Showing papers in "Journal of the Structural Division in 1966"

Behavior of Square Infilled Frames

Abstract: An investigation of the behavior of diagonally-loaded square infilled frames is described first. Series of experiments on diagonally-loaded models with a range of frame stiffnesses indicated that a small increase in frame stiffness has a magnified effect on the over-all stiffness and strength of the structure. Approximate theoretical analyses, based on the length of contact between the frame and infill, are developed to explain this composite behavior, and to provide methods of predicting the over-all diagonal stiffness and strength. The behavior of laterally-loaded infilled frames is considered next. The methods proposed for the diagonally-loaded case are adapted to predict the lateral stiffness and strength of single or multi-story square infilled frames. The results of experiments on single and double-story models support the pro-posed methods of prediction.

The Analysis of Structural Safety

Abstract: The work of the Task Committee on Factors of Safety, ASCE, to date (as of 1965) is summarized with a brief review of the work that has been done elsewhere in the field of structural reliability. On the basis of the assumption that the resisting strength of and the load applied to a structure are usually random variables, the probability of failure and reliability function are introduced as possible measures of structural safety, and related to the conventional safety factor. Reliability functions of structures consisting of multiple members are derived for the cases when the loads are applied at equal intervals or at prescribed instants and where the number of occurrences of the load is governed by a Poisson law, assuming that the resistance of the structure is either deterministic or random. Two numerical examples dealing with safety of a transmission tower and of an aircraft wing are presented to illustrate the proposed method of evaluation of structural safety.

Rotational Capacity of Reinforced Concrete Beams

Abstract: All limit design theories are based on the principals of equilibrium of forces and compatibility of deformations at the state of impending collapse. Use of these theories is dependent on an ability to predict the moment rotation relationships of structural members. An investigation was carried out to improve on the accuracy of methods for predicting moment-rotation relationships of reinforced concrete beams. Tests on 40 beams are reported. In addition, the results of these tests and of tests previously reported on 37 beams are analyzed. The variables considered include size, beam width, reinforcement index, and binding by closed stirrups. A method is proposed for the computation of the rotational capacity of hinging regions in reinforced concrete beams.

Tabular Decision Logic for Structural Design

Abstract: As computer applications shift from analysis to design, increased attention must be given to algorithms which are primarily logical in character. The common approach to the programming through involved flow-charts has been generally found unsatisfactory. The technique of tabular decision logic provides one means of formulating complex logical decisions. The technique is described and illustrated. It is shown that the technique eliminated most of the shortcomings of conventional flow-charting. The application of the technique is contingent on the availability of clear, precise rules defining engineering decisions. The paper concludes with a brief description of the conversion of decision tables into conventional flow diagrams and of some processors which convert decision tables directly into execution programs.

Iterative Design and Structural Optimization

Abstract: Methods of automatic design of structures are viewed, proposed, and evaluated by a numerical example. Sensitivity coefficients are introduced to help predict the consequences of design changes. Simultaneous linear equations are used to suggest new designs. Linear programming is introduced to generate optimum designs. Non-fully stressed designs and non-convex design spaces are examined. The effect of the choice of the design variables is demonstrated. A number of illustrative examples are included.

Structural Optimization by Nonlinear Programming

Abstract: Optimum structural design is formulated as a problem in nonlinear mathematical programming, i.e., a problem of selecting n design variables subject to m > n constraints such that an objective function is minimized. The design variables correspond to the geometrical or mechanical properties of the structural system, the constraints correspond to safety requirements such as limitations on stresses and deflections, and the objective function corresponds to weight or cost. The gradient projection method of nonlinear programming is described and an algorithm is presented for high-speed computation. Examples are presented in which the method is used to obtain least-weight designs of typical indeterminate rigid frames made of standard steel wide flange shapes. The examples illustrate that the programming approach affords a sound mathematical basis on which to develop rational methods of structural design.

