Journal of Structural Engineering

A full-scale two-story unreinforced masonry (URM) building was tested in a quasistatic fashion to investigate the nonlinear properties of existing URM structures and to assess the efficiency of several common retrofit techniques. This paper presents the main experimental findings associated with the nonlinear properties of the original URM structure. The test structure exhibited large initial stiffness and its damage was characterized by large, discrete cracks that developed in masonry walls. Significant global behavior such as global rocking of an entire wall, and local responses such as rocking and sliding of each individual pier were observed in the masonry walls with different configurations. In addition, formation of flanges in perpendicular walls and overturning moments had significant effects on the behavior of the test structure. A comparison between the experimental observations and the predictions of FEMA 356 provisions shows that major improvements are needed for this latter methodology.

A variety of elastic and inelastic analytical approaches were used to investigate the response of a full-scale unreinforced masonry (URM) structure tested in the laboratory. Elastic analyses, employing a three-dimensional finite element model, revealed little coupling between parallel walls, and pointed to the appropriateness of two-dimensional analytical tools for further simulation of the test structure. The nonlinear analytical methods employed included, in order of increasing complexity, a rigid body analysis, a two-dimensional nonlinear pushover analysis, and a three-dimensional nonlinear finite element analysis. All methods considered important structural characteristics such as failure modes of perforated walls, flange effects, and global overturning moment effect. All methods predicted the experimental behavior fairly well. Strengths and weaknesses of these analytical approaches are discussed, and recommendations for analyzing old URM buildings are presented.

Based on the results of a full-scale lateral load test of a two-story unreinforced masonry (URM) structure, modifications are suggested for the model implied by FEMA 356 for the in-plane analysis of perforated URM walls. These modifications allow the model to address global issues such as flange participation, overturning effects, and global rocking. In addition, changes are proposed to the pier model as well as to the definition of effective pier height. Following a description of each modification, the analysis results obtained using the proposed model and FEMA 356 are compared with experimental results. In terms of base shear resistance, the proposed model displayed an average error (absolute value) of 13% compared with an average error of 21% from FEMA 356. In addition, the proposed model also provided more accurate representation of failure modes. The improved accuracy of the proposed model is primarily attributed to the consideration of global issues. The results of a parametric analysis are also presented to provide insight into the relative influence of each modification proposed.

Since a diagonally cracked deep beam behaves as a tied arch, the conventional plane section remaining plane approach is not applicable to analyses of deep beams. Besides, for beams without web reinforcement, it has been shown that shear strength decreases as member size increases. This is associated with a phenomenon called size effect. In this study, the causes of size effect on shear strength of deep beams are investigated using both the strut-and-tie model (STM) and finite element model. The study shows that size effect in concrete beam arises primarily from an inappropriate adoption of the shear transfer concept for steel beams. In addition, size effect also depends on secondary factors such as the geometry of strut, and the spacing and diameter of web reinforcement. The modified STM is verified with three published case studies comprising a total of 36 beams. Generally, the predictions are accurate and consistent, with a uniform safety margin for different member sizes considered.

In design for shear forces with stress fields, three failure criteria are usually considered: failure of the chords, of the compression struts, and of the stirrups. Bond failure along the chords is usually not explicitly checked. The effective concrete strength in the struts and the bond strength along the chord are combined with the stresses in the stirrups to determine critical inclinations of the compression struts. An expression for the effective concrete strength is proposed considering compression softening, while the proposed expression for bond strength considers concrete strength, bar roughness, and the beneficial effect of lateral pressure exerted by the stirrup forces. Parametric studies are discussed and conclusions are drawn on the governing failure criteria and the critical inclination of the compression struts in the ultimate limit state. An Appendix summarizes the calibration of the proposal for the effective concrete compressive strength and compares it to other proposals from the literature.

