steel and timbe
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Chapter One: Introduction, Material and Design Concepts
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Design of Steel and Timber Structures CE-519 Yibeltal T.
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Chapter One: Introduction, Material and Design Concepts
1.1 Introduction
Structures whose major constituent components are steel are known as steel structure
while those with large proportion of timber components timber structures. As it will be
noted from subsequent presentations, there are great many steel and timber structures in
engineering practice
Steel and timber are used both in structural and non-structural members in various civil
engineering applications such as buildings of various types, bridges, power transmission and
communication towers, windmills, off-shore oil and gas facilities, reservoirs and other
storage structures, mines, among others. In particular, steel may also be used as a cable
system in suspension- and cable-stayed structures such as suspension bridges, cable-
supported roofs and cable-stayed towers. Their structural engineering applications of steel
also extend to manufacture of space- and aircrafts, ship structures
The main component of this coursework will be dealing with steel structures. The various
design concepts and detailing procedures for timber are similar to those involved in steel
structures and, thus, similar computational and detailing operations are followed for their
planning. Steel structures are of so many types that it is difficult, if not impossible, to
classify them on the bases of their service, shape, size or methods involved in their design.
However, from structural point of view they can be broadly categorized as either frame or
skeletal types, or shell- and plate-type structures.
Framed structures are the primary topic for discussion in this course work. They consist of
an assemblage of elongated or one-dimensional members such as roof trusses, latticed
towers, beams, columns, etc
Shell- and plate-type structures are mostly made up of steel sheets. In such structures
loads are mostly taken up by the sheet plates, which also serve as covering materials. Tanks,
aircrafts and shell-roof coverings are some examples of shell structures
Areas of Application
While some of the main applications outlined below are also related to timber, steel
structural members have found, the widest use in the fol1owing types of structures.
Framework or skeletal systems
The framework of industrial building and related structures like crane girders, platforms, etc.
Railway, highway, pedestrian and other large- and small-span bridges. Very tall multi-story buildings, exhibition pavilions, roofs, floors, domes, sports-facility
Sheds, as well as building components such as staircases, fire-escape facilities, etc Special-purpose buildings such as airport terminals and railway stations, aircraft hangars,
shipyards, railway platforms Special structures. such as, for example, power transmission pylons, television and radio
as well as telecommunication towers, headwork for mines, underground tunnels, oil derricks, hydraulic engineering works such as dam gates and spillway structures, cranes,
etc
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Shell and plate structures
Gas holders and tanks for the storage and distribution of gases
Tanks and reservoirs for the storage of water, fuels and other liquids
Bins and bunkers for the storage of loose materials like cement, grain. Etc
Special structures such as blast furnace air heaters, gas scrubbers.
Large diameter steel piping employed at iron and steel works coke and by-
product works, hydroelectric power plants and oil and gas pipe lines.
Ship bulls, airplane fuselage, tank armor, etc.
Steel is finding diverse application in the construction industry. The following pictures will
reveal a number of such applications in various kinds of constructions.
Structural steel can be used to constitute the complete framing system in a high-rise
building. Either medium-sized, such as the hotel building or very tall buildings, such as the
office building can be constructed from steel (see Fig. 1.1).
Fig. 1.1 Multi Story Buildings
Special purpose buildings such as airport terminals, railway stations, exhibition pavilions,
conference halls, aircraft hangars, shipyards, railway platforms, in which large space should
be covered with out obstruction of columns, are constructed from structural steels trusses
(see Fig. 1.2 and Fig. 1.3).
Fig. 1.2 Exhibition Halls (Long Span Roofs)
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Cross section
Fig. 1.3 Aircraft Maintenance Hangars
Steel is a preferred choice when it comes to industrial structures as it also provides large
column-free space with fewer framing elements. Fig. 1.4 shows the model of such an
industrial building facility making use of steel framing.
Fig. 1.4 Industrial Building (columns, beams, and roofs)
Another area where steel and timber find their use is in bridge construction. There are
various kinds of bridges where structural steel can be used effectively and efficiently. in
suspension- and cable-stayed bridges, steel plays a predominant role at least as the cabling
system. Some of the main types of steel bridges are plate girder bridges, truss arch
bridges, cable stayed and suspension bridges (see Fig. 1.5).
a) Plate Girder Bridge b) Truss Arch Bridge
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c) Cable-stayed Bridge d) Suspension Bridge
Fig. 1.5 Use of Steel in Bridge Construction
Several industries and communication facilities call for towers for a variety of purposes.
Steel towers are used for types of towers including microwave transmission for
communications, radio transmission, television transmission, satellite reception, air traffic
controls, flood light stands such as in stadiums and large fly-over intersections, power
transmission lines, metrological measurements, tower-test. Set ups, derricks and crawler
cranes, oil drilling masts both in-land and off-shore facilities, and overhead water tanks,
among others. Figs. 1.6 show the various tower-related application of steel
a) Microwave Communication Facilities b) Power Transmission Facilities
Fig. 1.6 Use of Steel Members and Plates in Tower Construction
A number of temporary structures and shed facilities for car parks, gasoline stations,
storage facilities can also be constructed from steel. One such facility is shown in Fig. 1.7
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Fig. 1.7 Use of Steel Members and Panels for Gasoline Station
The corrosive nature of sea water calls for special kind of construction materials for
building off-shore oil and gas facilities. Specially treated steel responds to these
requirements better than most other possible construction materials (see Fig. 1.8).
