8/16/2019 00b4952b21beda06a0000000

1/6

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/225671965

Structural Engineering: Seeing the Big Picture

 Article  in  KSCE Journal of Civil Engineering · December 2007

Impact Factor: 0.48 · DOI: 10.1007/s12205-008-8025-7

CITATIONS

8

READS

78

1 author:

Wai Fah Chen

University of Hawaiʻi at Mānoa

377 PUBLICATIONS  6,191 CITATIONS 

SEE PROFILE

All in-text references underlined in blue are linked to publications on ResearchGate,

letting you access and read them immediately.

Available from: Wai Fah Chen

Retrieved on: 27 May 2016

https://www.researchgate.net/institution/University_of_Hawaii_at_Mnoa?enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2&el=1_x_6https://www.researchgate.net/profile/Wai_Chen2?enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2&el=1_x_5https://www.researchgate.net/?enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2&el=1_x_1https://www.researchgate.net/profile/Wai_Chen2?enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2&el=1_x_7https://www.researchgate.net/institution/University_of_Hawaii_at_Mnoa?enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2&el=1_x_6https://www.researchgate.net/profile/Wai_Chen2?enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2&el=1_x_5https://www.researchgate.net/profile/Wai_Chen2?enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2&el=1_x_4https://www.researchgate.net/?enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2&el=1_x_1https://www.researchgate.net/publication/225671965_Structural_Engineering_Seeing_the_Big_Picture?enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2&el=1_x_3https://www.researchgate.net/publication/225671965_Structural_Engineering_Seeing_the_Big_Picture?enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2&el=1_x_2

8/16/2019 00b4952b21beda06a0000000

2/6

KSCE Journal of Civil Engineering

Vol. 12, No. 1 / January 2008

 pp. 25~29

DOI 10.1007/s12205-008-8025-7

 Structural Engineering 

Vol. 12, No. 1 / January 2008   − 25 −

Structural Engineering: Seeing the Big Picture

By W. F. Chen*

···································································································································································································································

Abstract

The state-of-the-art of progress of structural engineering over the last 50 years is examined in three areas: (1) The spatialidealization of structural elements in the form of kinematical assumptions; (2) The constitutive idealization of materials in the form of generalized stresses and generalized strains relations; and (3) The computational implications of solution strategy in the form of closed form, approximate, and numerical procedures on the structural level.

Keywords: structural engineering, stress-strain, kinematics, finite element, strength of materials, modeling and simulation, state-of-

the-art 

···································································································································································································································

1. Introduction

Structural engineering is a part of the broad and fascinating

subject of mechanics of materials or continuum mechanics,

which spans the spectrum from the fundamental aspects of 

elastic and inelastic behavior of materials to the practical solution

of engineering problems in engineering practice.

Mechanics is a branch of applied physics involving

mathematical formulation of a physical problem and its solution

strategy for engineering applications. The process must involve

three basic conditions or equations for solutions:

1. Equilibrium equations or motion reflecting law of physics

(Newton’s law or Physics).

2. Constitutive equations or stress-strain relations reflecting

material behavior (Materials or Experiments).

3. Compatibility equations or kinematical assumptions reflect-

ing the geometry (Continuity or Logic).

The required simplicity of equilibrium, material behavior, and

kinematics to be usable with the most powerful computers, for 

the analysis or design of engineering structures over their life

cycle simulation, requires drastic idealizations and simplifications

to achieve realistic and practical solution for engineering design.

This paper shows how structural engineering field has been

evolved and progressed over the last 50 years along with the

rapid growth and development of computing power over the last

several decades.

2. Strength of Materials Approach to StructuralEngineering in the Early Years

The methods of formulation and calculation of a structural

 problem must be adapted to a wide class of structural forms so

that the basic equations to be written for a structural element are

manageable and not too excessively complex. To this end, the

concept of  generalized stresses  and  generalized strains  were

introduced in the 1950’s for solutions of strength of materials

types of problems including beams, columns, beam-columns that

form the basis of analysis for frame design. This was later 

extended to include plate and shell types of structural analysis

and design.