Finite Beams on Elastic Foundations

Abstract: The differential equation of beams of finite length, resting on a Winkler foundation is solved in terms of the initial conditions, i.e., the conditions at one of the ends of the beam. With the solution in this form, which contains the initial conditions as the constants of integration, it is then possible to write merely by inspection the equation of the elastic line. The solution of the resulting boundary value problem is simplified through the use of special functions, which possess interesting properties, and a table of values of these special functions.

Torsional Restraint of Lateral Buckling

Abstract: Elastic solutions to six problems in lateral-torsional buckling of I-beams with torsional restraint are presented The loadings considered are equal moments at the end, concentrated load at mid-span at the shear center, and uniform load at the shear center Two types of torsional restraint are considered: point torsional restraint, and continuous torsional restraint All solutions, with one exception, are obtained by numerical methods and the results are presented in the form of charts

Behavior of Stainless Steel Columns and Beams

Abstract: Use of stainless steel in structural applications is most economical in the form of light-gage members. In this type of construction, local buckling and post buckling strength is of major importance. Stainless steels are anisotropic, exhibit different shapes of stress-strain curves in tension and compression, are highly susceptible to cold work, and have low proportional limits. Because of the wide variation in properties this investigation is limited to Type 304, annealed and skin passed. Post buckling strength of stiffened, compressed plate elements is examined and experimental results are presented. The flexural strength and working load deflections of simply-supported hat section beams are calculated, using an effective width concept in the post buckling domain, and recognizing the nonlinearity of the stress-strain curves. Comparison with experimental results is given.

Framing Connections for Square Structural Tubing

Abstract: Five types of simple connections for framing beams into square and rectangular structural steel tubular columns are treated Two types were adequate in all respects—the conventional angle seat, and a connection made by welding a length of structural tee to the tube face A beam web connection consisting of a piece of plate fillet welded to the center of the tube wall tended to induce excessive local deformation and weakening of the tubular column section A similar connection made by welding the plate on the corner of the tube, at 45○ to the principal axes, also produced tube distortion as well as being excessively stiff The final type studied consisted of a plate inserted through vertical slots cut in the center of the tube wall and then welded at the faces of both walls It proved to be excessively stiff and probably should not be classed as a simple connection

Longitudinal Stiffeners for Compression Members

Abstract: Simplified methods based on buckling strength are developed for proportioning stiffening lips on thin flanges and intermediate stiffeners on thin sheet subjected to uniform compression. Symmetrical and unsymmetrical stiffeners and lips are considered. Buckling strengths are determined from the equivalent slenderness ratio formulas presented and column buckling equations. The radius of gyration of stiffener or lip required to provide essentially a hinge support for the flange or sheet at the stiffener is developed. Compression tests of thingage hat sections of aluminum alloy 6061-T6 provide information on the buckling strength and behavior of sections with lipped flanges. These and other previously published test data substantiate the equations developed for buckling of lipped flanges.

Optimum Design — Minimum Weight Versus Fully Stressed

Abstract: The substitute problem of fully stressed design or simultaneous failure modes design is often solved in place of the minimum weight design. A method is presented which can be used to determine the validity of the substitute problem of fully stressed or simultaneous failure modes design. The equivalence of these two solutions can be demonstrated for a large class of discrete and continuous structures subjected to a single load condition. This equivalence can also be extended to a stress limited determinate truss subjected to several independent mechanical loads. However, it can also be shown that the simultaneous failure modes is not necessarily the minimum weight design for waffle plates subjected to a multiplicity of biaxial loads.

