Journal of Structural Engineering

Accurate and efficient response gradient computations for nonlinear geometry are required in structural reliability, optimization, system identification, and response sensitivity analysis of frame structures that undergo large displacements. In this paper, the exact response gradient of beam-column finite elements under large displacements is derived considering uncertain material and geometric parameters. The element response formulation takes place in a corotational reference frame that displaces and rotates with the element, thus permitting the separation of nonlinear material from nonlinear geometric effects in the computation of the response, as well as of the gradient of the response. Relative to the corotational reference frame, small deformation theory suffices for all structural engineering applications. Thus, the proposed response gradient computations are applicable to most beam-column element formulations available in the literature, including force-based and mixed formulations.

A hybrid analytical-numerical procedure has been presented to take into account the effect of concrete cracking and time-dependent effects of creep and shrinkage in composite beams of the composite frames subjected to service load. The procedure is analytical at the element level and numerical at the structural level. The cracked span length beam element consisting of an uncracked zone in middle and cracked zones at the ends has been proposed for the composite beams to reduce the computational effort. The progressive nature of cracking of concrete of composite beams has been taken into account by division of the time into a number of time intervals. Closed form expressions for flexibility coefficients, end displacements, crack lengths, and midspan deflection of the cracked span length beam element have been presented in order to reduce the computational effort. The procedure has been validated in a limiting case by comparison with the experimental and analytical results reported elsewhere and also by comparison with FEM. The proposed procedure would lead to a considerable saving in computational time in case of large composite structures, e.g., tall composite building frames.

This paper presents the development of a nonprismatic beam element for modeling the elastic behavior of steel beams with reduced beam section (RBS) connections. The accuracy of this element is evaluated by comparisons with finite element solutions. A simplified approach is also suggested, which uses a prismatic beam element to model beams with RBS connections. The effect of the RBS on the elastic stiffness of beams and frames is then investigated through a series of parametric studies, and by analysis of 3-, 9-, and 20-story moment frames. With a 50% flange reduction, the increase in maximum story drift ranges from 6 to 8% for typical moment frame buildings. With a 40% reduction, the increase in maximum story drift is 4.5–6%.

In this paper an attempt is made to automatically calculate the bifurcation of the buckling path of shallow lattice domes. This calculation is performed in a two-stage analysis of the space structure without introducing any geometrical imperfections. The method is implemented in a combined materially and geometrically nonlinear finite element analysis computer program based on an incremental/iterative Newton-Raphson solution procedure. In the first stage analysis, the load factors at which critical points occur are determined and the primary path is obtained. In the second stage analysis the perfect structure is lead toward the lowest bifurcation path using the technique described in this paper. The resulting theoretical predictions are verified by existing experimental observations on two model domes.

This paper presents the test results on 12 two-span continuous T-beams strengthened using different external tendon types and profiles and subjected to third-point loadings. Test results indicated that an increase in ultimate strength with sufficient ductility could be achieved using short tendons located over the critical sections. Such a strengthening scheme led to a more ductile beam behavior compared to those with continuous tendons over both spans or with draped tendons within each span. Parabolic tendons anchored beyond the interior support however effectively strengthened the negative moment region with improved ductility at ultimate limit state. Furthermore, beams strengthened with carbon fiber-reinforced polymers tendons showed similar response to those with steel tendons, while beams subjected to unsymmetrical loading suffered from larger deflections and lower ultimate load compared to those subjected to symmetrical loading. Theoretical predictions based on the concept of bond reduction coefficients were found to agree with the test results. Finally, a parametric study was carried out to establish design charts that can be used for the strengthening of continuous beams. A design example is presented to illustrate the use of the charts.

The basic methods of structural concrete design that have been developed so far cannot directly control damage, either at the local or the global level. In order to develop an integrated scheme for direct damage control during design and study its application in practice, a new design philosophy, named direct damage controlled design, is proposed. In spite of the generality of the presented design philosophy, this paper focuses on the beam type of structures composed of plain concrete or other quasi-brittle materials, such as masonry or ceramics, and subjected to statically applied loading. The proposed methodology appropriately combines code-based stress-strain relations with a simple expression for damage to determine with the aid of the fiber model and the finite-element method axial force and bending moments of a beam-column element as functions of deformation and/or damage. Five characteristic numerical examples are presented to illustrate the proposed methodology and demonstrate its direct applicability to structural design.

