Analysis and Design of Open Web Steel Joist-Girders.docx

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1 Analysis and Design of Joist Girder
Analysis and Design
of
Joist Girder
A graduation project
Submitted to the department of civil engineering at
The University of Baghdad
Baghdad - Iraq
In partial fulfillment of the requirement for the degree of Bachelor of
Science in civil engineering
By
Jalil & Mohammed
Supervised by
Assistant lecturer, A. N. LAZEM
(M.Sc., in Structural Engineering)
July /2008

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Analysis and Design
of
Joist Girder

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I certify that study entitled “Analysis and Design of Steel Joist Girders”, was
prepared by ( and ) under my
supervision at the civil engineering department in the University of Baghdad, in
partial fulfillment of requirements for the degree of Bachelor of Science in civil
engineering.
Supervisor
Signature:
Name: A. N. LAZEM
Assistant lecturer
(M.Sc., in Structural
Engineering)
Date:

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We certify that we have read this study “Analysis and Design of Steel Joist Girders”
and as examining committee examined the students in its content and in what are
connected to with it and that in our opinion it meets the standard of a study for the
degree of Bachelor of Science in civil engineering.
Committee Member Committee Member
Signature: Signature:
Name: Name:
Date: Date:
Signature:
Name:
Head of Civil Engineering Department
College of Engineering
Baghdad University
Date:

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ABSTRACT:
The objective of this study is to develop a better understanding for the basic principles of the
structural analysis and design of Joist girder so they can be efficiently implemented into
modern computers.
Develop an in-plane structure stiffness matrix that takes into the joist girder variable
Geometry (coordinates, depth, and length) and elements properties (built up sections) and
axial strengths (tensile and compressive) into consideration.
In addition several important parameters have been incorporated in the analysis and design
process; Buckling and stability of web members, chord critical buckling stress, maximum
allowable deflection due to live load, maximum allowable flexural strength (Tensile and
Compressive) according to AISC-89-ASD, and different built-up cross-section (web to chord
elements).
To evaluate the results of presented method were compared with result given in reference
number one. The agreement between both results was quit well.
PROJECT LAYOUT
The project is divided into five chapters as follows:
Chapter one: presents a general introduction to the subject of Joist Girder.
Chapter two: presents the previous literatures published about this subject.
Chapter three: presents the theoretical bases for the Matrix analysis method and Joist
Girder design.
Chapter four: presents a brief description of a computer program developed in this study.
Chapter five: discuses the results of this Analysis/Design method. And recommend future
steps.

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CONTENTS:
Title……………………………………………………………………………………2
Supervisor words……………………………………………………………….3
Committee words………………………………………………………………4
Thanks……………………………………………………………………………….5
Abstract…………………………………………………………………………….6
Project Layout………………………….……………………………………….6
Contents…….……..………………………………………………………………7
Chapter one; introduction…………..….…………………………………8
Chapter two; literature………………….………………………………..12
Chapter three; theory………………………………………………………17
Chapter four; computer program…………………………………….25
Chapter five; conclusions and recommendations…….…….36
References…………………………………………………………………..….39
Appendix I…………………………………………………………………..……40

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Chapter one
Introduction

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1.1.OPEN WEB STEEL JOISTS
Open web steel joists, or “Bar Joists” are very efficient structural members commonly used to
support roofs, and to a lesser degree, floors. Steel joists are NOT considered structural steel.
As such, they are manufactured as proprietary structural members by various manufacturers.
The Steel Joist Institute, SJI, is an organization founded in 1928 that was established to set
standards for manufacture, design and construction of joists. It recognizes manufacturers who
comply with their standards. Some of the larger SJI recognized manufacturers include
Vulcraft, Canam Steel Corp. and SMI Joist Company.
1.2. K-SERIES JOISTS
The most commonly-used joist style is the so-called “K” series. It has a depth ranging from 8”
up to 30” and is used economically to span up to 60’-0”. A typical K series joist is as shown
below:
Fig.(1.1)
Steel joists are fastened to its supporting members usually by field welding as shown
below:

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Fig.(1.2)
Unlike structural steel beams, steel joists must use bridging placed perpendicular to the span
to obtain its stability. This bridging can be one of 2 types:
• Horizontal Bridging
• Diagonal Bridging
Bridging requirements are shown in the Vulcraft Joist Catalog p. (9 and 35) and is a function
of the Section Number and span Joists using horizontal bridging is shown below:
Fig.(1.3)
1.3. LH AND DLH SERIES JOISTS
The LH series joists have depths ranging between 18” and 48” and are suitable for spans up to
96’-0”. The DLH series joists have depths ranging between 52” and 72” and are suitable for
spans up to 144’-0”. They are not as commonly used as K series joists, but provide an
inexpensive alternative to spanning longer distances than the K series joists. One difference
between K series joists is the required end bearing width and height are 6” and 5” respectively
for the LH and DLH (vs. 4” and 2½” for the K series).

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Fig.(1.4)
1.4. JOIST GIRDERS
Joist girders are designed to carry the end reactions from equally-spaced joists applied to the
panel points. Typical depths of joist girders range from 20” up to 96” with spans of 100’-0” or
more.
Fig.(1.5)
A typical joist girder connection to steel column is shown below:

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Fig.(1.6)
Chapter two

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Literature
2.1 LINEAR ANALYSIS OF IN-PLANE STRUCTURES USING STIFFNESS MATRIX METHOD
The theoretical foundation for matrix (stiffness) method of structural analysis was laid and
developed by many scientists:
James, C. Maxwell, [1864] who introduced the method of Consistent Deformations
(flexibility method).
Georg, A. Maney, [1915] who developed the Slope-Deflection method (stiffness method).
These classical methods are considered to be the precursors of the matrix (Flexibility and
Stiffness) method, respectively. In the pre-computer era, the main disadvantage of these
earlier methods was that they required direct solution of Simultaneous Equations (formidable
task by hand calculations in cases more than a few unknowns).
The invention of computers in the late-1940s revolutionized structural analysis. As computers
could solve large systems of Simultaneous Equations, the analysis methods yielding solutions
in that form were no longer at a disadvantage, but in fact were preferred, because
Simultaneous Equations could be expressed in matrix form and conveniently programmed for
solution on computers.

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Levy, S., [1947] is generally considered to have been the first to introduce the flexibility
method, by generalizing the classical method of consistent deformations.
Falkenheimer, H., Langefors, B., and Denke, P. H., [1950], many subsequent researches
extended the flexibility method and expressed in matrix form are:
Livesley, R. K., [1954], is generally considered to have been the first to introduce the stiffness
matrix in 1954, by generalizing the classical method of slop-deflections.
Argyris, J. H., and Kelsey, S., [1954], the two subsequent researches presented a formulation
for stiffness matrices based on Energy Principles.
Turner, M. T., Clough, R. W., and Martin, H. C., [1956], derived stiffness matrices for truss
members and frame members using the finite element approach, and introduced the now
popular Direct Stiffness Method for generating the structure stiffness matrix.
Livesley, R. K., [1956], presented the Nonlinear Formulation of the stiffness method for
stability analysis of frames.
Since the mid-1950s, the development of Stiffness Method has been continued at a
tremendous pace, with research efforts in the recent years directed mainly toward formulating
procedures for Dynamic and Nonlinear analysis of structures, and developing efficient
Computational Techniques (load incremental procedures and Modified Newton-Raphson for
solving nonlinear Equations) for analyzing large structures and large displacements. Among
those researchers are: S. S. Archer, C. Birnstiel, R. H. Gallagher, J. Padlog, J. S.
przemieniecki, C. K. Wang, and E. L. Wilson and many others.
LIVESLEY, R. K. [1964] described the application of the Newton- Raphson procedure to
nonlinear structures. His analysis is general and no equations are presented for framed
structures. However, he did illustrate the analysis of a guyed tower.