Plastic Hinging in Reinforced Concrete

Abstract: The complete load-deflection history of 18 beams tested during 1952-54 and 18 beams tested during 1959-61 at the Univ. of Ill. allowed a study of the factors which contribute to ductility. All tests involved simple spans with load applied through a column stub at midspan to simulate the beam-column connection in a reinforced concrete frame. This study involved only beams without axial load. Primary variables studied included depth, compression steel ratio, concrete strength, amount of transverse reinforcement, and ratio of compression steel area to tension steel area. The tests indicate clearly the contribution of compression steel to ductility of reinforced concrete beams. The modes of failure reflected the importance of confinement of concrete in the compression zone in insuring the capacity for large plastic rotation at the joint. In all cases the first crushing of concrete (ϵ c = 0.004), usually considered as ultimate, was found to be associated with a deflection much smaller than that corresponding to the ultimate load. For beams with compression steel the reverse ductility beyond first crushing was large, the deflection at ultimate load in some cases being more than ten times the first crushing deflection.

Three-Dimensional Analysis of Tier Building

Abstract: Three-dimensional analysis of tier buildings using a digital computer is feasible and perhaps mandatory in some cases. It is no longer necessary to simplify the problem by resorting to the notion of analyzing the building as a system of parallel and perpendicular plane frames. Errors inherent in the two-dimensional approach may be significant, whereas the three-dimensional analysis contains no theoretical discrepancies. The analytical model of the structure is examined in detail, and individual member stiffnesses are enumerated. Pertinent geometric transformations for displacements, actions, and stiffnesses are also formulated. The stiffness method of solution is described, followed by a brief outline of the computer program. Results for an example 20-story building show that the effect of axial strains in columns is substantial, whereas the influence of torsional rigidities is small.

Theoretical analysis of suspension bridges

Abstract: THE ANALYSIS OF SUSPENSION BRIDGES IS A TYPICAL PROBLEM OF STRUCTURAL FRAMES THAT ARE ASSOCIATED WITH LARGE DEFLECTIONS THAT PLAY AN IMPORTANT PART IN THE BEHAVIOR OF THE FRAME. THEORETICAL AND PRACTICAL TREATISES ON SUSPENSION BRIDGES WERE DEVELOPED BY MANY AUTHORS. THEIR ATTEMPT TO IDEALIZE THE PROBLEM AND MAKE IT SUITABLE FOR HAND CALCULATIONS HAS EXPOSED THESE SOLUTIONS TO CRITICISM. A SYSTEMATIC METHOD IS INTRODUCED FOR THE ANALYSIS OF SUSPENSION BRIDGES BASED ON THE FINITE DEFLECTION THEORY AND THE N-DIMENSIONAL GENERALIZATION OF THE NEWTON-RAPHSON PROCESS FOR SOLVING THE SIMULTANEOUS NON-LINEAR EQUATIONS. THE BASIC ASSUMPTIONS ARE REPORTED AND THE APPLICATION OF THE NEWTON-RAPHSON PROCESS IS EXAMINED. A DERIVATION IS GIVEN FOR THE TANGENT STIFFNESS MATRIX OF A STRUCTURAL FRAME AT A STATE OF DEFORMATION. THE ANALYSIS FOR TWO PROBLEMS, A CABLE AND A TRUSSED GIRDER, IS GIVEN TO INTRODUCE THE APPLICATION OF THE NEW APPROACH. THE CONCEPT OF THE TANGENT STIFFNESS MATRIX IS A NEW TECHNIQUE FOR RAPID CONVERGENCE OF THE ANALYSIS. THE METHOD IS GENERAL AND OF PARTICULAR INTEREST FOR THE ANALYSIS OF SUSPENSION BRIDGES UNDER CONSTRUCTION CONDITIONS. IT IS ALSO SUITABLE FOR ELECTRONIC COMPUTERS. /AUTHOR/

Interaction of Continuous Frames and Soil Media

Abstract: A solution to the response of fully continuous orthogonal space frames supported on a viscoelastic soil media is presented. Matrix expressions containing slope-deflection equilibrium equations are used to formulate the structural problem in terms of joint rotations and elemental translations. The support reactions, derived in terms of the deformations, are incorporated into the equations of motion describing the consolidation of the soil mass. These expressions are written for mechanical models which are assumed to have viscoelastic characteristics analogous to the time-displacement properties of soils. Finite differences are used to reduce the differential equations of motion to linear algebraic forms such that a composite solution can be found when these expressions are substituted in the equilibrium equations. The methods of converting soil properties into equivalent viscoelastic mechanical model factors are examined and illustrative examples demonstrate the method.

