Showing papers in "Journal of the Structural Division in 1972"

Concept of structural control

Abstract: In an ideal situation, completely safe structures can be designed if exact information is known concerning loads and strengths involved during the lifetime of these structures, and exact methods of structural analysis are available. In the real world uncertainties exist in this information as well as in the method of analysis. To account for these uncertainties, various factors of safety have been used in the design of structures. Probabilistic methods have been applied for the interpretation as well as determination of these factors of safety. Techniques in structural analysis are being refined continuously. The objective herein is to present the concept of structural control as an alternative approach to the safety problems of structural engineering. Pertinent points of the control theory are reviewed along with certain pioneering work in this direction. The practicality of this concept is illustrated with an example using analog parallel logic devices.

Post-Buckling of Geometrically Imperfect Plates

Abstract: Explicit expressions are derived for the collapse and elastic post-buckling of simply supported, geometrically imperfect plates with stress-free edges. For the purposes of design, such plates can be taken as representative of the stiffened compression elements of thin-walled structural sections. Different generalized geometric imperfection parameters are studied and the effects compared to established test data obtained from cold-formed steel sections subjected to either bending or compression. For these sections a suitable and completely general parameter describing the imperfection amplitude, e\d0t, of a plate of thickness t is shown to be e\d0=0.2σ\dy/σ\Dcr\N in which σ\dy is the yield strength of the plate material; σ\Dcr\N is the theoretical local buckling stress of the equivalent ideal plate and is a direct function of its width to thickness ratio. This parameter is recommended for the design of cold-formed steel sections against local buckling.

Reinforced concrete members with cyclic loading

Abstract: Theoretical moment-curvature relationships for reinforced concrete members with cyclic loading are derived using stress-strain curves for steel and concrete. The theoretical curves compare well with test results and illustrate the variation in flexural stiffness due to the Bauschinger effect of the steel and to the presence of open cracks in the compression zone of the concrete which may eventually close. These cracks mean that for large portions of the moment-curvature curves after the first yield excursion the moment of resistance is provided by a steel couple alone. During this part of the cyclic loading the main role of the concrete is to prevent buckling of the steel. For beams with a marked difference between the top and bottom steel areas and for columns the moment-curvature loops show a pinching in effect and the loop area is significantly smaller than that of the commonly used elastoplastic idealization.

Lift or Across-Wind Response to Tapered Stacks

Abstract: In the present study, the structure of the shedding forces from a slender tapered structure was studied in considerable detail in both smooth uniform flow and turbulent shear flow. From this study a simplified description of the forces in shear flow is developed and successfully employed to predict the response of an aeroelastic model. A significant finding is that the maximum response in the fundamental mode occurs when the shedding frequency at about one third of the stack height is equal to the natural frequency. The observations made during the study are employed to develop an equation that might be used to predict the behavior of full-scale structures. The significance of loads due to vortex shedding from tapered structures is examined. For typical concrete structures it is deduced that drag loads are likely to be dominant with regard to stresses over the lower 2/3 of the structures while vortex excitation of the second mode is likely to be the dominant consideration for the upper one third or thereabouts.

Shear Strength of Large Beams

Abstract: This paper considers the problem of the effect of absolute size on the shear strength of reinforced concrete beams. The results of previous tests are compared and a brief description is given of the way in which beams carry shear force, which is consistent with recent data. Tests on a series of 15 beams in which true scale models were used, with a depth range of 150-1000 mm (6-40 in.) are described. The test results indicate that, when beams are modeled correctly, the effect of absolute size is small. In practice it may not always be possible to design beams of the type in which the size effect is insignificant. For these cases, design advice is given.

Stability of Monosymmetric Beams and Cantilevers

Abstract: There is a shortage of information on the elastic flexural-torsional buckling of monosymmetric cantilevers, while some differences of opinion exist on the effects of monosymmetry. The buckling of beams and cantilevers is studied in this paper, and theoretical critical loads are tabulated for a wide range of sections. The loadings considered include central concentrated loads on beams, end concentrated loads on cantilevers, and uniformly distributed loads, and these are applied at various distances above or below the shear center axis. It is shown that while the effects of monosymmetry and of height of the point of application of the load above the shear center on the critical loads of simply supported beams are additive, the reverse is true for cantilevers. The differences of opinion as to the effects of monosymmetry are resolved by an experimental investigation, the results of which support the most common expression for the monosymemtry section property.

Automated Design of Trusses for Optimum Geometry

Abstract: Three-dimensional indeterminate elastic trusses subjected to multiple loading conditions are optimally designed for least weight. The member areas and joint coordinates are treated as design variab...

