• Structural Engineering and Mechanics
• /
• v.82 no.1
• /
• pp.41-53
• /
• 2022

We developed an accurate and simple vibration model to calculate the natural frequencies and their corresponding vibration modes for multi-span beam bridges with non-uniform cross-sections. A closed set of characteristic functions of a single-span beam was used to construct the vibration modes of the multi-span bridges, which were considered single-span beams with multiple constraints. To simplify the boundary conditions, the restraints were converted into spring constraints. Then the functional of the total energy has the same form as the penalty method. Compared to the conventional penalty method, the penalty coefficients in the proposed approach can be calculated directly, which can avoid the iteration process and convergence problem. The natural frequencies and corresponding vibration modes were obtained via the minimum total potential energy principle. By using the symmetry of the eigenfunctions or structure, the matrix size can be further reduced, which increases the computational efficiency of the proposed model. The accuracy and efficiency of the proposed approach were validated by the finite element method.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.18 no.1
• /
• pp.138-149
• /
• 2014

This study proposes an estimation method of strain distribution for multi-span steel beam structure under unspecific loading conditions. The estimation method in this paper employs the curve fitting using the least square method from measured strain data, not analytical method. To verify the proposed estimation method, a static loading test for multi-span steel beam on which distributed and concentrated loads act was conducted. The strain data for verification was measured by FBG sensors that have multiplexing technology. The analysis of the accuracy of strain estimation for distributed and concentrated loads and the errors by considering the number of measured points used in the estimation were conducted. In the maximum strain points, the strains could be estimated with the errors of 5.89% (loading step 1) and 6.26% (loading step 2). In case of decreasing the number of sensors, it was also confirmed that the errors increased (0.26~0.37%). Through the curve fitting method, it is possible to estimate the strain distribution (maximum strains and their locations) of multi-span beam for unspecific loads and go over the limit of the analytical estimation method which is suitable for specific distributed loads.

• Earthquakes and Structures
• /
• v.16 no.6
• /
• pp.757-769
• /
• 2019

The seismic performance of a coupled shear wall system is governed by the shear resistances of its coupling beams. The plate-reinforced composite (PRC) coupling beam is a newly developed form of coupling beam that exhibits high deformation and energy dissipation capacities. In this study, the shear capacity of plate-reinforced composite coupling beams was investigated. The shear strengths of PRC coupling beams with low span-to-depth ratios were calculated using a softened strut-and-tie model. In addition, a shear mechanical model and calculating method were established in combination with a multi-strip model. Furthermore, a simplified formula was proposed to calculate the shear strengths of PRC coupling beams with low span-to-depth ratios. An analytical model was proposed based on the force mechanism of the composite coupling beam and was proven to exhibit adequate accuracy when compared with the available test results. The comparative results indicated that the new shear model exhibited more reasonable assessment accuracy and higher reliability. This method included a definite mechanical model and reasonably reflected the failure mechanisms of PRC coupling beams with low span-to-depth ratios not exceeding 2.5.

• Structural Engineering and Mechanics
• /
• v.90 no.2
• /
• pp.159-175
• /
• 2024

In order to solve the problem of calculating the reasonable completed bridge state of a self-anchored hybrid cable-stayed suspension bridge (SA-HCSB), this paper proposes an analytical method. This method simplifies the main beam into a continuous beam with multi-point rigid supports and solves the support reaction forces. According to the segmented catenary theory, it simultaneously solves the horizontal forces of the main span main cables and the stay cables and iteratively calculates the equilibrium force system on the main beam in the collaborative system bridge state while completing the shape finding of the main span main cable and stay cables. Then, the horizontal forces of the side span main cables and stay cables are obtained based on the balance of horizontal forces on the bridge towers, and the shape finding of the side spans are completed according to the segmented catenary theory. Next, the difference between the support reaction forces of the continuous beam with multiple rigid supports obtained from the initial and final iterations is used to calculate the load of ballast on the side span main beam. Finally, the axial forces and strains of each segment of the main beam and bridge tower are obtained based on the loads applied by the main cable and stay cables on the main beam and bridge tower, thereby obtaining analytical data for the bridge in the reasonable completed state. In this paper, the rationality and effectiveness of this analytical method are verified through a case study of a SA-HCSB with a main span of 720m in finite element analysis. At the same time, it is also verified that the equilibrium force of the main beam under the reasonably completed bridge state can be obtained through iterative calculation. The analytical algorithm in this paper has clear physical significance, strong applicability, and high accuracy of calculation results, enriching the shape-finding method of this bridge type.

• Steel and Composite Structures
• /
• v.50 no.1
• /
• pp.107-122
• /
• 2024

Following an internal column failure, adjacent double-span beams above the failed column will play a critical role in the load transfer and internal force redistribution within the remaining structure, and the span-to-depth ratios of double-span beams significantly influence the structural resistance capacity against progressive collapse. Most existing studies have focused on the collapse-resistant performances of single-story symmetric structures, whereas limited published works are available on the collapse resistances of multi-story steel frames with unequal spans. To this end, in this study, numerical models based on shell elements were employed to investigate the structural behavior of multi-story steel frames with unequal spans. The simulation models were validated using the previous experimental results obtained for single- and two-story steel frames, and the load-displacement responses and internal force development of unequal-span three-story steel frames under three cases were comprehensively analyzed. In addition, the specific contributions of the different mechanism resistances of unequal-span, double-span beams of each story were separated quantitatively using the energy equilibrium theory, with an aim to gain a deeper level of understanding of the load-resistance mechanisms in the unequal-span steel frames. The results showed that the axial and flexural mechanism resistances were determined by the span ratio and linear stiffness ratio of double-span beams, respectively.