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Chapter three
Theory
3.1.1. GENERAL INTRODUCTION TO STIFFNESS METHOD
This method of analyzing structures is probably(14)
used more widely than the flexibility
method, especially for large and complex structures (with multiple nodes). Such structures
require the use of electronic computers for carrying out the extensive numerical calculations,
and the stiffness method is much more suitable for computer programming than the flexibility
method!
The reason is that the stiffness method can be put into the form of a standardized procedure
which dose not requires any engineering decisions during the calculation process. And also
the unknown quantities in the stiffness method are prescribed more clearly than the flexibility
method.
When analyzing a structure by the stiffness method, normally we use the concepts of
kinematic indeterminacy, fixed-end reactions, and stiffnesses. These definitions will be
explained as follows:

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3.1.2. KINEMATIC INDETERMINACY
In stiffness method the unknown quantities in the analysis are the joint displacements of the
structure, rather than the redundant reactions and stress resultants as is the case of flexibility
method. The Joints in any structure will be define as points where two or more members
intersect, the points of support, and the free ends of any projecting members.
When the structure is subjected to loads, all or some of the joints will undergo displacements
in the form of translations and rotations. Of course, some of the joints displacements will be
zero because of the restraint conditions; for instance, at a fixed support there will be no
displacements of any kind.
The unknown joint displacements are called kinematic unknowns and their number is called
either the degree of kinematic indeterminacy or the number of degrees of freedom (DOF) for
joint displacements.
3.1.3. FIXED-END ACTIONS
In stiffness method we regulatory encounter fixed-end beam, because one of the first steps in
this method is to restrain all of the unknown joint displacements. The imposition of such
restrains causes a continuous beam or plane frame to become an assemblage of fixed-end
beams. Therefore, we need to have readily available a collection of formulas for the reactions
of fixed-end beams for multiple case. These reactions which consist of both; forces and
couples (moments), are known collectively as Fixed-End actions. Values of fixed-end actions
for multiple cases are shown in Appendix I.
3.1.4. STIFFNESSES
In the stiffness method we make use of actions caused by unit displacement. These
displacement may be either unit translation (or unit rotation for in-plane frame), and the
resulting actions are either forces of couples (moments). These actions caused by unit
displacement are known as stiffness influence coefficients, or stiffnesses. These coefficients
called also member stiffnesses which they are frequently used in this method. Here by two of
the most useful cases as shown in fig. (3.1).

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Fig.(3.1) Axial Member Stiffnesses.
K14= 0.0
K34 = 0.0
U44= 1.0
K44 = 0.0
K24 = 0.0
L
L = L’
K12= 0.0 K32= 0.0
U22= 1.0
K42 = 0.0
K22 = 0
L
L = L’
K11 = +EA/L K31= - EA/L
U11= 1.0
K41 = 0.0
K21 = 0.0
L
K13= -EA/L K33= +EA/L
U33= 1.0
K43= 0
K23= 0
L

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3.1.5. GENERAL EQUATION OF STIFFNESS METHOD
Now most of the preliminary ideas and definitions have been set fourth, and the problem of
analyzing a structure can be established. Interpreting of Equilibrium Equations, and making
use of the Principles of Superposition, for the case of a structure having (n x n) Degrees of
Kinematic Indeterminacy will lead to the following sets of linear equations are obtained:
𝑆11𝐷1
𝑆21𝐷1
+ 𝑆12𝐷2
+ 𝑆22𝐷2
+ 𝑆13𝐷3
+ 𝑆23𝐷3
: : :
𝑆𝑛1𝐷1 + 𝑆𝑛2𝐷2 + 𝑆𝑛3𝐷3
… … . + 𝑆1𝑛
… … . + 𝑆2𝑛
:
… … . + 𝑆𝑛𝑛
𝐷𝑛
𝐷𝑛
+ 𝐴1
+ 𝐴2
= 𝑃1
= 𝑃2
: : :
𝐷𝑛 + 𝐴𝑛 = 𝑃𝑛
……………….Eq. (1.1)
This can be reduced to General Equation form:
[𝑘]|∆| = |𝑝|…………..Eq. (1.2)
Hence, the principles of superposition are used in developing fixed-end actions (forces),
therefore, this method is limited to linearly elastic structures with small displacements. The n
equations can be solved for the n unknown joint displacement of the structure.
The important fact which need to be established: that Equilibrium Equations of the Stiffness
Method express the superposition of actions (forces) corresponding to unknown
displacements. While the compatibility equations of the Flexibility Method express the
superposition of displacements corresponding unknown actions (forces).
Also; it should be noticed that above equilibrium equations (1.1) are written in a form which
takes into account only the effects of applied loads on the structure, but the equation can be
readily modified to include the effects of temperature changes, restrains, and support
settlements. It is only necessary to include these effects in the determination of the actions
(forces) A1, A2,…, An. Furthermore, Eq. (1.2) apply to many types of structures, including
trusses and space frames, although in this project is limited to in-plane structure (beams), and
hence the stiffness method is applicable only to linearly elastic structures.
3.1.6. STIFFNESS METHOD VERSUS FINITE ELEMENT METHOD (FEM)
Stiffness method can be used to analyze structures only, finite element analysis, which
originated as an extension of matrix (stiffness and flexibility), it is detected to analyze surface
structures (e. g. plates and shells). FEM has now developed to the extent that it can be applied
to structures and solids of practically any shape or form. From theoretical viewpoint, the basic
difference between the two is that, in stiffness method, the member force-displacement
relationships are based on the exact solutions of the underlying differential equations, whereas
in FEM, such relations are generally derived by Work-Energy Principles from assumed
displacement or stress functions.
Because of the approximate nature of its force-displacements relations, FEM analysis yield
approximate results for small node numbers. However, FEM is always more accurate than
stiffness matrix especially in nonlinear analysis.