In the case of simple beam theory, for example, the stressed

state in a beam element is determined by only one generalized

stress, the bending moment, instead of six stresses; while the

corresponding deformation is defined by one generalized strain,

the curvature, instead of six strains. This drastic simplification is

achieved through the powerful kinematical assumption of plane

section remains plane after bending. This generalized stress and

generalized strain concept for a simple beam element can be

easily extended to the case of column element, for example, with

combined generalized stresses of bending moment and axial

force with the corresponding generalized strains of bending

curvature and axial shortening.

As a result of this simplification, the equilibrium equations are

used to relate the stresses in an element to its generalized

stresses, while the kinematical assumption is used to relate the

strains in an element to its generalized strains, and the stress-strain

relations of materials are then used to derive the generalized

stresses and generalized strains relations for a structural element.

The basic formulation for a structural member is now reduced to

a one-dimensional problem instead of six dimensions in the sense

of continuum mechanics approach to a structural engineering

 problem.

*Professor, Department of Civil Engineering, University of Hawaii, Honolulu, Hawaii 96822 (E-mail: chenwf@eng.hawaii.edu)

8/16/2019 00b4952b21beda06a0000000

3/6

W. F. Chen

− 26 − KSCE Journal of Civil Engineering

For an elastic problem, most of strength of materials problems

can be solved in closed form by power series expansion as well

documented in the famous work of Timoshenko. Many of these

well known classical solutions for beams, columns, beam-columns,

 plates and shells were reported in a series of widely popular 

 books by Timoshenko (1951, 1953, 1961, 1962), among others.

For high rise building frames, the entire length of a structural

member is selected as the basic element for engineering analysis.

To this end, the corresponding relationships between the

generalized stresses (member end moments and end forces) and

the corresponding generalized strains (member end rotations and

relative end lateral displacements) for a structural member were

represented in the form of the well-known “ slope-deflection

equations” for elastic structural system analysis (Chen and Lui,

1987, 1991). The slope deflection equations were simple and

 powerful and thus widely used in engineering practice for building

frame design based on the Allowable Stress Design codes in

early years.

In engineering practice, a more powerful companion approxi-

mate method known as the “moment distribution method ” was

also developed by Hardy Cross at the University of Illinois

(Gere, 1962). It was based on the St. Venant principle in that the

moment distribution in a particular structural member in a high

rise building frame is affected mostly by the surrounding

members adjacent to it. The influence of other members in some

distance from the member under consideration is relative small

and may be ignored after a few cycles of iteration.

For inelastic problems, a further simplification of material

 behavior is made by ignoring strain hardening and also to

eliminating entirely the factor of time from the formulation. This

leads to the time independent idealization for plastic behavior 

and enables us to use the simple plastic theory to determine the

 plastic collapse load with the equilibrium methods for lower 

 bound solutions and the mechanism methods for upper bound

solutions.

For low rise building, simple plastic theory was developed in

which the material model used was elastic perfectly plastic

(ASCE Manual 41, 1971). The kinematical assumption used was

the powerful concept of “ plastic hinge.” Upper and lower bound

solutions were obtained by the simple mechanism methods

 bounded above; and the simple equilibrium methods with

moment check bounded below (see for example, Chen and

Sohal, 1995). The Plastic Design method was officially adopted

 by the American Institute of Steel Construction in the early

1960’s (see, for example, ASCE Manual 41, 1971).

As a result of this advancement, plastic design methods for 

steel structures were spread widely and introduced quickly in

various new codes around the world for steel design; while the

companion ultimate strength design for reinforced concrete was

advanced quickly and adopted widely in the reinforced concrete

codes for building design. Similar advancements were also made

for the plate theory for plate type of steel structural design; while

the yield line theory was introduced at the same time for slab

design in reinforced concrete code.

Based on these simple and practical solution techniques using

drastic simplifications and idealizations for materials, geometry

and equations of equilibrium, the traditional “ Allowable Stress

 Design Method ” and the newly developed “ Plastic Design

Method ” were widely used in engineering practice in those years.

