Post-yield Range Research Articles

SHEAR RESISTANCE AND DUCTILITY OF RC COLUMNS AFTER YIELD OF MAIN REINFORCEMENT

During Hanshin-Awaji Earthquake, catastrophic shear failure accompanying plenty of diagonal shear cracks were experienced in RC structures and bridge piers serving transportation facilities. In this paper, shear capacity and ductility of RC columns in the post-yield range of longitudinal reinforcement are discussed for seismic resistant design. First, the shear failure of large scale RC column is computationally simulated for understanding the mechanism of shear collapse of bridge piers. FEM computational results on ductility are compared with the experiments and parametric study is conducted concerning factors that affect the post-yield deformability of RC columns. Finally, a simple formula for ductility is presented for summarizing the sensitivity of influential factors.

Design procedures for profiled metal sheeting and decking

When designing profiled metal sheeting and decking at the ultimate limit state, the conditions at the internal supports, where the bending moment interacts with the support reaction force, are critical. Design code provisions for estimating the moment of resistance over an internal support are known to be inadequate and the problem is aggravated if account is taken of the redistribution of bending moment accompanied by post-yield buckling. This paper shows that the performance at the internal support can be predicted by finite element analysis and that continuing the analysis into the drooping post-yield range allows a relatively simple pseudo-plastic design method to be developed.

Optimization of plastic shallow shells exhibiting nonstable behaviour

An optimal design technique is suggested for axisymmetric shallow shells exhibiting nonstable behaviour in the post-yield point range. The material of the shells is ideally rigidplastic obeying the von Mises yield condition, which is satisfied in the average and the associated deformation law. Spherical shells pierced with a hole and subjected to uniformly distributed transverse pressure are studied. Different cases of the support conditions are considered. Making use of the methods of the optimal control theory the problem is transformed into a boundary value problem which is solved numerically.

Optimization of rigid-plastic shallow spherical shells of piecewise constant thickness

An approximate method developed earlier for the investigation of large plastic deflections of circular and annular plates is accommodated for shallow spherical shells. The material of the shells is assumed to obey Tresca's yield condition and the associated deformation law. The minimum weight problem concerning shells operating in the post-yield range is posed under the conditions that (i) the thickness of the structure is piece-wise constant and (ii) the maximal deflections of the optimized shell and a reference shell of constant thickness, respectively, coincide. Necessary optimality conditions are derived with the aid of the variational methods of the optimal control theory. The set of equations obtained is solved numerically.

異種強度軸筋の混使用によるRC柱断面曲げ性能の改善

A new method to enhance the moment-curvature relations of reinforced concrete column sections in post-yield range of deformation was developed. The point of the idea is to introduce the sequential yielding of various grade longitudinal bars in a section. The section then does not show any significant reduction in load carrying capacity up to the yielding of highest grade bars. To confirm the advantages of the new method, flexural analyses and loading tests were carried out on reinforced concrete columns with various grade longitudinal bars. The results indicated the advantages of the combined use of various grade longitudinal bars.

BOND CHARACTERISTICS IN POST-YIELD RANGE OF DEFORMED BARS

Bond characteristics in post-yield range of deformed bars were investigated by means of pull-out test. In the test, the bars were embedded in massive concrete in order to have no effect of splitting crack and unbond region was set at loaded end to have no effect of location along the bar. Bond stress in post-yield range is much lower than that in elastic range and it decreases suddenly with yielding of steel. Slip at the loaded end is mostly controlled by location at which steel bar yields. Bond-slip relationship in post-yield range depends on properties of steel bar such as yield strength, hardening strain and tensile strength. Bond-slip-strain relationship obtained from test in elastic range is applicable in post-yield range. The lower bond stress and different bond-slip relationships can be expressed by the analysis of using the unique bond-slip-strain relationship.