A numerical study of interior flat plate–column connections subjected to unbalanced moments was performed by using nonlinear finite element analysis. The distribution and strength of the eccentric shear and flexural moment that develop at the connections were studied. The results showed that the distribution of the eccentric shear stress was different from those specified in current design codes, and the eccentric shear strength was significantly affected by the flexural moment acting at the same critical section. Based on the findings, an improved design method for the interior flat plate–column connections was developed and was verified by the comparisons with existing test results. These comparisons showed that the proposed design method predicted the punching shear strength of the connections subject to unbalanced moments better than the current design methods.

A cast modular connector (MC) has been developed for use as an energy dissipating detail in seismic-resistant bolted steel moment frames. The MC relies on a series of variable section elements (arms) to minimize plastic strain demand and a stiff end region joined by a base to virtually eliminate bolt prying forces and provide a hysteresis characteristic absent of degradation. The MC was developed through a comprehensive program that included heavy industry partner involvement, analytical research, and experimental verification. This paper describes the portion of the analytical research focused on establishing the optimum geometry for the energy-dissipating arm elements. Key parameters were evaluated through parametric studies using nonlinear (material and geometry) finite element analysis and supported by basic theoretical models. The outcome was a set of optimum geometric ratios covering width reduction, length to thickness, aspect ratio, and fillet radius. A MC prototype was cast on the basis of these recommendations. These prototypes were tested under monotonic and cyclic loading and exhibited remarkable ductility, far exceeding qualifying rotational capacities.

The structural behavior of welded hollow structural sections (HSS) connections in which one member is laterally offset from the plane of a connection is investigated experimentally and compared with corresponding planar connections. Sixteen full-scale test connections, consisting of either T or N configurations fabricated from class C HSS, were tested at load levels comparable with those expected to occur in actual trusses. In all cases the mode of failure was by localized large deflections of the flange face and sidewalls of the compression chord. It was found that in the case of T connections, the reduction in capacity due to offsetting a member by as much as 17% of the width of the chord member from the central plane of the truss was marginal. N configurations, whose diagonal members were offset by 8% of the width of the chord member, showed a slight increase in ultimate strength. The design values obtained using both AISC LRFD and CIDECT specifications are compared with the test results where appropriate.

In structural design of steel structures in fire, the failure criterion needs to be checked for all members under individual design actions or a combination of them. For space frames, combined design actions usually include forces due to bending, axial, shear, and torsion. An increase in temperature will result in changes to these forces as well as the diminution of the failure criterion due to reduced member capacities as a result of these combined design actions. This paper presents an elastic method for the prediction of limiting temperature of members in space steel frames. Since the critical temperature of the structure corresponds to the ultimate failure of the member with the lowest limiting temperature, this elastic method is equivalent to finding the location of the first plastic hinge in a general plastic analysis. By considering the degradation of the mechanical properties of steel in fire, a formulation based on the failure criterion of combined design actions including torsion is presented for limiting temperature calculation. The fundamentals of the solution strategy are also explained.

Seismic responses and reliability of a one-story L-shaped woodframe building tested at the CSIRO Structures Laboratory and a hypothetical two-story L-shaped building based on the test house were investigated using a three-dimensional hysteretic frame model under bidirectional ground motions. Parameters of the degrading and pinching hysteresis used for the shear walls were identified from whole house testing. The SAC ground motions for the Los Angeles area were used and the effects of torsion, bidirectional excitations, the variability in ground motion, structural modeling, collapse capacity, and vibration period were investigated. It was found that uncertainties due to ground motion and structural modeling are the major sources for increase in estimated structural demand. Coupling of torsion and bidirectional excitation also causes significant response magnification. Overall, the adverse effects considered could cause more than 150% increase in demand or, in probabilistic terms, a 1 order of magnitude increase in exceedance probability for a given demand. These findings could be helpful in putting into context the findings and conclusions of analytical studies of woodframe building performance under earthquakes that ignore these uncertainties and effects. Torsion should be minimized in design to alleviate coupling magnification with bidirectional excitations.

