Journal of Structural Engineering

The load‐carrying mechanism in concrete slabs of composite beams at web holes is studied. Using a truss analogy, the shear studs in the hole region are considered as vertical tension‐carrying members, and inclined struts in the concrete are considered to act between bearing zones at the heads of the studs and at their bases at the steel beam flange. The structural action between the concrete slab and the shear connectors is clearly identified, and rational truss idealizations for determination of the slab shear‐carrying capacity are developed. This approach relates the shear capacity to the location of studs, and three idealizations are used to provide solutions for three typical stud configurations. In this way, the ultimate resistance of composite beams containing large web holes is estimated. Both solid slabs and ribbed steel deck‐supported slabs are considered.

Nine full‐scale tests are described in which composite beams containing web holes are studied in an attempt to understand the mechanisjns by means of which the slab participates in carrying vertical shearing force. In particular, the test evidence is examined for support of a truss analogy in which shear studs are considered as vertical tension members, and diagonal compression struts act in the concrete. Parameters investigated include stud configurations, the width of the concrete slab, and detailing of the studs in the hole region. The latter details are varied based on expectation of improved performance deduced from consideration of the truss analogy. Strength predictions are made by the truss analogy, described in a companion paper, and also based on previously published analyses, and test results are summarized for a total of 44 tests collated from many sources. Good agreement between observed and predicted failure loads is demonstrated for both theories. The truss analogy enables a clearer understanding of the slab behavior.

This paper deals with the analysis of uncertain creep and shrinkage effects, and in particular the computation of the probability of serviceability failure for a reinforced concrete structure subjected to stochastic loadings. A sustained load of uncertain magnitude, a stationary Gaussian loading process, and a Poisson loading process are considered. To model the creep and shrinkage phenomena. Bažant‐Panula model is employed. The resulting time‐variant reliability problem is an upcrossing problem in stochastic process theory that is, in general, difficult or computationally demanding to solve. The problem can be simplified to allow prediction at end of a given time period, using the so‐called time‐independent reliability theory (e.g., the first‐order second‐moment method). However, this can be achieved only once the statistics of the load effects have been obtained by Monte Carlo simulation, but is considerably less demanding than a complex Monte Carlo solution. A numerical example is given to illustrate the method, and the results are compared with simulation results.

The lateral loads imposed on a structure during an earthquake are functions of the peak ground acceleration and the total mass of the structure among other parameters. For structures located in snowy regions, the question arises as to the appropriate roof‐snow load to be used in earthquake calculations. Various codes and load standards suggest values for the snow load, which is to be combined with dead load in earthquake analysis. In this paper statistical information on daily ground‐snow loads and statistical information on the conversion factor between roof and ground loads are used to determine appropriate roof‐snow loads for earthquake analysis. As defined herein, the appropriate roof‐snow load is such that the exceedance probability for the design seismic base shear is identical to the exceedance probability for the design peak ground acceleration. The analysis suggests that the appropriate roof‐snow load for seismic calculations is 20%, of the 50‐year mean recurrence interval ground‐snow load.

A critical strain‐energy‐density failure criterion is introduced to describe the load‐duration (creep‐rupture) behavior of structural lumber. From extensive ramp, constant, and step‐constant load tests in various constant and cyclic environments, a critical strain‐energy density is identified, which forecasts impending failure. Impending failure is defined as the initiation of member failure, excluding partial failures that do not influence subsequent member behavior. Most previous load‐duration research defined failure as the complete collapse of a test member and modeled the response using cumulative damage theory. Select structural and no. 2 grade Douglas‐fir nominal 2 in. by 4 in. lumber are used here. The critical strain‐energy density is found to be invariant with respect to load history, load level, grade, and hygrothermal condition. A model is developed and used to predict the observed load‐duration behavior of the Douglas‐fir lumber sample. A comparison between the damage accumulation approach to modeling load‐duration effects and the developed strain energy approach is also presented.