Large Deflection Analysis of Prestressed Networks

Abstract: A finite element computer procedure is developed, based on the matrix displacement method, for the analysis of large prestressed networks. The mathematical theory including the effect of the nonlinear contribution of the so-called geometrical stiffness are first reviewed on a novel basis. The iterative attainment of the equilibrium is considered in detail, both as far as theory and practice are concerned. The important question of the determination of an initial trial geometry of the network surface in which the equilibrium is only satisfied approximately is considered next. Attention is also paid to the layout of the initial net on the mathematical surface. The last main section reviews the practical organization of a network analysis in a computer. Following the assembly of the initial data, the measures are enumerated which are necessary for ensuring a given prestress condition. Finally practical steps for accelerating convergence and the selection of a simplified net are presented.

Biaxial Stress-Strain Relations for Concrete

Abstract: On the basis of an extensive experimental investigation reported more fully elsewhere, an analytical form of stress-strain relationship for plain concrete in biaxial compression is proposed. This plane-stress orthotropic constitutive relationship accounts for the influence of microcrack confinement as well as Poison's ratio. Other equations found in the literature are shown to be special cases of the one proposed. Also based on experimental results, a simple equation is offered which accounts for the increase in compressive strength of plain concrete when biaxial compressive stress is introduced. Both the biaxial stress-strain equation and the strength equation are shown to give good agreement with the experimental results obtained by the writers as well as by others. Finally, a constitutive law, stated in matrix terms, is given for concrete in biaxial plane stress. This relation is suitable for use in the finite element analysis of reinforced or presstressed concrete.

Elastic stability of tapered i-beams

Abstract: In this paper, the differential equation for the nonuniform torsion of tapered I-beams is derived by analyzing the deformations of the flanges, and this equation is used to study the elastic flexural-torsional buckling of simply supported tapered I-beams For constant flange beams which are tapered in depth, it is found that the changes in the torsional stiffness with the degree of taper are small, and that consequently the elastic critical loads do not vary greatly The elastic critical loads of constant depth beams which have tapered flanges decrease significantly as the degree of taper increases Torsion tests were carried out on tapered depth cantilevers and the results of these were in close agreement with the theoretical predictions Buckling tests were carried out on simply supported I-beams which were tapered in flange width, thickness or web depth, and the experimental critical loads confirmed the theoretical predictions

Eccentrically Loaded Welded Connections

Abstract: Although present methods of investigating eccentrically loaded weld groups have produced safe designs, the factor of safety is, in general, unknown. An analytical method of predicting the ultimate load on eccentrically loaded weld groups is developed. The method uses the true load-deformation response of the welds rather than some idealized one. The validity of the approach has been verified by a testing program using 13 full-size specimens. By making use of the more accurate predictions presented, the factor of safety can be brought into line with that of other structural components and can be established at a constant value for all connections of this type.

Human Perception Thresholds of Horizontal Motion

Abstract: Data are presented on the thresholds of perception of horizontal simple harmonic motion. Such data are needed in the evaluation of the designs of tall buildings with respect to the comfort of the occupants during severe storms. Measurements were made on 112 subjects in two motion simulators each of which represented an office environment. Periods of the oscillations were 5 sec, 10 sec and 15 sec. The frequency distributions of the perception thresholds among the subjects may be represented by the lognormal distribution. Period of oscillation, body movement, expectancy of building motion and body posture are found to be significant factors in the perception thresholds of horizontal periodic motion.

Convenient Form of Stress Invariants for Plasticity

Abstract: The results given herein have been found extremely useful in the context of a unified numerical solution of plasticity problems and may therefore be of interest to workers in this field

Beam-Column Subassemblages Under Repeated Loading

Abstract: The behavior of two types of structural steel half-scale subassemblages of a multistory unbraced frame have been investigated experimentally. These subassemblages were subjected to simulated gravity and cyclic seismic loads. The results obtained in the tests of the upper story specimens show that the weakest element of the subassemblage was the panel zone, where large shear deformation and diagonal buckling occurred. The weakness of the subassemblages representing a lower story, was associated with lateral torsional instability of the beams, which was triggered by local instabilities. From the interpretation of the results, it is concluded that for an efficient design of earthquake resistant structure, it is advisable to have a design which provides a balance between the inelastic deformations, which may take place in each of the critical regions (beam ends and panel zone). It also appears that the energy absorption and dissipation capacity of properly designed steel subassemblages exceeded the required energy even for cases of extreme earthquakes.

Structure--foundation interaction analysis

Abstract: An analysis was developed which considered the structure, continuous foundation and supporting soil as a single compatible unit. The influence of the choice of model for the soil (Winkler or linear elastic) on the moments induced in the foundation was studied for a typical three bay frame and for a range of soil and foundation stiffness. It was evident that the conventional method of analysis and the soil-line method overestimated the negative moments in the foundation but underestimated the positive moments. The bending moment diagrams were similar for both soil models for the three bay frame but for four or more bays the bending moment diagrams are vastly different. The maximum bending moments for the two models is opposite in sign.