Sheathing materials such as plywood, oriented strand board (OSB), drywall, and fiberboard are commonly attached to one or both sides of load-bearing stud walls in residential and commercial construction. There is no consensus among structural engineering professionals as to which of these sheathing materials provide protection against weak-axis buckling of the load-bearing wood studs. Plywood is generally accepted as providing the necessary bracing, but building codes do not specifically state which of the other sheathing materials are acceptable for bracing studs against compression buckling. This study involves testing of $2.44\mathrm{m}$ $\left(8\mathrm{ft}\right)$ tall by $1.22\mathrm{m}$ $\left(4\mathrm{ft}\right)$ wide stud wall specimens sheathed with OSB both sides, OSB one side, drywall one side, drywall both sides, Thermo-Ply one side, fiberboard one side, and no sheathing. The allowable axial load according to the wood specification for a $1.22\mathrm{m}$ $\left(4\mathrm{ft}\right)$ long wall specimen with studs braced in the weak direction is $42.5\mathrm{kN}$ $\left(\mathrm{9,546}\mathrm{lb}\right)$ . Each of the sheathed specimens failed at more than 2.9 times the allowable load; i.e., each sheathing material provided a factor of safety of at least 2.9 against strong-axis buckling under compression load. Therefore, each of the materials, when properly attached, was capable of resisting weak-axis stud buckling. Specimens with drywall fastened to one or both sides had a higher ultimate load than specimens with oriented strand board fastened to one side.

A total Lagrangian finite element (FE) model has been formulated for the nonlinear inelastic analysis of both composite beams and columns. An accurate rotation matrix is used in the position vector analysis and nonlinear strain derivations. The slip between the steel and concrete components due to the flexible shear connection at their interface is considered as an independent displacement in the formulation which makes it easier to assign the corresponding proper slip conditions at the connections between composite beams and columns. The effects of nonlinearities and slip on the deformations and strains in the steel and concrete components, and so on the stress resultants (i.e., internal forces), stiffness, and strength of the composite member are thus combined together in the formulation. The constitutive models for steel and concrete in this investigation are based on the longitudinal normal stress and the shear stress induced by the slip between the steel and concrete components. Hence, these models include the effects of the slip at the interface on the von Moses yield surface, associated flow rule and isotropic hardening rule. These constitutive models can be used in association with any type of uniaxial stress–strain curves for steel and concrete, including hot-rolled or cold-formed steel, and confined or unconfined concrete. The constitutive models are expressed in terms of engineering stresses and strains. The total Lagrangian formulation is applicable for these constitutive models directly, and most convenient for the slips at the interface between the steel and concrete components.

In the companion paper, a total Lagrangian finite element (FE) model was formulated for the second order nonlinear inelastic analysis of steel–concrete composite members. This paper describes the implementation of the incremental–iterative procedure for the FE model. It has been found that using the standard tangent modulus matrix in an incremental–iterative solution procedure may cause error accumulations. These errors in turn lead to an unsafe drift from the yield surfaces, and the yield criteria may be violated. Consequently, the quadratic asymptotic rate of convergence of the Newton–Raphson method is lost. To solve this problem, a consistent tangent modulus matrix is needed in the incremental–iteration solution process, and this is described. This paper presents the implementation of the FE model and shows how to use the constitutive models in the companion paper in association with the uniaxial stress–strain relations including that for confined concrete. Some of the applications of the FE model to various problems are also shown in this paper. The comparisons between numerical and experimental results demonstrate that the FE model provides excellent numerical performance for the nonlinear inelastic analysis of steel–concrete composite members.

Vibrations of horizontal, variable-arc-length beams considering the effects of large initial static sag deflections due to self weight are investigated. The variability in beam arc length arises from one end being pinned, and the other end being supported by a frictionless roller at a fixed distance from the pinned end. Using Lagrange’s equation, the large amplitude, free-vibration, equation of motion can be derived and simplified for small amplitude motion. These formulations represent small amplitude vibration about the large deformed static sag configurations. A solution is obtained by using the nonlinear finite element method. The vibration eigenvalue problem is solved using inverse iteration techniques to obtain the natural frequencies and corresponding mode shapes. Free and forced vibration experimental studies were conducted. Frequencies and mode shapes are shown for a range of beam specimens to complement the analytical results.