These simple and powerful design methods are ideal and suitable

with the basic computing facility available at the time such as

slide rule and calculators. Drastic idealizations and simplifications

were the key elements for a rapid and successful implementation

of these methods for design of real world engineering problems.

In summary, the idealizations and simplifications used in the

strength of materials approach to structural engineering problems

can be highlighted by the following seven steps of progress:

1. Structural elements – beam, column, beam-column, plate

and shell.

2. Generalized stresses – stress resultants such as moment and

axial force.

3. Generalized strains – strain resultants such as curvature and

axial displacement.

4. Stresses to generalized stresses – through equilibrium equa-

tions.

5. Strains to generalized strains – through kinematical as-

sumptions.

6. Generalized stress and generalized strain relations – 

through stress-strain relations of materials.

7. Solution strategy – series expansion, approximate and

numerical.

3. Finite Element Approach to Structural Engi-neering in Recent Years

In the 1970’s, our computing power changed drastically with

mainframe computing. The “ Finite Element methods” were well

developed and widely used in structural engineering. The basic

material model used was the extension from linear elasticity to

inelasticity, or plasticity in particular. The basic kinematical or 

compatibility condition used for a finite-element formulation

was known as the “ shape function.” The equilibrium condition

was achieved through a weak format of “equation of virtual 

work ” instead of the usual free body equilibrium formulation.

As a result of these simplifications, the force displacement

relation for a finite element was expressed in the form of the

generalized stress and generalized strain relationship. This basic

relationship for an element in a discrete continuum of a structural

system is known as the “nodal force and nodal displacement 

equation.” The stresses in elements were related to the

generalized stresses or nodal forces through the virtual work 

equation. Elemental strains were related to the generalized strains

or nodal displacements through the kinematical assumption, or 

shape function. The incremental generalized stress and generalized

strain relation for a finite element was then obtained through the

constitutive equation of a particular material.

In summary, the three basic conditions for a valid solution of a

typical finite element formulation are achieved with the following

https://www.researchgate.net/publication/246379698_History_of_Strength_of_Materials?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/246379698_History_of_Strength_of_Materials?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/44725858_The_Theory_of_Elasticity?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2

8/16/2019 00b4952b21beda06a0000000

4/6

Structural Engineering: Seeing the Big Picture

Vol. 12, No. 1 / January 2008   − 27 −

idealizations and simplifications:

(1) Equilibrium Condition (Newton’s Law or Physics)

The virtual work equation is used exclusively to establish the

relationship between the stress in an element to the generalized

stresses or nodal forces at nodal points.

(2) Kinematics Condition (Continuity or Logic)

The shape function is introduced to establish the relationship

 between the strains in an element to the generalized strains of 

nodal displacements at the nodal points.

(3) Constitutive Relations (Material or Experiment)

The theory of plasticity or viscosity is used to relate the

generalized stresses to generalized strains or the nodal forces and

nodal displacements relationships through the use of constitutive

equations of engineering materials.

The two-volume treatise on constitutive equations for engineer-

ing materials by Chen and Saleeb (1982), and Chen (1994) covers

most of these developments, among others (Chen and Baladi,

1985). During this period, we were able to solve almost any kind

of structural engineering problems with computer simulation.

For the first time in the history of computing, the physical theory

is lagging behind the computing power. By now, engineers need

to develop a more refined theory of constitutive equations for 

engineering materials for their special finite element types of 

applications.

As a result of these simplifications, the structural engineering

 problem is now reduced to the solution of a set of simultaneous

incremental equations for a structural system. Since the solution

includes the inelastic behavior of materials which is load path

dependent, the numerical scheme used was an incremental and

iterative process (Chen and Han, 1988). Many numerical proce-

dures were developed during the period, most notably the

“tangent stiffness method”, among others.