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3.2. STANDARD SPECIFICATIONS FOR JOIST GIRDERS
AMERICAN NATIONAL STANDARD SJI-JG–1.1, SECTION 1001
Adopted by the Steel Joist Institute November 4, 1985
Revised to November 10, 2003 - Effective March 01, 2005
SECTION 1000- SCOPE
This specification covers the design, manufacture and use of Joist Girders. Load and
Resistance Factor Design (LRFD) and Allowable Strength Design (ASD) are included in this
specification.
DEFINITION
The term “Joist Girders”, as used herein, refers to open web, load-carrying members utilizing
hot-rolled or cold-formed steel, including cold-formed steel whose yield strength* has been
attained by cold working.
The design of Joist Girder chord and web sections shall be based on a yield strength of at least
36 ksi (250 MPa), but not greater than 50 ksi (345 MPa). Steel used for Joist Girder chord or
web sections shall have a minimum yield strength determined in accordance with one of the
procedures specified in Section 1002.2, which is equal to the yield strength assumed in the
design. Joist Girders shall be designed in accordance with this specification to support panel
point loadings.
*The term “Yield Strength” as used herein shall designate the yield level of a material as
determined by the applicable method outlined in paragraph 13.1, “Yield Point” and in
paragraph 13.2, “Yield Strength”, of ASTM Standard A370, “Standard Test Methods and
Definitions for Mechanical Testing of Steel Products”, or as specified in Section 1002.2 of
this Specification.
SECTION 1002- MATERIALS
1002.1 STEEL
The steel used in the manufacture of chord and web sections shall conform to one of the
following ASTM Specifications:
• Carbon Structural Steel, ASTM A36/A36M.
• High-Strength, Low-Alloy Structural Steel, ASTM A242/A242M.
• High-Strength Carbon-Manganese Steel of Structural Quality ASTM A529/A529M, Grade 50.
• High-Strength Low-Alloy Columbium-Vanadium Structural Steel, ASTM A572/A572M
Grade 42 and 50.
• High-Strength Low-Alloy Structural Steel with 50 ksi (345 MPa) Minimum Yield Point to 4
inches (100 mm) Thick, ASTM A588/A588M.
• Steel, Sheet and Strip, High-Strength, Low-Alloy, Hot-Rolled and Cold-Rolled, with
Improved Corrosion Resistance, ASTM A606.
• Steel, Sheet, Cold-Rolled, Carbon, Structural, High-Strength Low-Alloy and High-Strength
Low-Alloy with Improved Formability, ASTM A1008/A1008M.
• Steel, Sheet and Strip, Hot-Rolled, Carbon, Structural, High-Strength Low-Alloy and High-
Strength Low-Alloy with Improved Formability, ASTM A1011/A1011M. or shall be of
suitable quality ordered or produced to other than the listed specifications, provided that such

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material in the state used for final assembly and manufacture is weldable and is proved by
tests performed by the producer or manufacturer to have the properties specified in Section
1002.2.
1002.2 MECHANICAL PROPERTIES
The yield strength used as a basis for the design stresses prescribed in Section 1003 shall be at
least 36 ksi (250 MPa), but shall not be greater than 50 ksi (345 MPa). Evidence that the steel
furnished meets or exceeds the design yield strength shall, if requested, be provided in the
form of an affidavit or by witnessed or certified test reports.
For material used without consideration of increase in yield strength resulting from cold
forming, the specimens shall be taken from as-rolled material. In the case of material
properties of which conform to the requirements of one of the listed specifications, the test
specimens and procedures shall conform to those of such specifications and to ASTM A370.
In the case of material the mechanical properties of which do not conform to the requirements
of one of the listed specifications, the test specimens and procedures shall conform to the
applicable requirements of ASTM A370 and the specimens shall exhibit a yield strength equal
to or exceeding the design yield strength and an elongation of not less than (a) 20 percent in 2
inches (51 millimeters) for sheet and strip, or (b) 18 percent in 8 inches (203 millimeters) for
plates, shapes and bars with adjustments for thickness for plates, shapes and bars as
prescribed in ASTM A36/A36M, A242/A242M, A529/A529M, A572/A572M,
A588/A588M, whichever specification is applicable on the basis of design yield strength.
The number of tests shall be as prescribed in ASTM A6/A6M for plates, shapes, and bars; and
ASTM A606, A1008/A1008M and A1011/A1011M for sheet and strip. If as-formed strength
is utilized, the test reports shall show the results of tests performed on full section specimens
in accordance with the provisions of the AISI Specifications for the Design of Cold-Formed
Steel Structural Members and shall indicate compliance with these provisions and with the
following additional requirements:
a) The yield strength calculated from the test data shall equal or exceed the design yield
strength.
b) Where tension tests are made for acceptance and control purposes, the tensile strength
shall be at least 6 percent greater than the yield strength of the section.
c) Where compression tests are used for acceptance and control purposes, the specimen
shall withstand a gross shortening of 2 percent of its original length without cracking.
The length of the specimen shall not be greater than 20 times its least radius of
gyration.
d) If any test specimen fails to pass the requirements of the subparagraphs (a), (b), or (c)
above, as applicable, two retests shall be made of specimens from the same lot.
Failure of one of the retest specimens to meet such requirements shall be the cause for
rejection of the lot represented by the specimens.
1002.3 WELDING ELECTRODES
The following electrodes shall be used for arc welding:
a) For connected members both having a specified yield strength greater than 36 ksi (250
MPa).
1. AWS A5.1: E70XX
2. AWS A5.5: E70XX-X
3. AWS A5.17: F7XX-EXXX, F7XX-ECXXX flux electrode

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4. combination
5. AWS A5.18: ER70S-X, E70C-XC, E70C-XM
6. AWS A5.20: E7XT-X, E7XT-XM
7. AWS A5.23: F7XX-EXXX-XX, F7XX-ECXXX-XX
8. AWS A5.28: ER70S-XXX, E70C-XXX
9. AWS A5.29: E7XTX-X, E7XTX-XM
b) For connected members both having a specified minimum yield strength of 36 ksi (250
MPa) or one having a specified minimum yield strength of 36 ksi (250 MPa), and the other
having a specified minimum yield strength greater than 36 ksi (250 MPa).
1. AWS A5.1: E60XX
2. AWS A5.17: F6XX-EXXX, F6XX-ECXXX flux electrode
3. combination
4. AWS A5.20: E6XT-X, E6XT-XM
5. AWS A5.29: E6XTX-X, E6XT-XM
or any of those listed in Section 1002.3(a). Other welding methods, providing equivalent
strength as demonstrated by tests, may be used.
1002.4 PAINT
The standard shop paint is intended to protect the steel for only a short period of exposure in
ordinary atmospheric conditions and shall be considered an impermanent and provisional
coating. When specified, the standard shop paint shall conform to one of the following:
a) Steel Structures Painting Council Specification, SSPC No. 15
b) Or, shall be a shop paint which meets the minimum performance requirements of the
above listed specification.
SECTION 1003-DESIGN AND MANUFACTURE
1003.1 METHOD
Joist Girders shall be designed in accordance with this specification as simply supported
primary members. All loads shall be applied through steel joists, and will be equal in
magnitude and evenly spaced along the joist girder top chord. Where any applicable design
feature is not specifically covered herein, the design shall be in accordance with the following
specifications:
a) Where the steel used consists of hot-rolled shapes, bars or plates, use the American
Institute of Steel Construction (AISC), Specification for Structural Steel Buildings.
b) For members that are cold-formed from sheet or strip steel, use the American Iron
and Steel Institute, North American Specification for the Design of Cold-Formed
Steel Structural Members.
Design Basis:
Designs shall be made according to the provisions in this Specification for either; Load and
Resistance Factor Design (LRFD), or for Allowable Strength Design (ASD).
Load Combinations:
LRFD: When load combinations are not specified to the joist manufacturer, the required
stress shall be computed for the factored loads based on the factors and load combinations as
follows:
1.4D
1.2D + 1.6 ( L, or Lr, or S, or R )

