaluate the stiffness coefficients of the restraining base or roof system, a general analysis of the effect of the end restraints on the state of stress of the silo near the ends would be valuable. The object of this study is to obtain a general solution for the deflection of the wall for any lateral pressure and any combination of stiffness coefficients and forces applied at the ends. The analysis of the effects of the end restraints is based on the general solution for the lateral pressure given by the specialized Janssen's formula adopted by ISA (1981). Eccentricity of discharge is not considered.

Effect of End Restraint on Column Strength - Practical Applications

The behavior, strength and design of columns constitute a subject area that probably has received more study and discussion than most structural engineering problems. As a result, a large number of increasingly more accurate solutions have been developed, and the design approaches are legion. The basic column is a centrally loaded, pinned-end member. The original solution for the elastic case was provided by Euler in 1759, and advances over the years have incorporated the influences of residual stresses, initial crookedness and load eccentricity, to mention some of the primary factors. Recognizing that columns are rarely, if ever, pinned-end in actual structures, but rather connected to the other components of the structure by a variety of connection types, recent studies have developed solutions that also take into account the effect of end restraint. As can be expected, there is good agreement between theoretically determined column strengths and those obtained in column tests. This has been facilitated by the use of computer programs that can take into account the many column strength parameters, including their random characteristics.

Geometric Nonlinearities in Nonsway Frames

The geometric nonlinearities in elastic nonsway frames are examined and used to review the rationale and accuracy of the ACI slender column design method. The use of nonsway effective length factors to account for effects of end restraints, and the assumptions of idealized end restraints in the conventional alinement chart for effective length factors are investigated. The discussion is also applicable to the moment magnifier portion of the AISC column interaction equation.

Buckling and cyclic inelastic analysis of steel tubular beam-columns

An numerical procedure combining the Finite Segment Method (FSM) with the Influence Coefficient Method (ICM) is presented for estimating the inelastic behaviour of steel tubular beam-columns under post-buckling and cyclic loading conditions. This combination takes the advantages of FSM and ICM, overcoming the difficulties encountered in numerical analysis at the stages of buckling and post-buckling. The effects of initial imperfections, residual stresses, and end-restraints are taken into account. Generalized stress-strain relationships are used in the analysis. Complete results obtained for a pin-ended beam-column are discussed and compared with available theoretical results.

Discussion of “ Small End Restraint Effects on Strength of H‐Columns ” by Hironori Sugimoto and Wai F. Chen (March, 1982)

Discussion of “ <i>Small End Restraint Effects on Strength of H‐Columns</i> ” by Hironori Sugimoto and Wai F. Chen (March, 1982)

Closure to “ Small End Restraint Effects on Strength of H‐Columns ” by Hironori Sugimoto and Wai F. Chen (March, 1982)

Closure to “ <i>Small End Restraint Effects on Strength of H‐Columns</i> ” by Hironori Sugimoto and Wai F. Chen (March, 1982)

Discussion of “ Small End Restraint Effects on Strength of H‐Columns ” by Hironori Sugimoto and Wai F. Chen (March, 1982)

Discussion of “ <i>Small End Restraint Effects on Strength of H‐Columns</i> ” by Hironori Sugimoto and Wai F. Chen (March, 1982)

End Restraint Effect on Steel Column Strength

Nonsway columns with initial crookedness and residual stresses, and partially restrained by linear, elastic‐plastic, or nonlinear end restraints are studied in the inelastic range. An algorithm based on an iterative tangent stiffness approach coupled with a finite‐difference equilibrium method is developed relative to the minor axis of the column cross section. The effect of end restraint on the response of imperfect columns is explained. The influence of imperfections on the behavior of partially restrained columns is identified by means of stiffness degradation curves. Finally, new design expressions are proposed for evaluating steel column strength which make use of a “plastic effective length factor” and the use of the proposed procedure illustrated by means of a design example.