With a large amount of numerical data so generated, it became

necessary for engineers to use probability theory and reliability

analysis to analyze the data and develop design procedures for 

 practical implementation. As a result of this development, a new

generation of codes based on an extensive computer simulation

and reliability analysis was developed and adopted around the

world. For the first time in engineering practice ever, the load

effect and structural resistance effect were treated separately in

design, each with its own safety or load factor. The new code in

US, for example, was adopted by the American Institute of Steel

Construction entitled “the load and resistance factor design

 specifications for steel buildings” in 1986.

The following is a brief summary in a tabular form of the

impact of the applications of finite element methods with

 plasticity theory on structural engineering practice.

3.1 In the 1970s: Development of Structural Member 

Strength Equations

• Beam strength equation – beam design curve.

• Column strength equation –column design curve.

• Beam-Column strength equation – beam-column interaction

design curve.

• Bi-axially loaded column strength equation for plastic design

in steel building frames.

These developments were summarized in the two-volume

 beam-columns treatise by Chen and Atsuta (1976, 1977) and the

SSRC Guide edited by Galambos (1988), among others.

3.2 In the 1980s: Limit States to Design

• Development of reliability-based codes.

• The publication of the 1986 AISC/LRFD Specification.

• The introduction of the second-order elastic analysis to the

design codes.

• The explicit consideration of semi-rigid connections in frame

design (now known as the PR Construction) (Chen and Kim,

1998).

These developments were summarized in the structural

stability books by Chen and Lui (1991) and Chen (1993), among

others.

3.3 In the 1990s: Structural System Approach to Design

• Second-Order inelastic analysis for steel frame design was

under intense development (White and Chen, 1993).

• The theory of plasticity is combined with the theory of 

stability for a direct steel frame design (Chen and Kim,

1997).

• The advanced analysis considers explicitly the influence of 

structural joints in analysis/design process (Chen, 2000).

These developments were summarized in the structural

stability books by Chen and Toma (1994), and Chen and Lui

(2005), among others.

4. Model-Based Simulation in Civil Engineering:Challenges and Opportunities

We are now in a desk top environment for free computing. We

are able to do a large scale simulation of structural system over 

its life-cycle performance analysis. Computer simulation has

now joined theory and experimentation as a third path for 

engineering design and performance evaluation.

The development of model-based simulation for any civil

engineering structures or facilities must involve the following

four steps:

4.1 Modeling of Materials

The constitutive equations for materials are now moving from

time-independent to time-dependent behaviors such as creep,

relaxation, temperature variation, and deterioration or aging.

These equations must be developed by engineers on the basis of 

mechanics, physics, and materials science. In a numerical

analysis of these materials in a structural system, the proper 

modeling of discontinuity and fracture or crack for tension-weak 

materials becomes increasing important.

4.2 Solution Algorithm

For a realistic life-cycle simulation of constructed facilities, it

https://www.researchgate.net/publication/37408257_Soil_Plasticity_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/37408257_Soil_Plasticity_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/265620704_Plasticity_for_Structural_Engineers?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/279957993_Design_of_Steel_Structures_with_LRFD_Using_Advanced_Analysis?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/279957993_Design_of_Steel_Structures_with_LRFD_Using_Advanced_Analysis?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/265620704_Plasticity_for_Structural_Engineers?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/279957993_Design_of_Steel_Structures_with_LRFD_Using_Advanced_Analysis?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/279957993_Design_of_Steel_Structures_with_LRFD_Using_Advanced_Analysis?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/37408257_Soil_Plasticity_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/37408257_Soil_Plasticity_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2

8/16/2019 00b4952b21beda06a0000000

5/6

W. F. Chen

− 28 − KSCE Journal of Civil Engineering

is not uncommon for engineers to deal with the mathematical

modeling of radically different scales, in time and/or space. The

computational effort for different parts of a large structural

system may be drastically different. For example, in the analysis

of reinforced concrete bridge system under seismic loading, a

macro scale is necessary to model the overall behavior of the

structure-soil interaction. Yet, a micro scale is needed at a local

level to trace crack initiation and propagation.