Shear Strength of Continuous Plates

Abstract: Results of punching shear test of 15 reinforced concrete specimens of a new type of test specimen that simulates continuous two-way construction are reported. Conclusions for these tests are that: (1) Circular columns permit development of higher shear strength than square columns of equal periphery; (2) increasing moment reinforcing results in slight shear strength increase; (3) none of the empirical strength equations extant are reliable; and (4) conventional footing type test specimens are adequate for parameter studies.

Moment-Rotation Curves for Locally Buckling Beams

Abstract: Tests on composite steel-concrete beams have shown these sections to be highly susceptible to local buckling under negative bending. To further the application of plastic design to continuous composite beams an approxiamte method of predicting the moment-rotation curve of a locally buckling I-shape is developed. The method is based on the upper-bound plastic limit theorem. Solutions are given for two buckling mechanisms and their applicability is determined from test results and web slenderness criteria. Comparisons between the theoretical predictions and several test curves show consistently conservative, but reasonable agreement.

Buckling of Inelastic I-Beams under Uniform Moment

Abstract: Many different theoretical models have been proposed for the flexural-torsional buckling of inelastic steel beams under uniform moment These models are considered and what is argued to be a more accurate model is proposed, which is based on the tangent modulus theory of buckling, which uses the strain-hardening moduli for the inelastic material, and which accounts for residual stresses The predictions for this model for a W 8 x 31 beam are compared with those for the previous models and the relative significance of the assumptions are determined It is found that the critical moment of the beam is not very sensitive to the assumptions concerning the moduli of the inelastic material, but that the effects of monosymmetry induced by the residual stresses should be accounted for The most important assumptions are found to be those of the magnitude and distribution of the residual stresses, which cause significant variations in the strength of the beam

General Treatment of Structural Modifications

Abstract: In order to perform modifications of structures analyzed by the Matrix Displacement Method, a direct computer-oriented approach is presented enabling the treatment of coupled combinations of three possible types of modifications, namely, removal of freedoms, addition of freedoms, and modification of elements. The formulation is extended to cover modifications of elements in substructures together with the corresponding modification to the main structure. The method is derived from the laws of partitioned matrices and Boolean transformation of freedoms within the structural stiffness matrix, and fully exploits symmetry and positive-definiteness. The presented form of the modification equations allows the use of an alternative existing approach of updating the triangularized factor of the structural stiffness matrix due to the modification of elements. The method is extended to provide a recursive hypermatrix Cholesky algorithm. All formulations are accompanied by operation counts to enable rapid determination of break-even points for reanalysis or possible iterative solutions.

Basic Design Criteria of the Recommended Lateral Force Requirements and Commentary

Abstract: The review by the Ad Hoc Committee is limited, as charged, to basic principles. The committee recommends that paid consultants, knowledgeable and expert in structural engineering, in earthquake engineering and in structural dynamics, and knowing the practical elements that enter into structural design from the point of view of practicing engineers, be retained on a reimbursable basis to formulate the code and write the Commentary. The several good parts of the present code should be retained and the other parts replaced by practical provisions based upon current knowledge and technology.

Optimum Design by Partitioning into Substructures

Abstract: A method is developed for the optimum design of large framed structures. Optimization is carried out iteratively by partitioning the structure and thus dividing the optimization problem into a number of smaller subproblems. In the solution of a subproblem only part of the design variables and constraints are considered. Analysis is performed by the stiffness method. An approximate method for reanalysis of the substructures is suggested. The partitioning approach and the reanalysis method are based on the fact that changes of a design variable of one substructure do not appreciably affect the behavior of the other substructures. The cost function is set up for the whole structure and the subproblems are optimized by a direct search technique using external penalty functions on the constraints. Numerical examples of beam and beam grid structures demonstrate applications of the method.

Plastic Behavior of Hollow Structural Sections

Abstract: A series of tests on beams of hollow structural sections was conducted to determine their adequacy in plastic design. A minimum plastic rotation requirement of law times the elastic limit rotation prior to unloading below the fully plastic moment was used to separate sections into categories of plastic and allowable stress design. Local buckling caused by high residual stresses occurred for all but the very stocky sections (b/t < 15, in which b = flange width and t = thickness). The recommended slenderness limit is given by b/t < 150/(σ\do)\U1/2\N, in which σ\do = yield stress) a value considerably less than is currently recommended by CSA-S16 (1969) or AISC (1970).