Analysis of initially crooked, end restrained steel columns

A new and general method of analysis for steel columns, which can simultaneously take into account the effects of initial crookedness, end restraint, residual stress and load eccentricity, has been developed. The method gives the complete load-deflection relationship of a column, including both the ascending and descending branches. Unlike most of the currently used methods, the basic required input is the stress-strain relationships of the material, instead of some pre-determined moment-thrust-curvature relationships for the cross sections. Application is first made to develop theoretical predictions for some selected columns which were tested using either the geometrical alignment or the load alignment procedure. It is shown that the latter tends to be stronger and gives a higher test load. The results of two parametric studies, which included such variables as magnitude of initial crookedness, amount of end restraint, pattern of residual stress distribution, and axis of bending, are also presented. Certain conclusions with regard to the relative importance of these variables are drawn.

End restraint effects on cyclic triaxial strength of sand : Lee, K L; Vernese, F J J Geotech Engng Div, ASCE, V104, NGT6, June 1978, P705–719

End restraint effects on cyclic triaxial strength of sand : Lee, K L; Vernese, F J J Geotech Engng Div, ASCE, V104, NGT6, June 1978, P705–719

End restraint effects on undrained static triaxial strength of sand : Lee, K L J Geotech Engng Div, ASCE, V104, NGT6, June 1978, P687–704

End restraint effects on undrained static triaxial strength of sand : Lee, K L J Geotech Engng Div, ASCE, V104, NGT6, June 1978, P687–704

End Restraint Effects on Cyclic Triaxial Strength of Sand

Cyclic triaxial tests were performed on various soils at different densities and different consolidation pressures, using regular and lubricated ends to explore the possible effect of end restraint...

End Restraint Effects on Undrained Static Triaxial Strength of Sand

Although many studies have been made on the effect of end restraint in triaxial testing of soils, no data were available pertaining to static undrained tests on saturated sands. Therefore, a series of tests were conducted using triaxial specimens with regular and frictionless ends. The results showed that for a medium dense sand there was a significant (up to 20%) increase in static undrained strength with frictionless ends as compared with tests using regular ends. The effect is significantly greater than observed for other studies pertaining to drained tests on sands and undrained tests on clays. The strong effect in this case was shown to be related to the difference in volume change/pore pressure change tendencies between tests with regular and frictionless ends as measured by the critical confining pressure. The study was undertaken as a prelude to a similar companion study on the influence of end restraint in undrained cyclic tests on saturated sand.

材端回転拘束を受ける鉄骨筋違の繰返し弾塑性性状に関する研究

Cyclic behavior of a steel brace elastically restrained at both ends was studied experimentally. The specimens were manufactured by shaping SS 41 mild steel sheet. Ratio of member length l to radius gyration of the cross section i, stiffness of rotational restraining spring at both ends, eccentricity of a load and shape of the cross section were varied in this test. The results may be summarized as follows, 1) Value of l/i and existence of restraining springs influence on the cyclic axial load-displacement curves remarkably. 2) Under the identical value of l/i, the plastic energy absorption capacity of a restrained brace is considerably larger than one of a pin supported brace. 3) Also under the identical value of l_k/i, the ratio of the effective buckling length l_k depending on the end restraints to i, the plastic energy absorption capacity of a restrained brace is larger than one of a pin supported brace. 4) As the stiffness of restraining spring increases the value of magnification factors α that explain the effects of end restraints on the cyclic behavior of braces under the identical value of l_k/i decreased. 5) Eccentricity of a load does not hardly influence on the cyclic behavior of a brace, expect for the difference in the maximum compression load attained in the initiate loading.