Computation efficiency can be achieved in this case by using

 parallel finite-element analyses for the structural system. Parallel

macro and micro analyses can be performed by multiple machines,

such as PC cluster systems. This computational method requires

repartitioning of the domain during the course of the analysis,

making the development of suitable interfaces, data communica-

tion tools, or central databases with different levels for different

scales in time and in space is of critical importance.

As another example, the finite-element method is preferred in

structural engineering and solid mechanics, while the finite-

difference method is more commonly used in fluid mechanics.

When dealing with structure-fluid interaction problems, as

frequently encountered in offshore structural engineering, the

development of suitable data translators or data communication

tools is necessary in order to use existing codes, which are based

on two different methodologies.

4.3 Software Development

There are hundreds of software systems on the market to

support software development. A software support system is a

compatible set of tools, usually based on a specific software

development methodology, which can be employed for several

 phases of software and operation.

The key to a domain-specific software development environ-

ment is software reuse. Software reuse enables the knowledge

obtained from the solution of a particular problem to be accu-

mulated and shared in the solution of other problems. If software

components accumulated from previous software development

can be utilized readily in the development of new applications,

substantial applications can be built more efficiently. This is an

ideal environment for university research and education. This

idea was carried out and implemented, for the first time, at

Purdue University with my former colleagues, D.W. White and

E. Sotelino (1994), and former doctoral students, H. Zhang and J.

Lu, among others with major financial supports from the

 National Science Foundation (NSF).

At present, the key to software development is software in-

tegration. Since most commercial software has its own particular 

function and input/output formats, it may prohibit direct data

access. It seems very necessary to unify the documentation from

different software and to make the newest and largest efforts in

the development of standard models, such as Industry Founda-

tion Class (IFC). Following the development of grid computing,

the interoperability of facilities and software at different location

in the network can be realized.

4.4 Visualization and Verification

Modeling is science, simulation is computing, and computing

requires solution algorithms and software development. Visual-

ization is a necessary step to aid in the interpretation of the

simulated results. Validation of the simulation of an engineering

 problem must be verified by experimental work.

Model-based simulation is inherently interdisciplinary in

science and engineering, where computation plays the key role.

The entire process of model-based simulation involves the

following seven steps:

1. Experimental measurements as the basis for the devel-

opment of relevant constitutive equations for a physical

system;

2. Design of a proper algorithm for its numerical solutions;

3. Implementation of the procedures with necessary docu-

mentation and software interface development;

4. Selection of appropriate hardware to run the computer 

simulation of the physical system;

5. Validation of the computer model with physical testing;

6. Graphical visualization of the simulated results; and finally;

7. Sharing of the simulation model with others through high

speed network communication.

 In the current high-performance computing environment, the

major challenges of modeling, simulation and validation are the

integration of material science, structural engineering and com-

 putational mechanics with proper simplifications and idealizations

for practical applications. As mentioned previously, modeling is

science, simulation is computing, and validation is experi-

mentation. All these three areas of further development require

structural engineer’s own effort and focus including, for 

example, the following issues for future structural engineering

implementation:

• From structural system approach to life-cycle structural

analysis of structures covering construction sequence

analysis during construction, performance analysis during

service, and degradation and deterioration analysis during

maintenance, rehabilitation, and demolition (Chong et al .,

2002).

• From finite element modeling for continuous media to finite

 block modeling for tension-weak materials with tensile crack 

development and subsequent changing of structural geometry

and topology.

• From time-independent elastic and inelastic material model-

ing to time-dependent modeling reflecting material degrada-

tion and deterioration science (Montero et al., 2001).

5. Concluding Remarks

Advancement in computer technology in recent years has

spurred the development of scientific simulation and visualization

in science and engineering. Such capability has spurred similar 

developments in structural engineering and allowed the solutions

of many structural engineering problems before thought of 

“unsolvable”, and consequently, are now driving progress in a

https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2

8/16/2019 00b4952b21beda06a0000000

6/6

Structural Engineering: Seeing the Big Picture

Vol. 12, No. 1 / January 2008   − 29 −

number of challenging areas of structural engineering including,

for example, life-cycle type of analysis for cost estimate and life-

cycle design considerations, finite block type of analysis for 

structures with tensile crack development and topology change

under an increasing loading, and degradation type of analysis for 

deterioration and aging of structural materials with time, among

others.