Most composite‐slab designs in the United States are based on the results of extensive testing programs. These programs result in the development of load tables that structural engineers use for the design of composite slabs. Details of the required test program and subsequent determination of design live loads are presented in the ASCE standard Specifications for the Design and Construction of Composite Slabs. A problem with a design approach based solely on test results is that a structural engineer has no specification criteria upon which to base design calculations. For the design of some structural systems this method may be unavoidable; however, the results presented in this paper indicate that design procedures for composite slabs may be developed based on calculations. A method is presented in this paper for determining the strength and initial stiffness of composite slabs. The method is based on traditional reinforced‐concrete analytical methods. Results from a series of nine experimental composite‐slab tests that incorporated typical construction details are presented and compared to results from the analytical expressions.

The lateral expansion of concrete subjected to compression (i.e., the Poisson effect) is shown to be a significant factor influencing the behavior of reinforced concrete elements in tension‐compression states in which the principal tensile strain is relatively small. A method is presented by which concrete lateral expansion can be incorporated into a nonlinear finite element algorithm. The formulations presented presume the use of a secant‐stiffness‐based solution procedure, involving the concept of material prestrains. Material behavior models are described for nonlinear concrete expansion, strength reduction due to transverse cracking, strength enhancement due to confinement, and pre‐ and post ultimate stress‐strain response. The accuracy of the formulations are examined through finite element analyses of a number of shear panels and shear walls previously tested. It is shown that the inclusion of concrete lateral expansion can, in some cases, significantly alter the computed response of an element or structure. Further, it is shown that the consideration of expansion and confinement effects generally results in a significant improvement in the accuracy of the analysis.

Current design methods for notched wood beams, based on either notch‐factor or linear‐elastic fracture mechanics (LEFM) approaches, are reviewed and compared with an alternative equation based on critical fillet hoop stress (CFHS) theory and with experimental data. The CFHS and LEFM equations are shown to account for the observed effects of notch corner location, load distribution, beam height, and fractional notch depth. The notch‐factor equation, currently the basis for U.S. design practice, does not reflect the effects of beam height and notch corner location on strength. The CFHS equation implicitly accounts for the effect of beam span‐to‐depth ratio, and was developed from combined results of finite element and statistical analyses and an extensive experimental program. Other potential advantages of the CFHS equation are: (1) Its ability to account for stress relief caused by rounding the notch; (2) its ability to account for Saint‐Venant end effects for notches located at, or close to, the support; and (3) its use of a notched beam material parameter κ that is easily determined by simple tests.

An analytical procedure is proposed for the force‐deformation relationship of a reinforcing bar anchored in concrete. The procedure leads to computation of deformations in two parts, as extension and slippage. The extension of reinforcement is determined by establishing inelastic strain distribution along the embedment length of the bar. Constant average bond along the elastic length and frictional bond over the plastic length are assumed. The rigid body slippage of the bar is computed when the bar is stressed to the far end. An increase in the elastic bond stress is considered to develop the bar force with the available anchorage length. The elastic bond at the far end of the bar is used with a previously derived local bond‐slip model to obtain the rigid body slippage of the bar. The procedure is applied to straight as well as hooked bars, subjected to pull, and simultaneous push and pull, simulating exterior and interior joints. The results are verified against a large volume of experimental data reported in the literature.

Large‐scale reinforced concrete columns were tested to investigate hysteretic behavior of anchorage slip in reinforced concrete structures. The columns were subjected to constant axial compression and unidirectional and bidirectional lateral‐deformation reversals. The results indicate a significant increase in column rotation due to anchorage slip. Penetration of yielding into the column footing was observed in the tension reinforcement, while the compression yielding was localized at the column‐footing interface. Axial compression resulted in early closure of the crack associated with anchorage slip, reducing related deformations. An analytical model was developed for hysteretic moment‐anchorage slip‐rotation relationship. The model consists of a primary curve and a set of rules defining unloading and reloading branches. The primary curve is constructed by computing the extension and slippage of tension reinforcement in the adjoining member. This is accomplished by considering inelastic strain distribution along the embedment length of reinforcement, as well as the local bond‐slip relationship. Hysteretic rules are obtained from experimental observations, and incorporate pinching of hysteresis loops as well as the effect of axial compression. Comparisons of experimental and analytical hysteretic relationships indicate excellent agreement.

