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CONTENTS
Volume 42, Number 6, June25 2012
 

Abstract
The collapse of structures due to snow loads on roofs occurs frequently for steel structures and rarely for reinforced concrete structures. Since the most significant difference between these structures is related to their ability to handle dead loads, dead loads are believed to play an important part in the collapse of structures by snow loads. As such, the effect of dead loads on displacements and stress couples produced by live loads is presented for plates with different edge conditions. The governing equation of plates that takes into account the effect of dead loads is formulated by means of Hamilton\'s principle. The existence and effect of dead loads are proven by numerical calculations based on the Galerkin method. In addition, a closed-form solution for simply supported plates is proposed by solving, in approximate terms, the governing equation that includes the effect of dead loads, and this solution is then examined. The effect of dead loads on static live loads can be explained explicitly by means of this closed-form solution. A method that reflects the effects of dead loads on live loads is presented as an example. The present study investigates an additional factor in lightweight roof structural elements, which should be considered due to their recent development.

Key Words
plates; dead load; initial stress; live load; snow load; Galerkin equation; linear and non linear; safety; static; roof

Address
Hideo Takabatake: Department of Architecture, Kanazawa Institute of Technology, Institute of Disaster and Environmental Science, 3-1, Yatsukaho, Hakusan City, Ishikawa Prefecture, 924-0838, Japan

Abstract
A new hybrid meta-heuristic optimization algorithm is presented for design of structures. The algorithm is based on the concepts of the charged system search (CSS) and the particle swarm optimization (PSO) algorithms. The CSS is inspired by the Coulomb and Gauss\'s laws of electrostatics in physics, the governing laws of motion from the Newtonian mechanics, and the PSO is based on the swarm intelligence and utilizes the information of the best fitness historically achieved by the particles (local best) and by the best among all the particles (global best). In the new hybrid algorithm, each agent is affected by local and global best positions stored in the charged memory considering the governing laws of electrical physics. Three different types of structures are optimized as the numerical examples with the new algorithm. Comparison of the results of the hybrid algorithm with those of other metaheuristic algorithms proves the robustness of the new algorithm.

Key Words
charged system search; particle swarm optimization; structural optimum design; hybrid methods; truss structures; frames; grillage systems

Address
A. Kaveh: Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran
S. Talatahari: Marand Faculty of Engineering, Tabriz University, Tabriz, Iran

Abstract
Five two-span reinforced concrete (RC) slabs and seven two-span RC beams were tested under the ISO 834 standard fire with different durations. CFRP strengthening was then applied to some of the specimens after the damaged concrete was removed from the specimens and replaced with polymer mortar. All the specimens were loaded to failure to investigate the influence of fire-damage and the effectiveness of strengthening methods. Test results indicated that the flexural capacities of specimens decrease with the fire duration increases. Moreover, fire exposure had more significant effect on the flexural rigidity than on the bearing capacity of the specimens. After rehabilitation, the bearing capacities of specimens reached or even exceeded that of the reference RC specimen, and the strengthening methods seemed to have limited effect on flexural rigidity recovery. From the analysis of moment redistribution of tested beams, elevated temperature is found having different impacts on sagging moment region and hogging moment region. The damage of RC continuous member is definitely a comprehensive response of different regions.

Key Words
fire damage; concrete; continuous members; rehabilitation; flexural rigidity; bearing capacity

Address
Jiang-Tao Yu, Yuan Liu, Zhou-Dao Lu: Research Institute of Engineering & Disaster Reduction, Tongji University, Siping Rd, Shanghai, 200092, China
Kai Xiang: Tianjin Fire Research Institution of the Ministry of Public Security, Weijin Rd, Tianjin, 300000, China

Abstract
This paper proposes a nonlinear computational modeling approach for the behaviors of structural systems subjected to fire. The proposed modeling approach consists of fire dynamics analysis, nonlinear transient-heat transfer analysis for predicting thermal distributions, and thermomechanical analysis for structural behaviors. For concretes, transient heat formulations are written considering temperature dependent heat conduction and specific heat capacity and included within the thermomechanical analyses. Also, temperature dependent stress-strain behaviors including compression hardening and tension softening effects are implemented within the analyses. The proposed modeling technique for transient heat and thermomechanical analyses is first validated with experimental data of reinforced concrete (RC) beams subjected to high temperatures, and then applied to a bridge model. The bridge model is generated to simulate the fire incident occurred by a gas truck on April 29, 2007 in Oakland California, USA. From the simulation, not only temperature distributions and deformations of the bridge can be found, but critical locations and time frame where collapse occurs can be predicted. The analytical results from the simulation are qualitatively compared with the real incident and show good agreements.