Computer Analysis of Plane and Space Structures

Abstract: A comprehensive compilation of the stiffness method is presented for the general analysis of plane and space structures At first, the stiffness matrices of members with uniform cross-sections are derived relative to both the member and common axes, for various end deformation conditions ranging from a plane truss to a space frame member The member stiffness matrices are suitably modified to include the effects of variable moment of inertia, shear deformations, wide supports and semirigid connections The solution technique for large-size band matrices with multiple load vectors is presented and some computer programming for important phases of the analysis is introduced The classification of structures with one or two dimensional members, is examined Numerical examples for space frames are also included

Inelastic Lateral-Torsional Buckling of Beam-Columns

Abstract: A procedure for the determination of the inelastic lateral-torsional buckling strength of steel wide-flange beam columns is presented. The beam columns are subjected to axial thrust and to moments applied at one and only. The end moments cause bending about the strong axis of the members, and the effects of initially present symmetric thermal residual stresses are included in the analysis. Two simultaneous differential equations with variable coefficients are derived, awl the corresponding finite difference equations are presented. The coefficients in these equations represent the pertinent section properties that vary along the length of the member in those portions that are partially yielded. The critical end moments are obtained when the value of the characteristic buckling determinant becomes zero.

Building Design Using Linear Programming

Abstract: An approach for the preliminary minimum weight design of tall framed steel buildings is presented. The design criteria are safety against collapse and a limitation on lateral deflections under service loads in the elastic range. The method of linear programming is used to generate the solution to the preliminary design. Plastic hinge theory is used to generate the equations of constraint on the moment carrying capacity of the members. The equations of constraint are compatible with the design criteria. To simplify the solution effort in the preliminary design, a building model is used in which the design requires that plastic hinges form only in the beams. This reduces substantially the number of collapse mechanisms which must be considered. A simple linear equation of constraint on the deflection under service loads is developed by separating the contributions of the columns and beams to the flexibility of a frame, and establishing a conservative ratio between these contributions. The proposed approach is illustrated by a numerical example in which the preliminary design of a 26-story building is generated.

Exact Solution of the Biaxial Bending Equations

Abstract: The exact solution of the differential equations governing the elastic deformational response of biaxially loaded columns is given. Several numerical examples are presented which illustrate this exact solution. Numerical values for stresses and deflections obtained from this exact solution are compared with the results of existing approximate solutions. The problem of stability and the influence of initial imperfections including residual stress and initial deflections and twist on the biaxially loaded column may be investigated in a manner similar to that used herein.

Optimum Design of Constant-Depth Plate Girders

Abstract: The iterative flange smoothing method is a computational method for determining the minimum-cost design of girders with constant web height on the basis of a given mathematical model for costs and specification for design, analysis, loading, and material. In this method, the problem is decentralized into an iterative cycle of a few simple, less dimensional operations. Each cycle consists of four major operations where each operation modifies the results of the previous one. These operations are (1) determination of the optimal arrangement of the section modulus along the girder, (2) determination of the cross section along the girder such that material cost is minimized, (3) modification of the design by balancing the cost of material versus fabrication using the smoothing method of operations research, and (4) optimization of the design variables such that the total cost is minimized. The method is found to be efficient, practical, and applicable to different cost models and specification requirements.

Analysis of High Guyed Towers

Abstract: A method of analysis for high, guyed towers under wind loading, readily adapted to computer use, is presented. The planes containing guys with or without insulators or ice loading are changed by drag and lift forces produced by wind; and these forces together with tower motion are used to compute the variable spring constants for determining guy reactions. All significant secondary effects including increase in shear caused by shaft distortion and web member strains, eccentricity of shaft between guy levels, and external moments produced at each level by the guys are considered. An analysis of two-way bending of guyed towers is also included and a method of solution presented.