A new viscoelastic‐type connection isolator (damper), made of elastomeric material, is presented in this paper. Based on experimental results, a Kelvin‐Voigt‐type model was developed to simulate the behavior of the connection. By comparing the stress‐strain curves of the model with those obtained from the tests, it was found that the durometer of the elastomeric is the predominant material parameter. An analytical method for the analysis of unbraced‐ and braced‐frame structures equipped with those viscoelastic‐type connections is presented. The effectiveness of these isolation connections (dampers) is studied numerically by comparing the responses to various dynamic excitations of structures equipped with these dampers with the responses of structures without isolation. The results of these comparisons show that the isolation connections provide significant improvement by reducing the lateral displacement of the structures.

Contribution of monolithic floor slabs to the negative (hogging) flexural resistance of beams in reinforced concrete frames may inadvertently affect the hierarchy of failure unless it is considered during the design. A qualitative model simulating participation of slabs to the behavior of beams is developed by establishing the kinematic relations between beam deformations and the state of strain in the slab. The slab is idealized as a membrane element by using a network of rigid links and flexible springs connecting the slab bars to the supporting beams. Support displacements of the rigid links, such as reinforcement slip, twist, weak axis rotation, and elongation of the transverse beams are considered. Reasonable correlation of test data from interior and exterior slab‐beam‐column subassemblies is possible. The computed responses were most sensitive to the assumed length of plastic hinge, and to a lesser degree, to the distribution of longitudinal strains within the plastic hinge. In the range of low deformations, results are somewhat sensitive to the assumed initial transverse beam stiffness. Available expressions for establishing length of plastic hinge seem sufficient.

An analytical model is developed that predicts the out‐of‐plane seismic behavior of reinforced masonry walls. The formulation and implementation of the model are briefly described. The model is validated by comparing the global responses (deflections, moments, and reactions) that it predicts with those obtained from full‐scale dynamic tests on nine clay brick walls and four concrete‐block walls. The test walls cover a typical range of key wall parameters ($H/t$ ratio, amount of vertical reinforcing, presence or absence of grouting and splices, and intensity of vertical load). Each test wall was subjected to a suite of at least 12 earthquake motions, with progressively increasing peak horizontal accelerations of 0.1 g to 0.8 g. An analytical model of each wall is subjected to the same suite of motions measured during the corresponding tests. It is concluded that the analytical model captures the global wall responses well, over the range of wall parameters and earthquake motions included in the tests.

A theoretical model is developed for predicting mechanisms of load transfer between a wood member and a metal die‐punched truss plate. The model, which treats a truss‐plate tooth as a beam on an inelastic foundation of wood and applies Runge‐Kutta numerical analysis to solve the governing differential equations, predicts the load‐displacement trace and ultimate load of truss‐plate joints. The model is verified with eight truss‐plate joint types, three of which varied the number of teeth and five the plate and grain angle. Theoretical and experimental load‐displacement traces show good agreement. Experimental traces show no significant difference between multiple teeth in rows and columns, indicating little stress interaction among teeth. The theoretical model accurately predicts the ultimate load and failure modes for complete joint test types, which vary with plate and grain geometry; teeth face bearing on end grain failed by tooth withdrawal or plate tensile failure, teeth edge bearing on end grain failed by plate peelback, and teeth bearing on side grain failed in wood perpendicular to grain.