Key Words
fire; thermomechanical behavior; transient-heat analysis; bridge; fire dynamics simulator; finite element analysis

Address
Joonho Choi: School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0355, USA; Engineering Department, O-Won General Construction & Develop Cooperation, Seoul, South Korea
Rami Haj-Ali: School of Civil and Environmental ngineering, Georgia Institute of Technology, Atlanta, GA 30332-0355, USA; School of Mechanical Engineering, Tel-Aviv University, Ramat Aviv, Israel
Hee Sun Kim: Architectural Engineering Department, Ewha Womans University, Seoul, South Korea

Abstract
Impact from water-borne debris during tsunami and flood events pose a potential threat to structures. Debris impact forces specified by current codes and standards are based on rigid body dynamics, leading to forces that are dependent on total debris mass. However, shipping containers and other debris are unlikely to be rigid compared to the walls, columns and other structures that they impact. The application of a simple one-dimensional model to obtain impact force magnitude and duration, based on acoustic wave propagation in a flexible projectile, is explored. The focus herein is on in-air impact. Based on small-scale experiments, the applicability of the model to predict actual impact forces is investigated. The tests show that the force and duration are reasonably well represented by the simple model, but they also show how actual impact differs from the ideal model. A more detailed threedimensional finite element model is also developed to understand more clearly the physical phenomena involved in the experimental tests. The tests and the FE results reveal important characteristics of actual impact, knowledge of which can be used to guide larger scale experiments and detailed modeling. The one-dimensional model is extended to consider water-driven debris as well. When fluid is used to propel the 1-D model, an estimate of the \'added mass\' effect is possible. In this extended model the debris impact force depends on the wave propagation in the two media, and the conditions under which the fluid increases the impact force are discussed.

Key Words
debris; tsunami; shipping container; impact force

Address
K. Paczkowski and H.R. Riggs: Department of Civil and Environmental Engineering, University of Hawaii at Manoa,
2540 Dole Street, Holmes 383, Honolulu, Hawaii 96822, USA
C.J. Naito and A. Lehmann: Department of Civil Engineering, Lehigh University, ATLSS Center, 117 ATLSS Drive,
IMBT Labs, Bethlehem, PA 18015, USA

Abstract
Single span historic bridges often contain non-prismatic members identified with a varying depth along their span lengths. Commonly, the symmetric parabolic height variations having the constant haunch length ratio of 0.5 have been selected to lower the stresses at the high bending moment points and to maintain the deflections within the acceptable limits. Due to their non-prismatic geometrical configuration, their assessment, particularly the computation of fixed-end horizontal forces (FEFs) and fixed-end moments (FEMs) becomes a complex problem. Therefore, this study aimed to investigate the behavior of non-prismatic beams with symmetrical parabolic haunches (NBSPH) having the constant haunch length ratio of 0.5 using finite element analyses (FEA). FEFs and FEMs due to vertical loadings as well as the stiffness coefficients and the carry-over factors were computed through a comprehensive parametric study using FEA. It was demonstrated that the conventional methods using frame elements can lead to significant errors, and the deviations can reach to unacceptable levels for these types of structures. Despite the robustness of FEA, the generation of FEFs and FEMs using the nodal outputs of the detailed finite element mesh still remains an intricate task. Therefore, this study advances to propose effective formulas and dimensionless estimation coefficients to predict the FEFs, FEMs, stiffness coefficients and carry-over factors with reasonable accuracy for the analysis and re-evaluation of the NBSPH. Using the proposed approach, the fixed-end reactions due to vertical loads, and also the stiffness coefficients and the carry-over factors of the NBSPH can be determined without necessitating the detailed FEA.

Key Words
historic bridge; non-prismatic member; finite element analysis; parabolic haunch; stiffness factor; fixed-end reactions

Address
S. Bahadir Yuksel: Department of Civil Engineering, Selcuk University, Konya 42075, Turkey

Abstract
Analytical (Rayleigh-Ritz method) and numerical studies are carried out and buckling interaction curves are developed for simply supported plates of varying aspect ratios ranging from 1 to 5, under the combined action of in-plane shear and tension. A multi-step buckling procedure is employed in the Finite Element (FE) model instead of a regular single step analysis in view of obtaining the buckling load under the combined forces. Both the analytical (classical) and FE studies confirm the delayed shear buckling characteristics of thin plate under the combined action of shear and tension. The interaction curves are found to be linear and are found to vary with plate aspect ratio. The interaction curve developed using Rayleigh-Ritz method is found to deviate in an increasing trend from that of validated FE model as plate aspect ratio is increased beyond value of 1. It is found that the observed deviation is due to the insufficient number of terms that is been considered in the assumed deflection function of Rayleigh-Ritz method and a convergence study is suggested as a solution.

Key Words
plate; shear; tension; buckling; Rayleigh Ritz; FEM; in-plane; interaction; classical solution; numerical study

Address
S. Sathiyaseelan and K. Baskar: Department of Civil Engineering, National Institute of Technology, Trichy-620015, India

Abstract
Cold-formed channel sections are used in a variety of applications in which they are required to absorb deformation energy. This paper investigates the collapse behaviour and energy absorption capability of cold-formed steel channels with flange edge stiffeners under large deformation major-axis bending. The Yield Line Mechanism technique is applied using the energy method, and based upon measured spatial plastic collapse mechanisms from experiments. Analytical solutions for the collapse curve and in-plane rotation capacity are developed, and used to model the large deformation behaviour and energy absorption. The analytical results are shown to compare well with experimental values. Due to the complexities of the yield line model of the collapse mechanism, a simplified procedure to calculate the energy absorbed by channel sections under large bending deformation is developed and also shown to compare well with the experiments.

Key Words
cold-formed steel; channels; yield line mechanisms; major-axis bending; energy absorption

Address
S. Maduliat: Department of Civil Engineering, Monash University, Clayton Campus, VIC 3800, Australia
M.R. Bambach: IRMRC, Faculty of Science, University of New South Wales, NSW 2052, Australia
X.L. Zhao: Department of Civil Engineering, Monash University, Clayton Campus, VIC 3800, Australia

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