Relationships between size, deformation and strength for cylindrical specimens loaded in uniaxial compression

An experimental investigation into the effects of size of cylindrical test specimens on observed axial, lateral and volumetric stress-strain behaviour and strength is described. The effects of end restraint were examined by (1) comparing the output from strain gauges located at different points on test specimens and (2) comparison of stress-strain relationships determined by overall deflection measurements with those from strain gauges bonded over the central zone of specimens. General empirical relationships between slenderness ratio, 50% tangent Young's modulus and ultimate strain, for the different methods of strain measurement were determined. Strain measurements on specimens less than 50 mm dia, are high and not representative of material behaviour. The degree of non-uniformity of strain distribution, in unixially loaded cylindrical specimens was found to increase with increasing stress.

Effect of End Restraint on High Pressure Tests of Granular Materials

Comparative drained triaxial tests at high confining pressures were carried out on a strong- and weak-grained granular material with 'rough' and 'lubricated' ends. The results indicated that the stress-strain relationships are significantly influenced by the end conditions. The use of 'lubricated' ends for high pressure tests results in much more uniform distribution of stress, strain, volume change, and crushing of particles throughout the samples.

Elasto-plastic Analysis of Strip Plates by Finite Difference Method

Non-linearity in structural Analysis is caused in most cases by two factors ; one is plastification of material and another is finite deformation. These two factors usually make the analysis so complicated that it is difficult to obtain the exact analytical solutions. Therefore, numerical analysis is used to get approximate solutions. In this paper, as a first step for solving square plates subject to lateral pressure, one approximate numerical procedure is used for solving the same kind of problem of strip plates. This procedure is based on linearization of non-linear equations by the concept of small increment and on solving these linearized equations by finite difference method.From the fact that analysis of strip plates can be regarded with good accuracy as the analysis of square plates subject to lateral pressure, provided that their aspect ratios are over about 3, the strip plates have been investigated by several researchers analytically and experimentally. The comparison showed that the computed load-deflection curve by the procedure in this paper coincided with the experimental ones published previously with fairly good accuracy. Another results of this paper is estimation of the effect of end restraints of strip plates. The behaviour of strip plates with linear and non-linear end restraints were investigated.

Further studies on the elastic stability of curved beams

In a previous article, 1 the authors investigated the instability of circular curved beams, the ends of which were hinged to fixed supports. For simplicity the loading was assumed to consist of equal but opposite end moments which tend to increase the span, and hence induce compression forces in the beam. The ranges of validity of three theories were investigated, viz. linear, extensible and nonlinear, inextensible and extensible theories. The present article extends the investigation to the more complicated problem of a circular curved beam with central concentrated loading. It was shown that buckling cannot occur if the initial rise span ratio λ 2l <0·96p (see Notation). Curves of critical loads t cr vs. initial rise span ratio were calculated for the three theories and comparisons made for values of p = 0·025 and 0·05. Finally, the effects of end restraints on the stability of small initial rise curved beams were studied by the linear theory. It is concluded that the translational restraint influences the buckling loads to a considerable extent whereas the rotational restraint has little effect.

Design implications of tests on a large 90° smooth bend

The paper details the design implications of a site strain gauge test carried out on the 6 ft 6 in diameter reactor outlet ducting of a nuclear power station. The test subjected a portion of the ducting to a horizontal load of 10 ton, and the strain gauge survey was taken on a smooth bend of the ducting which was inherently flexible and did not incorporate the usual bellows units to absorb thermal expansions. Theoretical stresses in the bend of the test portion were calculated under the horizontal load, and comparison made between experimental and theoretical values. At the design stage of the station a detailed analysis was carried out for the complete system under thermal expansions, and this analysis is briefly described. Using the comparison obtained from the test portion, an estimate is made of the probable stress levels that will exist in the complete duct system under reactor operating conditions. During fabrication of the smooth bends a dimensional survey was carried out on a complete component, and the tolerances achieved are discussed and compared with tolerances obtained on the more usual smaller diameter welding elbow. The effect of end restraints on the flexibility of smooth bends is also discussed, and the lack of design information on this aspect is emphasized. It is concluded that the stresses in the bends may be accurately predicted, but a larger error is likely to occur in the prediction of end reactions and the stresses induced in vessels subjected to these reactions.