In conjunction with load and resistance factor design specifications, advanced methods of inelastic analysis afford the opportunity to design steel structures based on realistic assessments of limit state behavior. This paper presents a summary of a study of the in‐plane behavior of a series of low‐rise frames. Designs are obtained that rely on a second‐order inelastic analysis to demonstrate that the frame and its members are adequate in resisting the effects of factored loads. The inelastic designs are compared with designs obtained using conventional elastic methods of design. A representative inelastic design is further evaluated with respect to strength and serviceability limit state behavior, including conformance with current load and resistance factor design specification provisions. The accuracy and reliability of using a second‐order concentrated plasticity analysis to model system behavior are also established. The investigation indicates that second‐order inelastic analysis can be used effectively to design steel structures. It also identifies the benefits, current status, and future directions for applying inelastic analysis in design. Use of the inelastic analysis/design method for a three‐dimensional multistory frame is presented in a companion paper.

A design study of a three‐dimensional 22‐story frame is presented to demonstrate the use of second‐order inelastic analysis in load and resistance factor design. This study is a follow‐up to a set of low‐rise planar frame studies presented in a companion paper. The limit state behavior of the inelastic design is evaluated with respect to strength and serviceability requirements. The strength requirements include investigating the inelastic rotation demands, effects of residual stresses, and conformance with a limit states design specification. The inelastic design is also compared to a design obtained using conventional elastic methods of analysis. The study indicates that with computer‐aided engineering, second‐order inelastic analysis provides a feasible alternative for designing steel structures of substantial size. It also concludes that existing limitations of current analytical techniques, e.g., the inability to model torsional‐flexural instabilities of beam‐columns, need to be overcome before inelastic analysis‐design approaches such as that presented can be generally applied.

The results of experimental and analytical investigation of the behavior of concrete members prestressed with unbonded tendons under static loading are described. In the experimental section, a total of 26 beam specimens are tested, and several parameters, including reinforcing index, partial prestressing ratio, member span‐to‐depth ratio, and type of load application, are investigated. In the following analysis a general method of section analysis of concrete members prestressed with unbonded tendons is developed and used to reproduce the experimentally observed service load stresses in the tensile reinforcement. Also, available methods proposed in the technical literature to predict the service load deflection of bonded prestressed and partially prestressed concrete members are generalized to account for the slip of prestressing steel in unbonded posttensioned members and then compared with the current experimental results.

A numerical analysis is presented for the determination of complete load‐moment‐curvature‐deflection relationships for both short and slender reinforced concrete columns under combined biaxial flexure and axial load. The computer method developed can be used for any end conditions and variable section geometries such as circular and rectangular (solid and hollow), cellular, oval, channel and T‐sections. Bending of the column is assumed to take place about principal axes of the cross section. The analysis takes into account an inelastic action and addresses all stages of behavior up to and beyond maximum load and moment. The method is also applicable to cases in which the cross section of the column is made up of different materials, where the cross section varies along the length of the column, and where prestressing and residual stresses are present. A comparison of the present analysis with experimental tests of biaxially loaded columns is examined. The computer analysis appears to show good correlation with experimental results obtained in this study, as well as those of others.

The prediction of the ultimate load capacity of composite bridges of slab‐on‐I‐steel girder construction is necessary. This is dictated by design requirements for the ultimate limit states of such bridges. In this paper, the prediction of the most probable yield‐line patterns of failure for relatively wide composite bridges is presented. The prediction is based on a parametric study as well as on laboratory test results on composite bridge models. The degree of fixity between the transverse steel diaphragms and the longitudinal steel girders is considered with respect to influence on the ultimate load capacity of the bridge. Good agreement is shown between the theoretical and experimental results. A method of relating AASHTO truck loading to the collapse load is presented. The derived equations can be used either to predict the ultimate load capacity or the required ultimate moments of resistance for design of simple‐span and of continuous‐span composite bridges. An illustrated design example is presented.