• Journal of Korean Society of Steel Construction
• /
• v.19 no.5
• /
• pp.527-537
• /
• 2007

The main girders and cross-beams of an H-beam bridge consisted of factory-made H-beams, providing better conditions for quality control. Also, on-site fabrication works can be minimized and most of the stiffeners can be omitted, enabling simple and economic construction. In this study, the effect of the Multi-Stepwise TPSM (M-TPSM) on improving the maximum span length and section efficiency is analyzed. Compared to a 30-m-long, five-girder conventional plate girder bridge, structural analysis results showed that 50.7~55.1% of the girder height and 24.1~26.2% of the self-weight may be reduced by the application of M-TPSM to a five-girder H-beam bridge constructed with H-$900{\times}300$beams. In case of conventional H-beam bridges without M-TPSM, it was found that seven girders are required for a similar level of load-carrying capacity. Therefore, it is concluded that by the application of the M-TPSM, the H-beam bridge would become one of most cost-competitive options for short- and medium-span bridges.

• Structural Engineering and Mechanics
• /
• v.52 no.5
• /
• pp.997-1017
• /
• 2014

According to the structure characteristics of the non-uniform beam bridge, a practical model for calculating the vibration equation of the non-uniform beam bridge is given and the application scope of the model includes not only the beam bridge structure but also the non-uniform beam with added masses and elastic supports. Based on the Bernoulli-Euler beam theory, extending the application of the modal perturbation method and establishment of a semi-analytical method for solving the vibration equation of the non-uniform beam with added masses and elastic supports based is able to be made. In the modal subspace of the uniform beam with the elastic supports, the variable coefficient differential equation that describes the dynamic behavior of the non-uniform beam is converted to nonlinear algebraic equations. Extending the application of the modal perturbation method is suitable for solving the vibration equation of the simply supported and continuous non-uniform beam with its arbitrary added masses and elastic supports. The examples, that are analyzed, demonstrate the high precision and fast convergence speed of the method. Further study of the timesaving method for the dynamic characteristics of symmetrical beam and the symmetry of mode shape should be developed. Eventually, the effects of elastic supports and added masses on dynamic characteristics of the three-span non-uniform beam bridge are reported.

• Structural Engineering and Mechanics
• /
• v.7 no.4
• /
• pp.361-375
• /
• 1999

This paper presents an analytic method of examining the out-of-plane vibration of continuous curved beam on periodical supports. The orthogonality of two distinct sets of mode shape functions is derived. The forced vibration of beam due to moving loads is examined. Two types of moving loads, which are concentrated load and uniformly distributed load, are considered. The response characteristics of beam induced by these loads are investigated as well.

• Structural Engineering and Mechanics
• /
• v.66 no.6
• /
• pp.737-748
• /
• 2018

The current study presents a new technique in the framework of the nonlocal elasticity theory for a comprehensive buckling analysis of Euler-Bernoulli nano-beams made up of bidirectional functionally graded material (BDFGM). The mechanical properties are considered by exponential and arbitrary variations for axial and transverse directions, respectively. The various circumstances including tapering, resting on two-parameter elastic foundation, step-wise or continuous variations of axial loading, various shapes of sections with various distribution laws of mechanical properties and various boundary conditions like the multi-span beams are taken into account. As far as we know, for the first time in the current work, the buckling analyses of BDFGM nano-beams are carried out under mentioned circumstances. The critical buckling loads and mode shapes are calculated by using energy method and a new technique based on calculus of variations and collocation method. Fast convergence and excellent agreement with the known data in literature, wherever possible, presents the efficiency of proposed technique. The effects of boundary conditions, material and taper constants, foundation moduli, variable axial compression and small-scale of nano-beam on the buckling loads and mode shapes are investigated. Moreover the analytical solutions, for the simpler cases are provided in appendices.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2006.04a
• /
• pp.159-166
• /
• 2006

Although the strain distribution along the length of a beam in buildings or infrastructures is non-uniform, most fiber optic sensors are point sensors that can measure the strain only at a local point of a beam. Long gage fiber optic sensors that measure integrated strain over a relatively long length can consider strain variation. This type of sensor was found to be efficient and useful for monitoring large-scale structures. On the other hand, the maximum strain or stress in a beam can not be measured with long gage optic sensors. However, for the assessment of the safety of multi-span steel beams subjected to various vertical loads, the maximum strain or stress measured during monitoring is required for comparison with the allowable stress of the beam calculated by a design code. Therefore, in this paper, mathematical models are presented for determination of the maximum values of strains in more three-span steel beams based on the average strains measured by long gage optic sensors.