Structural Analysis by Networks, Matrices, and Computers

Abstract: The analysis of systems of structural elements, as opposed to the analysis of the behavior of individual structural members, is examined. Parts of network theory having a bearing on structural analysis, and the network formulation of structural analysis, are briefly presented. The matrix formulation is summarized, and the transformations involved are examined. The two formulations are compared, and it is shown that they yield identical equations describing the systems, but that the network formulation has conceptual and computational advantages. This formulation also makes easier the transference of techniques from other disciplines, such as Kron’s method of piecewise solutions. Finally, it is shown that the network formulation can serve as a basis for efficient and general computer programs.

Repeated and Reversed Loading in Reinforced Concrete

Abstract: THREE BEAMS TESTED AT THE UNIVERSITY OF ILLINOIS, DURING 1959-61 WERE SUBJECTED TO REVERSAL IN THE DIRECTION OF LOADING AND 18 OTHERS WERE SUBJECTED TO REVERSAL OF LOADING IN ONE DIRECTION. THE BEHAVIOR OF THE THREE BEAMS SUBJECTED TO REVERSAL OF LOADING IS DISCUSSED IN DETAIL. THE REDUCTION IN STIFFNESS OF A REINFORCED CONCRETE BEAM WITH PROGRESSIVE DAMAGE RESULTING FROM REPEATED LOADING IS EXAMINED. THE THREE BEAMS WITH REVERSAL OF LOADING WERE FOUND TO POSSES LOAD-DEFLECTION CAPABILITY SIMILAR TO THAT FOR COMPANION BEAMS NOT SUBJECTED TO REVERSAL OF LOADING. ENVELOPE CURVES FOR COMPANION BEAMS SHOW THIS COMPARISON. ULTIMATE MOMENT FOR THE BEAMS SUBJECTED TO REVERSAL OF LOADING WAS FOUND TO BE PRACTICALLY UNAFFECTED BY THE PREVIOUS REVERSAL OF LOAD IN THESE TESTS. SOME LOSS IN DUCTILITY WAS OBSERVED, BUT LARGE PLASTIC ROTATION CAPACITY WAS OBSERVED IN ALL OF THESE BEAMS WHICH WERE DOUBLY REINFORCED. /ASCE/

STRUDL — A Computer System for Structural Design

Abstract: STRUDL (STRUctural Design Language) is a computer system for application to the structural design process. The system is designed to relieve the engineer of tedious clerical and computational tasks and to permit the more rapid implementation of engineering decisions. Some of the analytic and clerical user capabilities in the initial version of STRUDL are described. The system capabilities include data manipulation, a wide range of analysis and design operations, accounting procedures, and process control functions. In addition, some of the system requirements for implementing decisions are outlined, including data structuring with dynamic memory allocation, a data dictionary, and a command interpreter. On-line interaction through time-sharing is evaluated in terms of the need for sensitive control over interaction. The capabilities described represent the first stage of a dynamically developing system, oriented towards generating design information.

Elastic Stresses Around Holes in Wide-Flange Beams

Abstract: The theory of elasticity was used to develop equations for the stresses in uniformly loaded simply supported wide-flange beams with holes in the webs, when the hole is free of force. The equations were solved on a digital computer. The applicability of the analysis is examined by checking a moment equality and a shear-force equality. For circular holes (1) when the shear-moment ratio is 0, the analysis is applicable to a minimum beam depth-to-hole diameter ratio of about 2.0, and (2) when the shear-moment ratio is 2.4/L, in which L is the half-length of the beam, the analysis is applicable to a minimum depth-diameter ratio of about 6.0. However, limited experimental tests demonstrated that the accuracy is sufficient for beams with depth-to-diameter ratios as low as 2.0, even when the shear-moment ratio is not 0. The stresses predicted by the analysis are depicted for several conditions and the major effect of the variables is studied. The results of the investigation are not reduced for design use.