Application of structural optimization to transmission tower design is facilitated since major costs such as material, transportation, erection, and maintenance are directly proportional to structural mass. In this paper, structural topology and shape annealing (STSA), a structural topology optimization method that combines structural grammars with simulated annealing, is applied to reduce the structural mass of an existing tower. STSA has previously been validated only on smaller-scale benchmark tasks. The challenges of extending STSA for application to full-scale design tasks are presented. Key results include a 16.7% mass reduction of the existing primary members through combined optimization of the tower envelope, joint locations, and discrete section sizes. Also, the tower configuration was optimized to have 16 fewer joints and 80 fewer primary members. Promising results for a practical, full-scale application serve to validate the STSA method for combined structural optimization of topology, shape and discrete section size.

A methodology for semiactive control of building frames using multiple semiactive hydraulic dampers (SHDs) driven by fuzzy controllers is presented. The SHDs are installed in combination with steel bracings and are placed at different floor levels. The fuzzy controller is designed for the bottom-most SHD. Other controllers are assumed to provide control command for the variable damping coefficient of an SHD in certain proportion to that obtained for the bottom-most controller. Different proportions giving different distributions of the semiactive control force along the height of the frame are tried in order to arrive at the best distribution for obtaining the maximum control of a response quantity of interest. The methodology is developed in the MATLAB environment using the SIMULINK and FUZZY tool boxes. As an illustrative example, a five-storied steel frame is selected from the literature. The control of the responses of the frame under the El Centro earthquake record is obtained for a specified set of the frame, steel bracings, and SHD properties. An extensive parametric study is conducted to investigate the effectiveness of the control scheme under variation of the important parameters. The control strategy with the optimum values of parameters designed for the El Centro earthquake is tested for three synthetically generated earthquakes. The results of the study show that an efficient semiactive control strategy can be developed using a fuzzy rule base. Further, optimum combinations of parameters for maximum control are different for different response quantities of interest.

The results of numerical simulations to test a method to locate and estimate the severity of damage in a structure in the blind mode, by using the simulated data from a four-story steel frame structure analyzed at the Univ. of British Columbia, are reported here. The blind simulated data include the response in the time domain of the undamaged structure and the responses of the structure with two sets of simulated damage conditions. Elements of the theory utilized here for damage detection and localization (the so-called damage index method) are first summarized. Modal analyses are performed to extract the modal characteristics (i.e., resonant frequencies and mode shapes) for the undamaged structure (designated, Case 1) and the damaged structures (here designated, Damage Cases 2 and 3). The results of the modal analyses are reported in detail. Using the proposed nondestructive damage evaluation technique, the predicted damage locations, and estimation of the damage severity are provided for the two damage cases. The actual locations of damage in the test structure for each of the damage cases were revealed subsequent to the damage predictions proposed by the writers during the 16th International Modal Analysis Conference. The predicted damage locations and severity estimates are compared with the damage inflicted in the original test cases. The current method correctly predicts the inflicted damage locations and provides realistic estimates of the associated damage severities.

This paper presents a general approach to the probabilistic prediction of the structural service life and to the maintenance planning of deteriorating concrete structures. The proposed formulation is based on a novel methodology for the assessment of the time-variant structural performance under the diffusive attack of external aggressive agents. Based on this methodology, Monte Carlo simulation is used to account for the randomness of the main structural parameters, including material properties, geometrical parameters, area and location of the reinforcement, material diffusivity and damage rates. The time-variant reliability is then computed with respect to proper measures of structural performance. The results of the lifetime durability analysis are finally used to select, among different maintenance scenarios, the most economical rehabilitation strategy leading to a prescribed target value of the structural service life. Two numerical applications, a box-girder bridge deck and a pier of an existing bridge, show the effectiveness of the proposed methodology.