The crack widths of reinforced concrete flexural members are influenced by repetitive fatigue loadings. The bond stress-slip relation is necessary to estimate these crack widths realistically. The purpose of the present study is, therefore, to propose a realistic model for bond stress-slip relation under repeated loading. To this end, several series of tests were conducted to explore the bond-slip behavior under repeated loadings. Three different bond stress levels with various number of load cycles were considered in the tests. The present tests indicate that the bond strength and the slip at peak bond stress are not influenced much by repeated loading if bond failure does not occur. However, the values of loaded slip and residual slip increase with the increase of load cycles. The bond stress after repeated loading approaches the ultimate bond stress under monotonic loading and the increase of bond stress after repeated loading becomes sharper as the number of repeated loads increases. The bond stress-slip relation after repeated loading was derived as a function of residual slip, bond stress level, and the number of load cycles. The models for slip and residual slip were also derived from the present test data. The number of cycles to bond slip failure was derived on the basis of safe fatigue criterion, i.e., maximum slip criterion at ultimate bond stress.

Size effect is studied here with reference to the bonding of short, deformed bars, embedded in normal-strength concrete (NSC) and high-performance concrete (HPC). Tests on 48 cylindrical specimens reinforced with a single bar and subjected to a pull-out or push-in force show that bond exhibits a strong size effect, which is well described by Bazant’s general-type size-effect law. Four diameters are considered ( $d_b=5$ , 12, 18, and $26\mathrm{mm}$ ), with bonded length-to-bar diameter ratios equal to 3.5 (HPC) and 5 (NSC). All specimens are highly confined by means of a steel jacket to prevent or control cover splitting and to investigate bond behavior in highly confined conditions. Test results on short, anchored bars were instrumental in working out the local bond stress-slip law, taking into account size effect, which appears in the formulation of the maximum bond stress through the bar diameter. Short embedments also prevented bar yielding. The proposed local bond stress-slip law (1) is formulated as an extension of the law suggested in European Model Code MC90, also including some later proposals; (2) fits quite well with the available test data on short, well-confined anchored bars; (3) introduces the favorable effects that the confining reinforcement (generally consisting of stirrups and longitudinal bars) has on bond strength; and (4) may be easily introduced into a design code.

The effectiveness of semiactive control using variable dampers is studied for nonlinear isolated bridges, which exhibit inelastic response at both the columns and the isolators, under near-field ground motions. The linear quadratic regulator optimal control algorithm is used to command variable dampers. Time delay is inevitable in the operation of control systems and may deteriorate the control performance. A time-delay compensation method based on the Newmark’s method is proposed to mitigate the degradation of control performance due to time delay. A five-span viaduct with high-damping-rubber isolators is utilized for analysis. The results show that semiactive control with variable dampers is effective in reducing the seismic response and provides the similar performance by linear quadratic regulator active control. The semiactive control also shows similar or better performance than the passive control with the maximum damping coefficient of the variable damper. The proposed Newmark compensation method shows superior compensation performance on the time-delayed nonlinear system under semiactive control.

A semiactive magnetorheological device is used in a pendulum tuned mass damper (PTMD) system to control the excessive vibrations of building floors. This device is called semiactive pendulum tuned mass damper (SAPTMD). Analytical and experimental studies are conducted to compare the performance of the SAPTMD with its equivalent passive counterpart. An equivalent single degree of freedom model for the SAPTMD is developed to derive the equations of motion of the coupled SAPTMD-floor system. A numerical integration technique is used to compute the floor dynamic response, and the optimal design parameters of the SAPTMD are found using an optimization algorithm. Effects of off-tuning due to the variations of the floor mass on the performance of the PTMD and SAPTMD are studied both analytically and experimentally. From this study it can be concluded that for the control laws considered here an optimum SAPTMD performs similarly to its equivalent PTMD, however, it is superior to the PTMD when the floor is subjected to off-tuning due to floor mass variations from sources other than human presence. It is also found that for the case of off-tuning due to floor mass variations from the human occupants when the human-structure dynamic interactions are not considered in the analytical modeling, large inconsistencies between the analytical and experimental results can be expected.

The tuned liquid damper (TLD) is increasingly being used as an economical and effective dynamic vibration absorber to mitigate the dynamic response of structures. The ability to design a TLD to operate in two directions simultaneously is particularly attractive. In this paper the results of bidirectional (2D) structure-TLD tests are reported on. These include the free-surface motion, the resulting base shear forces, and the work done by bidirectional tuned liquid dampers (2D TLD) attached to simple structures and response displacements and accelerations of 2D structure-TLD systems. The importance of this experimental study is that it examines 2D structure-TLD behavior over a range of excitation amplitude values covering the practical range of serviceability accelerations for buildings subjected to wind loads. Experimental results are subsequently used to verify the applicability of a unidirectional structure-TLD numerical model to 2D structure-TLD analysis. Findings indicate that the structure-TLD model is capable of describing the structure-TLD response within the range of system response amplitudes experimentally tested.