AVERAGE STRESS-AVERAGE STRAIN RELATIONSHIP OF STEEL IN UNIAXIAL TENSION MEMBER IN POST-YIELD RANGE

Uniaxial tensile tests were conducted on prismatic reinforced concrete specimens. Stress distribution along bar in addition to the total elongation was measured and average stress-average strain relationship of steel in post-yield range was obtained. In the average stress-average strain curve, steel starts to yield below its yield strength and the length of yield plateau is zero.The average stress-average strain curve can be predicted by assuming a stress distribution of steel. Instead of assuming a bond stress versus slip relationship or the bond stress distribution, the stress distribution was assumed directly. The stress distribution can be simply expressed by sine curve.

Full-scale load test of three-span concrete highway bridge

A full-scale load test to failure of a 34-year-old three-span continuous reinforced concrete highway bridge located in southern Alberta is described. The opportunity to load test the structure to failure occurred as a result of the scheduled demolition of the bridge.Load was applied to the structure in two phases. In the first phase, precast concrete sections were placed at the centre of the middle span until a load of approximately 1900 kN was reached. At this load level a mid-span deflection of 28 mm was measured for the interior span. Additional load was applied by jacking the ends of the bridge at the abutment supports. Loading continued until a maximum deflection of 157 mm was reached at mid-span. Significant cracking as well as crushing of the compression flange at mid-span were evident. On removal of load at mid-span, a residual deflection of 118 mm was observed indicating that the bridge had been loaded well into the postyield range without collapsing.Results of the test are presented in the form of plots of load vs. deflection, reactions vs. deflection, mid-span moment vs. deflection, and deflection profiles at various loading stages. In addition the calculated flexural capacity is compared with measured values. Key words: highway bridge, load test, reinforced concrete.

Optimal design of rigid-plastic cylindrical shells in the post-yield range

An optimal design technique is developed for rigid-plastic cylindrical shells subjected to a distributed transverse pressure and a specified axial load. Moderately large deflections are taken into account and a deformation-type theory of plasticity is employed. The optimal design procedure results in a unified approach to optimization in the post-yield range. Necessary conditions for optimality are established by the aid of variational methods of the optimal control theory. Two examples are presented: (1) the optimal layout of rigid circular supports (stiffeners) is found which minimizes the mean deflection; (2) the optimal thickness distribution of a sandwich shell is established which corresponds to the minimum material consumption requiring the deflection of the design coinciding with that of the constant thickness shell.

Parametrical optimization of plastic cylindrical shells in the post-yield range

An optimal design technique is developed for rigid-plastic cylindrical shells accounting for the moderately large deflections. The study is confined to sandwich shells subjected to the axial dead-load and to the internal pressure loading. The optimization problem is posed in the parametrical form, the parameters being certain constant quantities which should specify the internal load distribution as well as cross-sectional dimensions of the shell or it support positions. Necessary optimality conditions are established using the variational methods of the optimal control theory. As an example the optimal layout for a set of the rigid circular supports (stiffeners) is stated.

On plastic shell theories at large strains and displacements

Geometrically nonlinear behavior of rigid-plastic shells is studied. Consistent sets of relations regarding stress and deformations of solids at finite strains and displacements are recalled first. Simplifying assumptions concerning mostly the kinematics are then introduced to arrive at geometrically nonlinear theories of plastic shells. A classification of theories is given in sequence. Influence of large strains on the load surfaces is discussed. Post-yield behavior of shells is studied as the allowance for large displacements modifies the load deformation behavior and affects stability at the yield point. Examples concerning cylindrical shells in the post yield range are given.

Parametrical optimization of plastic beams in the post-yield range

Optimal design of rigid-plastic beams is considered taking account of the post-yield behaviour. The analysis is carried out for the beams loaded by a transverse pressure and axial tension. A problem of optimal design is set up in the parametrical form. The parameters subjected to variation are certain constant quantities, which could specify the optimal distribution of the external loading as well as the cross sectional area of the beam. An unknown constant can serve as the position coordinate of an additional support. Necessary optimality conditions are derived by means of the variational methods of the optimal control theory. An illustrative example is given.