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ASD: When load combinations are not specified to the joist manufacturer, the required stress
shall be computed based on the load combinations as follows:
D
D + ( L, or Lr, or S, or R )
Where:
D = dead load due to the weight of the structural elements and the permanent features of the
structure
L = live load due to occupancy and movable equipment
Lr = roof live load
S = snow load
R = load due to initial rainwater or ice exclusive of the ponding contribution
When special loads are specified and the specifying professional does not provide the load
combinations, the provisions of ASCE 7, “Minimum Design Loads for Buildings and Other
Structures” shall be used for LRFD and ASD load combinations.
1003.2 DESIGN AND ALLOWABLE STRESSES
Design Using Load and Resistance Factor Design (LRFD)
Joist Girders shall have their components so proportioned that the required stresses, fu, shall
not exceed Fn where,
fu = required stress ksi (MPa)
Fn = nominal stress ksi (MPa)

Fn = design stress
Design Using Allowable Strength Design (ASD)
Joist Girders shall have their components so proportioned that the required stresses, f, shall
not exceed Fn/
where,
f = required stress ksi (MPa)
Fn = nominal stress ksi (MPa)

Fn/
Stresses:
(a) Tension: t = 0.90 (LRFD) t = 1.67 (ASD)
For Chords: Fy = 50 ksi (345 MPa)
For Webs: Fy = 50 ksi (345 MPa), or Fy = 36 ksi (250 MPa)
Design Stress = 0.9Fy (LRFD) (1003.2-1)
Allowable Stress = 0.6Fy (ASD) (1003.2-2)

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(b) Compression: c = 0.90 (LRFD) c = 1.67 (ASD)
Where Fe = Elastic bucking stress determined in accordance with Equation 1003.2-5.
For hot-rolled sections, “Q” is the full reduction factor for slender compression elements.
Design Stress = 0.9 Fcr (LRFD) (1003.2-6)
Allowable Stress = 0.6 Fcr (ASD) (1003.2-7)
i. In the above equations, l is taken as the distance, in inches (millimeters), between
panel points for the chord members and the appropriate length for web members, and
r is the corresponding least radius of gyration of the member or any component
thereof. E is equal to 29,000 ksi (200,000 MPa).
ii. Use 1.2 l/rx for a crimped, first primary compression web member when a moment-
resistant weld group is not used for this member; where rx = member radius of
gyration in the plane of the joist.
iii. For cold-formed sections, the method of calculating the nominal column strength is
given in the AISI, North American Specification for the Design of Cold-Formed Steel
Structural Members.
(c) Bending: b = 0.90 (LRFD) b = 1.67 (ASD)
Bending calculations are to be based on using the elastic section modulus.
1- For chords and web members other than solid rounds:
Fy = 50 ksi (345 MPa)
Design Stress = 0.90 Fy (LRFD) (1003.2-8)
Allowable Stress = 0.60 Fy (ASD) (1003.2-9)
2- For web members of solid round cross section:
Fy = 50 ksi (345 MPa), or Fy = 36 ksi (250 MPa)
3- For bearing plates:
Fy = 50 ksi (345 MPa), or Fy = 36 ksi (250 MPa)

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(d) Weld Strength:
Shear at throat of fillet welds:
Nominal Shear Stress = Fnw = 0.6Fexx (1003.2-14)
LRFD: w = 0.75
Design Shear Strength = Rn = wFnw A = 0.45Fexx A (1003.2-15)
ASD: w = 2.0
Allowable Shear Strength = (1003.2-16)
Rn /w = FnwA/w = 0.3Fexx A
A = effective throat area
Made with E70 series electrodes or F7XX-EXXX fluxelectrode combinations:
Fexx = 70 ksi (483 MPa)
Made with E60 series electrodes or F6XX-EXXX fluxelectrode combinations:
Fexx = 60 ksi (414 MPa)
Tension or compression on groove or butt welds shall be the same as those specified for the
connected material.
1003.3 MAXIMUM SLENDERNESS RATIOS
The slenderness ratio l/r, where l is the length center-to center of support points and r is the
corresponding least radius of gyration, shall not exceed the following:
Top chord end panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Top chord end panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Compression members other than top chord . . . . . . ………………… . . . 200
Tension members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
1003.4 MEMBERS
(a) Chords
i. The bottom chord shall be designed as an axially loaded tension member. The radius
of gyration of the bottom chord about its vertical axis shall not be less than l/240
where l is the distance between lines of bracing.
ii. The top chord shall be designed as an axial loaded compression member. The radius
of gyration of the top chord about the vertical axis shall not be less than Span/575.
iii. The top chord shall be considered as stayed laterally by the steel joists provided
positive attachment is made.
(b) Web

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i. The vertical shears to be used in the design of the web members shall be determined
from full loading, but such vertical shear shall be not less than 25 percent of the end
reaction.
ii. Interior vertical web members used in modified Warren type web systems that do not
support the direct loads through steel joists shall be designed to resist an axial load of
2 percent of the top chord axial force.
iii. Tension members shall be designed to resist at least 25 percent of their axial force in
compression.
(c) Fillers and Ties
In compression members composed of two components, when fillers, ties or welds are used,
they shall be spaced so the l/r ratio for each component does not exceed the l/r ratio of the
member as a whole. In tension members composed of two components, when fillers, ties or
welds are used, they shall be spaced so that the l/r ratio of each component does not exceed
240. The least radius of gyration shall be used in computing the l/r ratio of a component.
(d) Eccentricity
Members connected at a joint shall have their center of gravity lines meet at a point, if
practical. Eccentricity on either side of the centroid of chord members may be neglected when
it does not exceed the distance between the centroid and the back of the chord. Otherwise,
provision shall be made for the stresses due to eccentricity. Ends of Joist Girders shall be
proportioned to resist bending produced by eccentricity at the support. In those cases where a
single angle compression member is attached to the outside of the stem of a tee or double
angle chord, due consideration shall be given to eccentricity.
(e) Extended Ends
Extended top chords or full depth cantilever ends require the special attention of the
specifying professional. The magnitude and location of the loads to be supported, deflection
requirements, and proper bracing shall be clearly indicated on the structural drawings.
1003.5 CONNECTIONS
(a) Methods
Joint connections and splices shall be made by attaching the members to one another by arc or
resistance welding or other accredited methods.
(1) Welded Connections
a) Selected welds shall be inspected visually by the manufacturer. Prior to this
inspection, weld slag shall be removed.
b) Cracks are not acceptable and shall be repaired.
c) Thorough fusion shall exist between layers of weld metal and between weld
metal and base metal for the required design length of the weld; such fusion
shall be verified by visual inspection.
d) Unfilled weld craters shall not be included in the design length of the weld.
e) Undercut shall not exceed 1/16 inch (2 millimeters) for welds oriented
parallel to the principal stress.
f) The sum of surface (piping) porosity diameters shall not exceed 1/16 inch (2
millimeters) in any 1 inch (25 millimeters) of design weld length.
g) Weld spatter that does not interfere with paint coverage is acceptable.

