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Volume 11, Number 6, June 2001

This paper presents a simplified method for the design and analysis of non-prestressed,
partially prestressed, and fully prestressed concrete beams subjected to pure torsion. The proposed model
relates the torsional strength to the concrete compressive strength and to the amounts of transverse and
longitudinal reinforcement. To check the adequacy of this simple method, the calculated strength and
mode of failure are checked against the experimental results of 17 prestressed concrete 66 reinforced
concrete beam tests available in the literature, and very good agreement is found. The simplicity of the
method is illustrated by two examples, one for design and another for analysis.

Key Words
beams; code methods; design; mode of failure; prestressed concrete; reinforced concrete; shear; strength; torsion.

Khaldoun N. Rahal, Department of Civil Engineering, Faculty of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

In this paper, a finite element with embedded displacement discontinuity which eliminates the
need for remeshing of elements in the discrete crack approach is applied for the progressive fracture
analysis of concrete structures. A finite element formulation is implemented with the extension of the
principle of virtual work to a continuum which contains internal displacement discontinuity. By introducing a
discontinuous displacement shape function into the finite element formulation, the displacement discontinuity
is obtained within an element. By applying either a nonlinear or an idealized linear softening curve
representing the fracture process zone (FPZ) of concrete as a constitutive equation to the displacement
discontinuity, progressive fracture analysis of concrete structures is performed. In this analysis, localized
progressive fracture simultaneous with crack closure in concrete structures under mixed mode loading is
simulated by adopting the unloading path in the softening curve. Several examples demonstrate the
capability of the analytical technique for the progressive fracture analysis of concrete structures.

Key Words
embedded displacement discontinuity; progressive fracture analysis; concrete structures; finite element method; discontinuous displacement shape function; softening curves; fracture process zone.

Ha-Won Song, Byul Shim , Seung-Min Woo and Ja-Choon Koo, Department of Civil Engineering, Yonsei University, Seoul 120-749, Korea

The purpose of this study is to investigate the effect of the shear wall location in rigid
frames on the dynamic behavior of a roof structure due to vertical and horizontal earthquake motions. The
study deals with a gabled long span beam supported by two story rigid frames with shear walls. The
earthquake response analysis is carried out to study the responses of the roof: vibration mode, natural
period, bending moment and horizontal shear force of the bearings. The study results in the following
conclusions: First, a large horizontal stiffness difference between the side frames is caused by the shear
wall location, which results in a large vertical vibration of the roof and a large shear force at the side
bearings. Second, in this case, the seismic design method for ordinary buildings is not useful in
determining the distribution of the static equivalent loads for the seismic design of this kind of long span

Key Words
long span structure; earthquake response; horizontal rigidity; interaction of long span beam and bearing structure.

Koichiro Ishikawa, Yoshizo Kawasaki and Kengo Tagawa, Department of Architecture and Civil Engineering, Fukui University, Fukui-shi 910-8507, Japan

For the potential application of smart materials to seismic structural control, this paper reviews
seismic control techniques for civil engineering structures, and developments of smart materials for vibration
and noise control. Analytical and finite element methods adopted for the design of distributed sensors/
actuators using piezoelectric materials are discussed. Investigation of optimum position of sensors/actuators
and damping are also outlined.

Key Words
smart materials; seismic vibration control; finite element.

S. Valliappan and K. Qi, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia

A structural analysis of cracked R.C. members under instantaneous or sustained loads and
imposed displacements is presented. In the first part of the paper the problem of deriving feasible
moment-curvature diagrams for a long term analysis of R.C. sections is approached in an exact way by
using the Reduced Relaxation Function Method in state I uncracked and the method suggested by CEB in
state II cracked. In both states the analysis of the main parameters governing the problem has shown that
it is possible to describe the concrete creep behaviour in an approximate way by using the algebraic
formulation connected to the Effective Modulus Method. In this way the calculations become quite simple
and can be applied in design practice without introducing significant errors. Referring to continuous
beams, the structural analysis is then approached in a general way, applying the Force Method and the
Principle of Virtual Works. Finally, considering single members, the structural analysis is performed by
means of a graphical procedure based on the application of feasible moment-rotation diagrams which
allow to easily solve various structural problems and to point out the most interesting aspects of the long
term behaviour of cracked R.C. members with rigid or elastically deformable redundant restraints.

Key Words
creep; cracking; relaxation; curvature; rotations; structural analysis.

F. Mola, Department of Structural Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
M.C. Gatti, Rocksoil Consulting Engineering, Piazza San Marco 1, 20121 Milano, Italy
G. Meda, INPRO Consulting Engineering, Viale Certosa 34, 20155 Milano, Italy

In order to investigate the seismic behavior and seismic design methods in the transverse
direction of a shield tunnel, a series of model shaking table tests and a two-dimensional finite element
dynamic analysis on the tests are carried out. Two kinds of static analytical methods based on ground-tunnel
composite finite element model and beam-spring element model are proposed, and the validity of
the static analyses is verified by model shaking table tests. The investigation concerns the dynamic
response behavior of a tunnel and the ground, the interaction between the tunnel and ground, and an
evaluation of different seismic design methods. Results of the investigation indicate that the shield tunnel
follows the surrounding ground in displacement and dynamic characteristics in the transverse direction;
also, the static analytical methods proposed by the authors can be used directly as the seismic design
methods in the transverse direction of a shield tunnel.

Key Words
seismic behavior; seismic structural design; shield tunnels; shaking table testing; seismic deformation method.

Chuan He, School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China
Atsushi Koizumi, Department of Civil Engineering, Waseda University, Tokyo 169-8555, Japan

Numerous failures in welded connections in steel moment-resisting building frames (SMRF)
were observed when buildings were inspected after the 1994 Northridge Earthquake. These observations
raised concerns about the effectiveness of such frames for resisting strong earthquake ground motions.
The behavior of SMRFs during an earthquake must be assessed using nonlinear dynamic analysis, and
such assessments must permit the deterioration in connection strength to capture the behavior of the
frame. The uncertainties that underlie both structural and dynamic loading also need to be included in the
analysis process. This paper describes the analysis of one of approximately 200 SMRFs that suffered
damage to its welded beam-to-column connections from the Northridge Earthquake is evaluated.
Nonlinear static and dynamic analysis of this SMRF in the time domain is performed using ground
motions representing the Northridge Earthquake. Subsequently, a detailed uncertainty analysis is conducted
for the building using an ensemble of earthquake ground motions. Probability distributions for
deformation-related limit states, described in terms of maximum roof displacement or interstory drift, are
constructed. Building fragilities that are useful for condition assessment of damaged building structures
and for performance-based design are developed from these distributions.

Key Words
buildings (codes); design (buildings); connections; earthquakes; frames; loads (forces); probability; reliability; safety; strutural engineering; welding.

Jianlin Song and Bruce R. Ellingwood, Applied Insurance Research, 101 Huntington Ave., Boston, MA 02199-8001, U.S.A
School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A

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