Calibration of alloy steel bolts

Abstract: The performance of alloy steel structural bolts when subjected to various conditions of installation and load was determined. The bolts investigated were ASTM A354 Grades BC and BD and ASTM A490. Variables included bolt diameter, grip length, thread length under nut, and thread lubrication. The problems investigated included the behavior of bolts loaded in tension by either direct axial force or by torque, the response of bolts installed by torquing to subsequent application of direct tension, the effect of reinstallation, differences between tests performed in a hydraulic load cell and field behavior of bolts, incremental versus continuous torquing, and the effect of thread lubrication. Conclusions and recommendations are made concerning alloy steel bolts used as structural fasteners.

Local Instability in Plates and Channel Struts

Abstract: A theoretical and experimental Investigation of the initial buckling of a thin flat rectangular plate is presented. A method is outlined whereby the theoretical plate buckling load of plain and lipped channel sections are obtained from the individual buckling characteristics of the web and flange plates. It is shown that good agreement is obtained between these theoretical loads and the corresponding experimental values obtained by the author.

Optimum Design of Mixed Steel Composite Girders

Abstract: Steels having a variety of yield points are now available to the construction industry, allowing the designer to choose strength as well as size to meet design requirements. This work is concerned with the use of a variety of steel strengths in continuous, welded, composite plate girder bridges to produce minimum cost structures. The solution which is reported obtains the optimum design of a girder subject to the standard specifications of the American Association of State Highway Officials. Span lengths, material properties, concrete deck dimensions, and cost information on steel types and on splicing operations must be given. The capability selects the optimum combination of web height, flange width, plate thicknesses, and the arrangement of steel types for a continuous girder of constant depth. An iterative scheme is used between the material and splice location selection and the determination of the best web depth and flange width. Results are given for example problems considering seven available steels for the design of a composite plate girder.

A440 Steel Joints Connected by A490 Bolts

Abstract: THIS REPORT PRESENTS DATA FROM EIGHT STATIC TENSION TESTS OF FULL-SIZED BOLTED BUTT JOINTS FABRICATED FROM 1-IN. PLIES OF A440 STEEL PLATE AND CONNECTED BY 7/8-IN. ASTM A490 HIGH- STRENGTH BOLTS. IN ADDITION, THIS REPORT INCLUDES THE RESULTS OF A THEORETICAL ANALYSIS OF A440 STEEL JOINTS FASTENED WITH EITHER A490 BOLTS OR A502-GRADE 2 HIGH- STRENGTH RIVETS. BOTH THE THEORETICAL AND EXPERIMENTAL STUDIES WERE DESIGNED TO SHOW THE EFFECTS OF SPECIFIC VARIABLES ON THE ULTIMATE JOINT STRENGTH, INCLUDING VARIATIONS IN PITCH, JOINT LENGTH, AND CHANGES IN THE RATIO OF NET PLATE AREA A/N/ TO THE TOTAL FASTENER SHEAR AREA A/S/ THE THEORETICAL STUDIES SHOW THAT THE AVERAGE SHEAR STRENGTH DECREASES WITH INCREASING JOINT LENGTH. FASTENER PITCH HAD A MINOR EFFECT ON THE SHEAR STRENGTH. TOTAL JOINT LENGTH HAD THE MOST IMPORTANT EFFECT ON THE AVERAGE SHEAR STRENGTH AT ULTIMATE JOINT LOAD FOR A GIVEN A/N'A/S/ RATIO. VARIATIONS IN THE A/N/'A/S/ RATIO PRODUCED MAJOR CHANGES IN AVERAGE SHEAR STRENGTH. THE MAXIMUM DEVIATION BETWEEN THE THEORETICAL SOLUTION AND TEST RESULTS WAS 7%. EXPERIMENTAL DATA SHOW THAT THE PRESENT SLIP COEFFICIENT OF 0.35 USED IN THE RCRBSJ SPECIFICATION IS REASONABLE. /AUTHOR/