25
(2) Welding Program
Manufacturers shall have a program for establishing weld procedures and operator
qualification, and for weld sampling and testing.
(3) Weld Inspection by Outside Agencies (See Section 1004.10 of this specification).
The agency shall arrange for visual inspection to determine that welds meet the acceptance
standards of Section 1003.5(a)(1). Ultrasonic, X-Ray, and magnetic particle testing are
inappropriate for Joists Girders due to the configurations of the components and welds.
(b) Strength
(1) Joint Connections – Joint connections shall develop the maximum force due to any of
the design loads, but not less than 50 percent of the strength of the member in tension
or compression, whichever force is the controlling factor in the selection of the
member.
(2) Shop Splices - Shop splices may occur at any point in chord or web members. Splices
shall be designed for the member force but not less than 50 percent of the member
strength. Members containing a butt weld splice shall develop an ultimate tensile
force of at least 57 ksi (393 MPa) times the full design area of the chord or web. The
term “member” shall be defined as all component parts comprising the chord or web,
at the point of splice.
(c) Field Splices
Field Splices shall be designed by the manufacturer and may be either bolted or welded.
Splices shall be designed for the member force, but not less than 50 percent of the member
strength.
1003.6 CAMBER
Joist Girders shall have approximate cambers in accordance with the following:
TABLE 1003.6-1
Top Chord Length Approximate Camber
------------------------- ------------------------------
20'-0" (6096 mm) 1/4" (6 mm)
30'-0" (9144 mm) 3/8" (10 mm)
40'-0" (12192 mm) 5/8" (16 mm)
50'-0" (15240 mm) 1" (25 mm)
60'-0" (18288 mm) 1 1/2" (38 mm)
70'-0" (21336 mm) 2" (51 mm)
80'-0" (24384 mm) 2 3/4" (70 mm)
90'-0" (27342 mm) 3 1/2" (89 mm)
100'-0" (30480 mm) 4 1/4" (108 mm)
110'-0" (33528 mm) 5" (127 mm)
120'-0" (36576 mm) 6" (152 mm)
The specifying professional shall give consideration to coordinating Joist Girder camber with adjacent
framing.
1003.7 VERIFICATION OF DESIGN AND MANUFACTURE
(a) Design Calculations
Companies manufacturing Joist Girders shall submit design data to the Steel Joist Institute (or
an independent agency approved by the Steel Joist Institute) for verification of compliance
with the SJI Specifications.

26
(b) In-Plant Inspections
Each manufacturer shall verify their ability to manufacture Joist Girders through periodic In-
Plant Inspections. Inspections shall be performed by an independent agency approved by the
Steel Joist Institute. The frequency, manner of inspection, and manner of reporting shall be
determined by the Steel Joist Institute. The In-Plant Inspections are not a guarantee of the
quality of any specific Joist Girder; this responsibility lies fully and solely with the individual
manufacturer.
SECTION 1004-APPLICATION
1004.1 USAGE
This specification shall apply to any type of structure where steel joists are to be supported
directly by Joist Girders installed as hereinafter specified. Where Joist Girders are used other
than on simple spans under equal concentrated gravity loading, as prescribed in Section
1003.1, they shall be investigated and modified if necessary to limit the unit stresses to those
listed in Section 1003.2. The magnitude and location of all loads and forces, other than equal
concentrated gravity loading, shall be provided on the structural drawings. The specifying
professional shall design the supporting structure, including the design of columns,
connections, and moment plates*.
This design shall account for the stresses caused by lateral forces and the stresses due to
connecting the bottom chord to the column or other support. The designed detail of a rigid
type connection and moment plates shall be shown on the structural drawings by the
specifying professional. The moment plates shall be furnished by other than the joist
manufacturer.
* For further reference, refer to Steel Joist Institute Technical Digest #11, “Design of Joist-
Girder Frames”
1004.2 SPAN
The span of a Joist Girder shall not exceed 24 times its depth.
1004.3 DEPTH
Joist Girders may have either parallel top chords or a top chord slope of 1/8 inch per foot
(1:96). The nominal depth of sloping chord Joist Girders shall be the depth at mid-span.
1004.4 END SUPPORTS
(A) Masonry and Concrete
Joist Girders supported by masonry or concrete are to bear on steel bearing plates and shall be
designed as steel bearing.
Due consideration of the end reactions and all other vertical and lateral forces shall be taken
by the specifying professional in the design of the steel bearing plate and the masonry or
concrete. The ends of Joist Girders shall extend a distance of not less than 6 inches (152
millimeters) over the masonry or concrete support and be anchored to the steel bearing plate.
The plate shall be located not more than 1/2 inch (13 millimeters) from the face of the wall
and shall be not less than 9 inches (229 millimeters) wide perpendicular to the length of the

27
girder. The plate is to be designed by the specifying professional and shall be furnished by
other than the joist manufacturer.
Where it is deemed necessary to bear less than 6 inches (152 millimeters) over the masonry or
concrete support, special consideration is to be given to the design of the steel bearing plate
and the masonry or concrete by the specifying professional. The girders must bear a minimum
of 4 inches (102 millimeters) on the steel bearing plate.
(B) Steel
Due consideration of the end reactions and all other vertical and lateral forces shall be taken
by the specifying professional in the design of the steel support. The ends of Joist Girders
shall extend a distance of not less than 4 inches (102 millimeters) over the steel supports and
shall have positive attachment to the support, either by bolting or welding.
1004.5 BRACING
Joist Girders shall be proportioned such that they can be erected without bridging (See
Section 1004.9 for bracing required for uplift forces). Therefore, the following requirements
must be met:
a) The ends of the bottom chord are restrained from lateral movement to brace the girder from
overturning. For Joist Girders at columns in steel frames, restraint shall be provided by a
stabilizer plate on the column.
b) No other loads shall be placed on the Joist Girder until the steel joists bearing on the girder
are in place and welded to the girder.
1004.6 END ANCHORAGE
(A) Masonry and Concrete
Ends of Joist Girders resting on steel bearing plates on masonry or structural concrete shall be
attached thereto with a minimum of two 1/4 inch (6 millimeters) fillet welds 2 inches (51
millimeters) long, or with two 3/4 inch (19 millimeters) bolts, or the equivalent.
(B) Steel
Ends of Joist Girders resting on steel supports shall be attached thereto with a minimum of
two 1/4 inch (6 millimeters) fillet welds 2 inches (51 millimeters) long, or with two 3/4 inch
(19 millimeters) bolts, or the equivalent. In steel frames, bearing seats for Joist Girders shall
be fabricated to allow for field bolting.
(C) Uplift
Where uplift forces are a design consideration, roof Joist Girders shall be anchored to resist
such forces (Refer to Section 1004.9).
1004.7 DEFLECTION
The deflections due to the design live load shall not exceed the following:
I. Floors: 1/360 of span.
II. Roofs: 1/360 of span; where a plaster ceiling is attached or suspended.
III. 1/240 of span for all other cases.