Good progress has been made in recent years in structural

engineering, but much more remains to be done in terms of 

simplification and idealization in constitutive modeling of 

materials, structural modeling of elements, and computing

strategy for reliable solution scheme of large scale simulation in

time and space for large constructed facilities.

References

ASCE, American Society of Civil Engineers Manual 41 (1971). Plastic

 Design in Steel: A Guide and Commentary, ASCE, New York, p.

336.

LRFD, The Load and Resistance Factor Design Specification for Structural Steel Buildings (1986, 2005). American Institute of Steel 

Construction, Chicago.

Chen, W.F. and Atsuta, T. (1976). Theory of Beam-Columns, Vol. 1 -

In-Plane Behavior and Design, McGraw-Hill, New York, p. 513

Chen, W.F. and Atsuta, T. (1977). Theory of Beam-Columns, Vol. 2 -

Space Behavior and Design , McGraw-Hill, New York, p. 732.

Chen, W.F. and Lui, E.M. (1987). Structural Stability: Theory and 

 Implementation, Elsevier, New York. p. 486.

Chen, W.F. and Lui, E.M. (1991). Stability Design of Steel Frames, CRC 

 Press, Boca Raton, Florida, p. 380.

Chen, W.F., Editor (1993). Semi-Rigid Connections in Steel Frames,

Council on Tall Buildings and Urban Habitat, McGraw-Hill, New

York, p. 318.

Chen, W.F. and Toma, S. (1994). Advanced Analysis of Steel Frames,

CRC Press, Boca Raton, Florida, p. 384.

Chen, W.F. and Sohal, I. (1995). Plastic Design and Second-Order 

 Analysis of Steel Frames, Springer-Verlag, New York, p. 509.

Chen, W.F. and Kim, S.E. (1997). LRFD Steel Design Using Advanced 

 Analysis, CRC Press, Boca Raton, Florida, p. 448.

Chen, W.F., Goto, Y., and Liew, J.Y.R. (1996). Stability Design of Semi-

 Rigid Frames, John Wiley & Sons, New York, p. 468

Chen, W.F. and Kim, Y.S. (1998). “Practical analysis for partially

restrained frame design,” Structural Stability Research Council ,

Lehigh University, Bethlehem, Pennsylvania, p. 82. 

Chen, W. F., Editor (2000). Practical Analysis for Semi-Rigid Frame

 Design, World Scientific Publishing Co., Singapore, p. 465.

Chen, W. F. and Lui, E. M., Editors (2005). Chapter 5: Steel Frame

 Design Using Advanced Analysis, In the Handbook of Structural

Engineering, CRC Press, Boca Raton, Florida, Second Edition.

Chen, W. F. and Han, D. J. (1988). Plasticity for Structural Engineers,

Springer-Verlag, New York, p. 606.

Chen, W.F. ana Baladi, G.Y. (1985). Soil Plasticity: Theory and

Implementation. Elsevier, Amsterdam, p. 231.

Chen, W.F. and Saleeb, A.F. (1982). Constitutive Equations for 

 Engineering Materials, Vol. 1 - Elasticity and Modeling, Wiley

Inter-science, New York, p. 580.

Chen, W. F. (1994). Constitutive Equations for Engineering Materials,

Vol. 2 - Plasticity and Modeling , Elsevier, Amsterdam, p. 1096.

Chong, K. P., Saigal, S., Thynell, S., and Morgan, H., Editors (2002).

Modeling and Simulation-Based Life-Cycle Engineering, Spoon

Press, London, UK, p. 348.

Galambos, T. V., Editor (1988). Guide to Stability Design Criteria for 

Metal Structures, 4th edition John Wiley & Sons, New York.

Gere, J. M. (1962). Moment Distribution, Van Nostrand, Princeton, New

Jersey.Montero, P., Chong, K. P., Larsen-Basse, J. and Komvopoulos, K.