Steel Column Buckling under Thermal Gradients

Abstract: The buckling loads for wide flange steel columns subject to elevated temperature are determined analytically. Buckling in both the elastic and elastic-plastic range are considered. The buckling loads are determined by solving the governing differential equation using finite differences. Various cases of nonuniform temperature along the length of the member are considered. The influence of elevated temperature on the material properties and the influence of residual stress on the buckling loads is taken into account. Results are presented in the form of column curves relating the critical stress and the column slenderness ratio for various types of boundary conditions.

Analysis of Nailed Joints with Dissimilar Members

Abstract: In order to predict the slope of the load-slip curve of two-member nailed wood joints under lateral load, a theoretical method of analysis is derived based on the theory of beams on elastic foundations The method derived allows analysis of joints where the members are dissimilar in properties and thickness It also accounts for nails of different sizes and materials, and for wood of different species by incorporating a foundation modulus determined from an elastic bearing constant proportional to the wood density Values of the elastic bearing constant are presented for various types of joints Experimental verification of the theoretical expressions are presented

Large Deflection Buckling of Space Frames

Abstract: Buckling loads of space rigid frames based on large deflection theory were determined herein by a method referred to as the constant load method. In this method, the load is maintained at certain constant level and the deflected position which will provide the necessary internal forces to balance the external load is determined by iteration. The load is then increased to the next level and the process repeated until the process becomes divergent or the determinant of the stiffness matrix becomes zero. The advantages of the method are: (1) the direct application of stiffness coefficients developed for the small deflection buckling and (2) the possibility of starting iteration at any level. Verification of the method with various published examples was made. An illustration was made for the determination of large deflection buckling mode of a symmetrically loaded framed dome.

Drag or Along-Wind Response of Slender Structures

Abstract: Theoretical approaches to the evaluation of the response of slender structures in turbulent shear flow have been proposed by a number of researchers. There are, however, limited experimental data supporting these developments and the assumptions upon which they have been based. In the present paper, the theory is reviewed briefly and the assumptions and necessary data examined in the light of recent experimental results. The theory is applied to predict the response of a slender tapered stack of circular cross section and the predictions compared with experimental observations of the behavior of a model stack in boundary layer flow. It is demonstrated that quasisteady approximations are adequate for wavelengths greater than about five to ten times the width of the structure and that the extension of the quasisteady approach to shorter wavelengths will, in general, yield a small overestimate of response. It is also shown that estimates of aerodynamic damping based on quasisteady assumptions are adequate.

Buckling of Steel Angle and Tee Struts

Abstract: An experimental study was conducted on steel angle and tee struts to provide verification of the theoretical solutions for flexural, torsional-flexural, and plate buckling. The effect of slenderness and width-thickness ratios was examined for single angle struts and double angle struts with separators, with hinged and fixed end conditions. The slenderness ratio was varied from approximately 21 to 89 and the overall width-thickness ratios ranged from 10.0 to 17.3. Tests on 27 tee sections with hinged ends were also conducted. Good agreement is shown between the experimental and theoretical results. It is suggested that the flexural, torsional-flexural and plate buckling stresses be computed as per the established rational buckling theory and the least value be taken as the critical stress for the given strut.

Algorithm for Matrix Bandwidth Reduction

Abstract: A method for reducing the bandwidth of matrices is presented. The method was developed for symmetric matrices, but it is also applicable for asymmetric matrices. A detailed flowchart for the algorithm is included. Numerical results obtained by applying this method, as well as several other previously published methods, 10 examples, are tabulated. While no mathematical proof of convergence is attempted, the numerical results indicate that, in general, the method does converge.

Load balancing analysis of cable stayed bridges

Abstract: The cable stayed bridge is a structure well suited for load balancing, that is for reduction of bending moments and displacements throughout the structure by post-tensioning the cables The problem was approached frist from the point of view of reducing bending moments A procedure was developed to achieve this reduction The first step of this method consists of determining the bending moments due to a unit force applied successively along each cable of the bridge system Next, a system of equations is written to express the condition that the sum of the bending moments due to unknown post-tensioning forces in the cables, shall be opposite in sign and equal to a fraction of the bending moment caused by the action of the dead load By solving this system of equations, the post-tensioning forces in cables are determined A computer program was written in FORTRAN language to carry out the computations

Interaction Equations for Biaxially Loaded Sections

Abstract: A simple method for obtaining the exact interaction relationships of doubly symmetric sections under combined axial force and biaxial bending moments is presented. Simple expressions for approximating the interaction curves of wide-flange sections are proposed, and the associated plastic deformations are calculated. For illustration, interaction curves for a wide-flange section, a box section and a circular section are developed using the method. Simple analytical expressions to approximate the interaction relations of wide-flange sections are proposed, and the associated plastic deformations are calculated.