28
The specifying professional shall give consideration to the effects of deflection and vibration*
in the selection of Joist Girders.* For further reference, refer to Steel Joist Institute Technical
Digest #5, “Vibration of Steel Joist-Concrete Slab Floors” and the Institute’s Computer
Vibration Program.
1004.8 PONDING*
The ponding investigation shall be performed by the specifying professional. * For further
reference, refer to Steel Joist Institute Technical Digest #3, “Structural Design of Steel Joist
Roofs to Resist Ponding Loads” and AISC Specifications.
1004.9 UPLIFT
Where uplift forces due to wind are a design requirement, these forces must be indicated on
the contract drawings in terms of NET uplift in pounds per square foot (Pascals). The contract
drawings must indicate if the net uplift is based on ASD or LRFD. When these forces are
specified, they must be considered in the design of Joist Girders and/or bracing.
If the ends of the bottom chord are not strutted, bracing must be provided near the first bottom
chord panel points whenever uplift due to wind forces is a design consideration.* * For
further reference, refer to Steel Joist Institute Technical Digest #6, “Structural Design of Steel
Joist Roofs to Resist Uplift Loads”.
1004.10 INSPECTION
Joist Girders shall be inspected by the manufacturer before shipment to verify compliance of
materials and workmanship with the requirements of this specification. If the purchaser
wishes an inspection of the Joist Girders by someone other than the manufacturer’s own
inspectors, they may reserve the right to do so in their “Invitation to Bid” or the
accompanying “Job Specifications”. Arrangements shall be made with the manufacturer for
such inspection of the Joist Girders at the manufacturing shop by the purchaser’s inspectors at
purchaser’s expense.
SECTION 1005-HANDLING AND ERECTION
Particular attention should be paid to the erection of Joist Girders. Care shall be exercised at
all times to avoid damage through careless handling during unloading, storing and erecting.
Dropping of Joist Girders shall not be permitted. In steel framing, where Joist Girders are
utilized at column lines, the Joist Girder shall be field-bolted at the column. Before hoisting
cables are released and before an employee is allowed on the Joist Girder the following
conditions must be met:
a) The seat at each end of the Joist Girder is attached in accordance with Section 1004.6.
When a bolted seat connection is used for erection purposes, as a minimum, the bolts
must be snug tightened. The snug tight condition is defined as the tightness that exists
when all plies of a joint are in firm contact. This may be attained by a few impacts of
an impact wrench or the full effort of an employee using an ordinary spud wrench.
b) Where stabilizer plates are required the Joist Girder bottom chord must engage the
stabilizer plate. During the construction period, the contractor shall provide means for
the adequate distribution of loads so that the carrying capacity of any Joist Girder is
not exceeded.
Joist Girders shall not be used as anchorage points for a fall arrest system unless written
direction to do so is obtained from a “qualified person”.(1) Field welding shall not damage
the Joist Girder. The total length of weld at any one cross-section on cold-formed members
whose yield strength has been attained by cold working and whose as-formed strength is used
in the design, shall not exceed 50 percent of the overall developed width of the cold-formed
section. * For a thorough coverage of this topic, refer to SJI Technical Digest #9, “Handling

29
and Erection of Steel Joists and Joist Girders”. (1) See Appendix E for OSHA definition of
“qualified person”.
SECTION 1006-HOW TO SPECIFY JOIST GIRDERS
For a given Joist Girder span, the specifying professional first determines the number of joist
spaces. Then the panel point loads are calculated and a depth is selected. The following tables
give the Joist Girder weight in pounds per linear foot (kilo-Newton per meter) for various
depths and loads.
1. The purpose of the Joist Girder Design Guide Weight Table is to assist the specifying
professional in the selection of a roof or floor support system.
2. It is not necessary to use only the depths, spans, or loads shown in the tables.
3. Holes in chord elements present special problems which must be considered by both
the specifying professional and the Joist Girder Manufacturer. The sizes and locations
of such holes shall be clearly indicated on the structural drawings.
Chapter four
COMPUTER PROGRAM

30
4.1 PROGRAM PROCEDURE
This chapter presents a brief description of the computer program developed in this study
which governs the problem of analysis and design of in-plane structure (JOIST GIRDER)
using Stiffness Matrix as Method (S.M.M.). The program was written using MATLAB
(version 7), it is consist of three major parts; first the analysis of the in-plane structure.
Second part is the design of plate girder elements. Third part is the checking of joist girder
elements stresses according to the AISC-89 Design Manual using ASD designing method.
Based on theoretical equations presented in previous chapter, the following step-by-step
procedure for the analysis of In-plane structures (Trusses) using Stiffness Matrix Method.
The sign convention used in this analysis is as follow: the joint translations are considered
positive when they act in positive direction of Y-axis, and joint rotations are considered
positive when they rotate in counterclockwise direction:
Prepare the analytical model of in-plane structure, as follows:
1. Draw a line diagram of the in-plane structure (beam), and identify each joint member
by a number.
2. Determine the origin of the global (X-Y) coordinate system (G.C.S.). It is usually
located to the lower left joint, with the X and Y axes oriented in the horizontal
(positive to the right) and vertical (positive upward) directions, respectively.
3. For each member, establish a local (x-y) coordinate system (L.C.S), with the left end
(beginning) of the member, and the x and y axes oriented in the horizontal (positive
to the right) and vertical (positive upward) directions, respectively.
4. Number the degrees of freedom and restrained coordinates of the beam elements and
nodes.
5. Evaluate the Overall Stiffness Matrix [k], and Fixed-End forces Vector {Pf}. The
number of rows & columns of [S] must be equal to the number of DOF of the
structure. For each element of the in-plane structure, perform the following
operations:
a) Compute the Element stiffness matrix [ke
] in (L.C.S) by apply the basic stiffness
equation, as follow:

31
a. {𝑓} = [𝑘𝑒]{𝑒}.
b) Transform the force vector {𝑓} form (L.C.S) to {𝑃} in (G.C.S.) using
transformation matrix [A], as follow:
a. {𝑃} = [𝐴]{𝑓}.
c) Transform the deformation vector {𝑒}form (L.C.S) to {𝑋} (G.C.S.) using
transformation matrix [B], as follow:
a. {𝑒} = [𝐵]{𝑋}.
d) It is evident that matrix [B] is the transpose of matrix [A], therefore ;
a. {𝑒} = [𝐴]𝑇{𝑋}.
e) Substituting step (d) in step (a), resulting in:
a. {𝑓} = [𝑘𝑒][𝐴]𝑇{𝑋}.
f) Substituting step (e) in step (b), resulting in:
a. {𝑃} = [𝐴][𝑘𝑒][𝐴]𝑇{𝑋}.
g) Inverting equation in step (f), resulting in:
a. {𝑋} = [[𝐴][𝑘𝑒][𝐴]𝑇
]−1{𝑃}.
h) Store the element stiffness matrix, in (G.C.S.), [𝑘𝑒
] = [[𝐴][𝑘𝑒][𝐴]𝑇
]−1
, for each
element.
6. Assemble Overall Stiffness Matrix [K] for the System of in-plane structure. By
assembling the element stiffness matrices for each element in the in-plane structure,
using their proper positions in the in-plane structure Stiffness Matrix [K], and it must
be symmetric.
7. Compute the Joint load vector {Pj} for each joint of the in-plane structure.
8. Determine the structure joint displacements {X}. Substitute {P}, {Pe}, and [K] into
the structure stiffness relations, {𝑃𝑗} = [𝐾]{𝑋} .and solve the resulting system of
simultaneous equations for the unknown joint displacements {X}.
9. Compute Element end displacement {e} and end forces {f}, and support reactions.
For each Element of the beam, as following:
10. Obtain Element end displacements {e} form the joint displacements {X}, using the
Element code numbers.
11. Compute Element end forces {f}, using the following relationship:
{𝑓} = [𝑘𝑒]{𝑒}.
12. Using the Element code numbers, store the pertinent elements of {f}, in their proper
position in the Support Reaction Vector {R}
13. Check the calculation of the member end-forces and support reactions by applying
the Equation of Equilibrium to the free body of the entire in-plane structure;
∑ Fy = 0
𝑛
𝑖=0 , ∑ Mz = 0
𝑛
𝑖=0