This study examined the effect of the width–thickness ratio ( $w∕t$ ratio) on the seismic behavior of cold-formed hollow structural section (HSS) bracing members. For this purpose, an experimental study was carried out. Quasi-static reversed cyclic loading was applied to the specimens. The loading pattern for the tests was determined based on a nonlinear dynamic time history analysis of a frame under earthquake ground motions (EQGM). For this purpose, a three-story specially concentric braced frame (SCBF) was designed according to the AISC LRFD manual. The analysis results showed that a displacement history during the EQGM experienced by bracing members is symmetric in compression and tension. This symmetry may be due to the strong beams in the SCBF connecting bracing members. According to the AISC LRFD manual these beams should resist the unbalanced force associated with compression and tension forces from the connected bracing members. This study adopted a symmetric loading history in compression and tension. Eleven specimens were made to satisfy the detail requirements specified in the AISC LRFD manual and the AISC HSS connection manual. This study showed that HSS bracing members with a small $w∕t$ ratio could not always guarantee larger energy dissipation capacity than those with a larger $w∕t$ ratio. This was due to early fracture at the slotted end of the bracing members with small $w∕t$ ratios.

This paper considers the trajectories of compact and rod-type wind-borne debris in horizontal winds, using a combination of experimental and numerical studies. These types are representative of the roof gravel and timber members currently used for testing building facades and storm shutters. These studies indicate that the ratio of horizontal debris speed to wind gust speed is primarily a function of the horizontal distance traveled by the debris as it accelerates toward the wind speed. Empirical expressions to approximate the horizontal speed of these debris as a function of travel distance and time are developed, and may be used to establish rational debris impact criteria.

Experimental investigations were conducted to evaluate the effects of multiple cycles of damage followed by heating repair on the structural properties and fracture toughness of A36, A588, and A7 bridge steels. The test specimens were subjected to multiple cycles of tensile damage followed by compressive restraining stress and heat shortening repair. The damage and repair parameters considered were the damage strain $\left({\epsilon }_d\right)$ , the restraining stress $\left({\sigma }_r\right)$ , the number of damage-repair cycles $\left(N_r\right)$ , and the maximum heating temperature $\left(T_{\max }\right)$ . Seventy-five A36, A588, and A7 steel specimens were subjected to multiple damage-repair cycles with $T_{\max }$ limited to the recommended limit of $650°\mathrm{C}$ . Sixteen additional A36 steel specimens were subjected to multiple damage-repair cycles with $T_{\max }$ greater than the recommended limit ( $T_{\max }$ =760 or $840°\mathrm{C}$ ). Standard material specimens were fabricated from the damaged-repaired steel specimens and tested according to the applicable ASTM standards. The results from the standard material tests indicate that multiple damage-repair cycles have a relatively small influence $(\pm 15\%)$ on the elastic modulus, yield stress, and ultimate stress, and a significant influence on the ductility (percent elongation) and fracture toughness of damaged-repaired bridge steels. These effects of the multiple damage-repair cycles on the fundamental structural properties and fracture toughness of various bridge steels are summarized in the paper.

This paper presents an experimental study on a steel moment frame with reinforced concrete (RC) floor slab that was subjected to horizontal cyclic loading leading to very large deformations. The primary objective of this test was to examine the interaction (composite action) between the steel beam and the RC floor slab. The steel beam moment capacity increased about 1.5 times in positive bending with the presence of the RC floor slab. During small beam rotations of $0.002–0.003\mathrm{rad}$ , the beam strength increased 1.2–1.4 times in negative loading, but composite action did not affect the negative beam moment capacity for larger rotations. The effective width estimated from the slab compressive force approximately equals the column width. Fracture at the bottom flange was notable due to the presence of the slab in the composite beam. Complete separation of the beam-to-column connections was not achieved even at a beam rotation of $0.13\mathrm{rad}$ , under which the composite connections still possessed bending resistance equal to about 10% of the maximum bending capacity when sustaining positive bending.

This note discusses applications of the well-known principle of stationary total energy as an effective approach for upper-bound solutions of bending problems for plate and slabs on elastic foundation. Material is assumed to be perfectly rigid plastic. The presented solutions demonstrate that this approach is similar to that in upper-bound solutions of limit analysis. For this purpose several simple problems are considered for plates of different forms with different support conditions. The obtained solutions show transformations of the form of deflections when the external load increases.