(2001). Long-Term Durability of Structural Materials. Elsevier,

 Netherlands, p. 296.

Sotelino, E. D. and Chen, W. F. (1998). “Future challenges for 

simulation in structural engineering,” Proceedings of the Fourth

World Congress on Computational Mechanics, Buenos Aires,

Argentina, June 30-July 3. (In CD-ROM).

Sotelino, E. D., White, D. W. and Chen, W. F. (1994). “An automated

environment for parallel computing ,” Proceedings of the 11th

 Analysis and Computation Conference, Editor, F.Y. Cheng, Atlanta,

GA, April 24-28, (1994) ASCE Publication, pp. 193-202.

Timoshenko, S. P. (1953). History of the Strength of Materials ,

McGraw-Hill, New York.

Timoshenko, S. P. and Gere, J. M. (1961). Theory of Elastic Stability,

McGraw-Hill, New York.

Timoshenko, S. P. and Goodier, J. N. (1951). Theory of Elasticity,

McGraw-Hill, New York.

Timoshenko S. P. and Young D. H. (1962). Elements of Strength of 

Materials, Van Nostrand, Princeton, New Jersey.

White, D. W. and Chen, W. F. (1993). “Plastic hinge based methods for 

advanced analysis and design of steel frames: An assessment of the

State-of-the-Art,” Structural Stability Research Council , Bethlehem,

Pennsylvania, p. 299.

https://www.researchgate.net/publication/262973125_Structural_Stability_-_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/262973125_Structural_Stability_-_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/262973125_Structural_Stability_-_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/262973125_Structural_Stability_-_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/262973072_Stability_Design_of_Steel_Frames?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/262973072_Stability_Design_of_Steel_Frames?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/262973072_Stability_Design_of_Steel_Frames?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/262973072_Stability_Design_of_Steel_Frames?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/279957993_Design_of_Steel_Structures_with_LRFD_Using_Advanced_Analysis?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/279957993_Design_of_Steel_Structures_with_LRFD_Using_Advanced_Analysis?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/279957993_Design_of_Steel_Structures_with_LRFD_Using_Advanced_Analysis?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/279957993_Design_of_Steel_Structures_with_LRFD_Using_Advanced_Analysis?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/265620704_Plasticity_for_Structural_Engineers?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/265620704_Plasticity_for_Structural_Engineers?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/265620704_Plasticity_for_Structural_Engineers?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/265620704_Plasticity_for_Structural_Engineers?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/37408257_Soil_Plasticity_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/37408257_Soil_Plasticity_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/44725858_The_Theory_of_Elasticity?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/44725858_The_Theory_of_Elasticity?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/44725858_The_Theory_of_Elasticity?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/44725858_The_Theory_of_Elasticity?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/285193331_Initiative_on_long_term_durability_of_materials_and_structures?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/265620704_Plasticity_for_Structural_Engineers?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/265620704_Plasticity_for_Structural_Engineers?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/245304235_Practical_Analysis_for_Partially_Restrained_Frame_Design?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/279957993_Design_of_Steel_Structures_with_LRFD_Using_Advanced_Analysis?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/279957993_Design_of_Steel_Structures_with_LRFD_Using_Advanced_Analysis?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/262973072_Stability_Design_of_Steel_Frames?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/262973072_Stability_Design_of_Steel_Frames?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/262973125_Structural_Stability_-_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/262973125_Structural_Stability_-_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/44725858_The_Theory_of_Elasticity?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/44725858_The_Theory_of_Elasticity?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/37408257_Soil_Plasticity_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2https://www.researchgate.net/publication/37408257_Soil_Plasticity_Theory_and_Implementation?el=1_x_8&enrichId=rgreq-3d0d9ff5-073f-47af-9525-757c06796158&enrichSource=Y292ZXJQYWdlOzIyNTY3MTk2NTtBUzo5OTE2NzQxNDI1OTcyMkAxNDAwNjU0NzYyNTg2