32
4.2 FLOW CHART OF COMPUTER PROGRAM
Is all checks
is OK?
Solve for unknowns displacement {d}=[K]-1
{d}
Assemble Overall Stiffness
Matrix of system [K]
Build Element Stiffness
Matrix in G.C.S.
[ke
] (I, ND, ND)
START
Re-correct
cross-section to
satisfy required
conditions
No
Yes
INPUT UNIT FOR LOADING CONDITIONS
For each node (1  NN) of the In-plane Structure read the following:
-Joint loads.
-Predefined displacements.
IN-PLANE STRUCTURE INPUT UNIT
For each element (1  NE) of the In-plane Structure read the following:
Geometry of In-plane structure (x, y), Elastic properties (E, G, µ…),
Cross-section properties (Ag, Ix, rx, d, b, t…), and Boundary conditions (DOF)

33
4.3 COMPUTER PROGRAM APPLICATION:
Two major case studies will be investigated to In the first case five different joist girder depth
will be investigated starting form (72”) to (80”).
4.3.1. First Case study:
Given A roof framing 36'-0" x 60"-0" bay (as shown bellow Figure). The following are the
service loads:
 Service Dead Load = 16 PSF
 Service Roof Live Load = 25 PSF
 Service Snow Load = 35 PSF
 Service Wind Uplift = -12 PSF
Required: design the joist girder that will carry a K series joist with maximum spacing of (6'-
0") center to center (based on metal roof deck). Assume the joist (28K6) accessories weights
is 10 PLF
Step 1: Determine joist girder depth and orientation:
END
Evaluate Internal Forces, in L.C.S., of in-plane structure
elements: F (NE, 6). Then calculate Reaction forces
OUTPUT UNIT
Printout global displacement, in G.C.S.,
(Vertical, horizontal and rotations) (1NN)
OUTPUT UNIT
Print Internal Forces, in L.C.S, (Axial Force, Sear Force,
and Bending Moment) for left and right side of each
element: (1NE)

34
Assuming that the K series joist are distributed equally parallel to the short dirction (36, for
higher strength) giving us a 10 even spaces (as shown bellow Figure).
Step 2: determine uniformly distributed service load (using ASD-IBC, load
combinations):
D + (W or 0.7E) + L + (Lr or S or R) Eq.(4.1)
where:
D = Dead Load
= 6’(16 PSF) + 10 PLF = 106 PLF
Lr = Roof Live Load
= 6’(25 PSF) = 150 PLF
S = Snow Load
= 6’(35 PSF) = 210 PLF
W = Wind Load
= 6’(-12 PSF) = -72 PLF
Applying Eq.(4.1), yields:
D + (W or 0.7E) + L + (Lr or S or R)= 106 + 210 = 316 PLF
Step 3: Determine 28K6 joist end reactions:
Joist end reaction = wL / 2
= (316 PLF)(36'−0") / 2
= 5688 lb.
= 5.7 KIPS → USE 6 kip
Step 4: depending on the provisions given by the SJI-2005(ASD) calculate the
following:
a) Determine number of actual joist spaces (N). In this Case, N = 10
b) Compute (total service load) concentrated load at top chord panel points
1. P = 6 kip.
c) Select Joist Girder depth:
I. Refer to the ASD Joist Girder Design Guide Weight Table for the 42'-0"
span, 8 panel, 18.0K Joist Girder. The rule of about one inch of depth for
each foot of span is a good compromise of limited depth and economy.
Therefore, select a depth of 72 inches (slightly larger).
II. The Joist Girder will then be designated 72G10N6K JOIST GIRDER. Note
that the letter “K” is included at the end of the designation to clearly indicate
that this is a service load.

35
III. The ASD Joist Girder Design Guide Weight Table shows the weight for a
72G10N6K as 35 PLF. AS it appear (35<< 106 PLF) which verify that the
weight is not greater than the weight assumed in the Dead Load above.
d) Select a trail joist girder section for assumed depth;
I. Select 2L2.1/2x2.1/2x8/16 for chord members (top & bot.) Fig(4.1.b.a)
II. Select 2L2.x2.x6/16 for web members (diagonal).
e) Check live load deflection:
Live load = 960 PLF
I. Approximate Joist Girder moment of inertia
a. = 0.018 NPLd
b. = 0.018 x 10 x 6 x 60 x 72 = 4665.6 in.4
II. Allowable deflection for plastered ceilings
a. = L/360 = 2.0 in.
1.38 in. < 2.0 in., Okay**
** Live load deflection rarely governs because of the relatively small span-depth ratios of Joist
Girders.
Step 5: apply calculated panel load with (P = 6 kip) into the computer program and
check internal forces and stresses with allowable limits given by AISC-89-ASD, as
follows;

36
Fig.(4.1) In-plane structure layout
Fig.(4.1.a), Joist Girder layout
(a) Double angles
with opposite web
angles joist girder
(d) Channel section with
opposite web angles joist
girder
(e) Circular section with triple
girder
Fig.(4.1.b), Different Joist Girder cross-sections
(c) Double angles with
single web bar joist
girder
Brick wall
(0.25 x L) m
P P P P P P P P P
Brick wall
(0.25 x L) m
Girder
Depth (D)
Spacing
Depth (S)
Span (L)

37
Fig.(4.2) Vertical Displacement Diagram
Fig.(4.3) Horizontal Displacement Diagram
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 72 144 216 288 360 432 504 576 648 720
Displacements
(in)
Joist Girder length (in)
load case one
load case two
load case three
load case four
load case five
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0 72 144 216 288 360 432 504 576 648 720
Displacements
(in)
load case one
load case two
load case three
load case four
load case five

38
Fig.(4.4) Compressive Forces Distribution
Fig.(4.5) Tensile Forces Distribution
0
5
10
15
20
25
30
35
0 72 144 216 288 360 432 504 576 648 720
Force
(kip)
load case one
load case two
load case three
load case four
load case five
0
10
20
30
40
50
60
70
80
0 72 144 216 288 360 432 504 576 648 720
Force
(kip)
load case one
load case two
load case three
load case four
load case five

39
Fig.(4.6) Actual Axial Stresses Versus Allowable Stress
-25
-20
-15
-10
-5
0
5
10
15
20
0 72 144 216 288 360 432 504 576 648 720
Stress
(ksi)
Allowable Compressive Stress
Allowable Tensile Stress
load case one
load case two
load case three
load case four
load case five

40
4.3.2. Second Case study:
Repeating same above design example but with different variable, i.e. variables Concentrated
Panel Loads will be investigated starting form (6 kip) to (8 kip);
Fig.(4.7) In-plane structure layout
Fig.(4.7.a), Joist Girder layout
(a) Double angles
with opposite web
angles joist girder
(d) Channel section with
girder
(e) Circular section with triple
girder
Fig.(4.7.b), Different Joist Girder cross-sections
(c) Double angles with
single web bar joist
girder
Brick wall
(0.25 x L) m
P P P P P P P P P
Brick wall
(0.25 x L) m
Girder
Depth (D)
Spacing
Depth (S)
Span (L)

41
Fig.(4.8) Vertical Displacement Diagram
Fig.(4.9) Horizontal Displacement Diagram
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 72 144 216 288 360 432 504 576 648 720
Displacements
(in)
load case one
load case two
load case three
load case four
load case five
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0 72 144 216 288 360 432 504 576 648 720
Displacements
(in)
load case one
load case two
load case three
load case four
load case five

42
Fig.(4.10) Compressive Forces Distribution
Fig.(4.11) Tensile Forces Distribution
0
5
10
15
20
25
30
35
40
45
0 72 144 216 288 360 432 504 576 648 720
Force
(kip)
load case one
load case two
load case three
load case four
load case five
0
20
40
60
80
100
120
0 72 144 216 288 360 432 504 576 648 720
Force
(kip)
load case one
load case two
load case three
load case four
load case five

43
Fig.(4.12) Actual Axial Stresses versus Axial Stresses
-25
-20
-15
-10
-5
0
5
10
15
20
0 72 144 216 288 360 432 504 576 648 720
Stress
(ksi)
Allowable Compressive Stress
Allowable Tensile Stress
load case one
load case two
load case three
load case four
load case five

44
Chapter five
Conclusions and Recommendations

45
CONCLUSIONS
Depending on the results obtained from the present study, several conclusions may be
established; these may be summarized as follows:
Results indicate that in-plane structures (Joist Girder) can be can be dealt with successfully
by the Stiffness Matrix Method.
Developed Program in this study is quite efficient and reliable for both analysis and design.
The analysis process can be carried out rapidly on electronic computer. On other hand the
design process developed in this study is quit forward and easy to implement which depends
on the design criteria given by AISC-89 design manual (Allowable Stress Design).
Two case studies have been investigated, the first is variable girder depth, and results indicate
the following:
1. Increasing Joist Girder Depth will increase the Flexural Capacity of joist girder.
2. Increasing Girder Depth will reduce both vertical and (in-less degree) horizontal
displacements of joist girder. Because joist girder become stiffer (larger stiffness
matrix).
3. Increasing Girder Depth will reduce both Tensile and Compressive forces of joist
girder. But it should make carful than compression members dose not crossed their
maximum slenderness ratio otherwise it will fail because of local buckling and not by
yielding.
4. Using Intermediate Vertical members (4-5, 8-9, 12-13, and 16-17) will prevent
future failure because of suspended accessories (HVAC) although it is redundant in
present case.
5. Continuously supported Joist girder (with same Depth) is more practical than simply
supported joist type. Because of their less developed displacements and internal axial
forces.
6. Using Bearing Stiffener will prevent both local buckling and web shearing failure
of joist girder at supports and uniformly transfer the reaction forces to supports
(brick, concrete wall, or structural steel section).
7. Using above solution (depth increasing) is more practical in reducing yielding stress
in tension members and also reducing displacements, but it is not recommended for
reducing compression stresses because it inversely proportional to slenderness ratio
for each member.
The second is the variable applied load till failure, results indicate the following:
1. Tension members are much vulnerable than compression members, as it appear form
their higher response in Stress Figure, this is because of their higher magnitude than
compression members which originally developed because of the joist girder certain
geometry.
2. Vertical displacements are directly proportional to applied joint loads magnitudes.
And in-less degree the horizontal displacements will be effected.
3. Increasing applied joint loads will significantly increase the tension forces. And in-
less degree horizontal displacements will be effected.
4. Increasing Girder Depth will reduce both Tensile and Compressive forces of joist
girder. But it should make carful than compression members dose not crossed their

46
maximum slenderness ratio otherwise it will fail because of local buckling and not by
yielding.
5. Tension members are much vulnerable than compression members, as it appear form
their high response in Stress Figure, this is because of their higher magnitude than
compression members which originally developed because of the joist girder certain
geometry.
Presented results indicate that:
In order to overcome member, Critical Tensile Stresses Case, an additional depth could be
implemented for entire joist girder as long as maximum slenderness ratio is not crossed or
simply increase the gross-section area of critical members, but it is not recommended since it
is not economical solution.
Another solution could be used is to make much revised program to find most appropriate
geometry (optimization process) which will produce minimum axial forces.
RECOMMENDATIONS
The analysis method, presented in this study for in-plane structures, could be extended to
include the following factors:
 Semi-rigid connections effects on internal forces.
 Three-dimension analysis is more accurate than in-plane analysis.
 Shear deformation especially for deep joist girder than long beam.
 Applying different cross-sections of joist girder, as shown in girder layout Fig(4.1),
and searching for best built-up section.
 Optimization process could be included to cover economical part.
 Camper joist with different geometry could be also studied to find best geometry for
certain case.
 Composite joist girder (only at joists of truss) to find the percentage of additional
strength given by this solution.

47
REFERENCES
1. AMERICAN NATIONAL STANDARD SJI-JG–1.1, SECTION 1001. Adopted by the Steel
Joist Institute November 4, 1985 ( Revised to November 10, 2003 - Effective March 01,
2005).
2. Manual Of Steel Construction (ASIC-1989,Allowable Stress Design), ninth edition.
3. Asalam Kassimali, “Matrix A nalysis of Structures”, Brooks/ Cole Publishing Company,
1999.
4. Syal, I. C., and Satinder S., "Design of steel structures.", Standard Publishers Distributers,
Delhi, 2000.
5. Dayaramtnam. P., "Design of steel structures.", Chand S. Company ltd. for publishing ,
NewDelhi, 2003.
6. Livesley, R. K., and Chandler D. B., "Stability Functions for Structural Frameworks."
Manchester University Press, Manchester, 1956.
7. Livesley, R.K., "The Application of an Electronic Digital Computer to Some Problem of
Structural Analysis." The Structural Engineer, Vol. 34, no.1, London, 1956, PP. 1-12.
8. Argyris, J.H., "Recent Advances in Matrix Methods of Structural Analysis." Pergamon Press,
London, 1964, PP. 115-145.
9. Livesley, R.K., "Matrix Methods of Structural Analysis." Pergamon Press, London, 1964.
PP. 241-252.
10. Bowles, J. E., "Analytical and Computer Methods in Foundation Engineering." McGraw-
Hill Book Co., New York, 1974, pp. 190-210.
11. Bowles, J. E., "Foundation analysis and design" McGraw-Hill Book Co., New York, 1986,
Fourth Edition, pp. 380-230.
12. BowMles, J. E., "Mat Design." ACI Journal, Vol. 83, No.6, Nov.-Dec. 1986, pp. 1010- 1017.
13. Timoshenko, S.P. and Gere, J.M., "Theory of Elastic Stability." 2nd Edition, McGraw-Hill
Book Company, New York, 1961, pp. 1-17.
14. Timoshenko, S.P. and Gere, J.M., "Mechanics of Materials." 2nd Edition, Von Nostrand
Reinhold Book Company, England, 1978.
15. KassimAli, A., "Large Deformation Analysis of Elastic Plastic Frames," Journal of Structural
Engineering, ASCE, Vol. 109, No. 8, August, 1983, pp. 1869-1886.
16. Lazim, A. N., "Large Displacement Elastic Stability of Elastic Framed Structures Resting On
Elastic Foundation" M.Sc. Thesis, University of Technology, Baghdad, 2003, pp. 42-123.

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