Specially treated steel finds its wide application in petrochemical industries where chemical
attack and temperature effects could be treated at their highest. Steel structures in
theses industries can form part of the facilities themselves or structural framing for the
housing structures (see Fig. 1.9).
Fig. 1.8 Use of Steel Members and Plates in Fig. 1.9 Use of Steel in a Petro-chemical Industrial Facility Offshore Oil and Gas Exploration/Drilling Facility
Most industrial buildings need to be provided with handling and hoisting equipment. There
are variety of such equipment used the factories and nearly all of them are built up from
structural steel. Some of the common types are cranes on gantry girders (overhead cranes),
chain pulley blocks, fork lift, derrick cranes, conveyor belts; rope ways, assembly lines,
among others. A typical overhead crane with gantry girders is shown in Fig. 1.10.
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Fig. 1.10 Typical Over Head Cranes
Roof trusses of stadiums and sport facilities are usually made of either cantilever (free-
standing) or cable-stayed structural steels (see Fig. 1.11)
Fig. 1.11 Use of Steel for Roof Trusses of Stadiums
Concrete construction requires some kind of temporary support during construction up until
when the concrete has set and attained the necessary strength to support itself. In this
scenario, scaffolding and formworks, that can be built up from steel members can be used
effectively and efficiently (see Fig. 1.12).
Fig. 1.12 Use of Steel Scaffolding in Tunnel Construction
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Bracing systems are usually made from structural steel and they provide lateral stability
for a building by resisting winds and earthquakes (see Fig. 1.13).
Fig. 1.13 Use of Steel Members for Bracing Systems
Steel is also used in composite construction with concrete as shown in Fig. 1.14. This
construction practice improves the fire-resistance property and prevents corrosion of steel
in addition to improving the load-resisting capacity of the resulting structural members.
Fig. 1.14 Use of Steel for Composite Construction
Merits of Steel Structures
The principal merits of steel members are:
The ability to resist high loads with a comparatively small size and light weight of
members. Thus for the same strength, steel members are smaller in size and lighter
in weight, as compared to members made of other materials (except for some high
strength aluminum alloys).
Due to its high density, steel is completely non-porous.
The possibility of industrializing the construction work by the use of pre-
fabricated members and mechanized erection at the construction site.
A very long service life, provided care is taken
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The possibility of disassembling or replacing some steel members of a structure, for
strengthening purposes.
It is an environmental friendly material by being recycled.
With particular reference to high-rise buildings, Steel is favored over other
construction materials such as reinforced concrete for various reasons. Among
these are:
Shorter erection period permits an earlier recovery of capital
Steel offers wide-span frames. It provides column-free, uninterrupted interior
space. This offers greater interior design scope and results in more cost-efficient
buildings.
Steel structural members offer the absolute accuracy of dimensions. Uniform
quality possible only with pre-fabrication under close control in the plant that
reduces man-hour requirements at the site-an important consideration in the face
of unavailability of skilled labor
Steel offers greater possibilities for imaginative architectural design
Finally, cost comparison studies have revealed that the construction cost of
structural steel is generally more economical than reinforced concrete
Thus, structural steel is the preferred choice for speed of erection, value and quality
The principal drawback of steel members is their susceptibility to corrosion, which
necessitates their painting or the use of other methods for their protection. The second
drawback of steel is its low fire resistance. At high temperatures steel loses most of its
strength, leading to excessive deformation or failure
1.2 Design Philosophy and design Formats
Engineered structures are of such variety that they defy any attempt to enumerate them
except in a general way. The countless problems which arise in their design have prompted
engineers to specialize in the design of particular structures or groups of related
structures, such as, for examples steel structures or timber structures for bridges,
buildings, towers, etc
Design Procedure
There are a number of phases in a design process - from inception to detailing and quantity estimation.
Functional Planning/Design
The first and often the most difficult problem in design is the development of a plan that
will enable the structure to fulfill effectively the purpose for which it is to be built. If the
structure is a building, for example, the designer must create a plan which is adapted to the
site; which provides a suitable arrangement of rooms, corridors, stairways, elevator, etc.;
which will be aesthetically acceptable and which can be built at a price the client is
prepared to pay. This phase of design, sometimes called functional planning.
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Structural Planning / Design
Structural design is the second major step in the design process although the planning of
structural scheme is never independent of the functional plan. Depending on the type of
structures, the extent to which the scheme must be developed during the functional
planning stage may depend upon the structure. For example, the location of the columns in a
building usually must be worked out with the functional plan and sufficient space must be
anticipated between finished ceiling and finished floor of adjacent stories to accommodate
the floor construction. On the other hand, the functional plans and structural schemes of
highway bridges or communication towers are usually not so strongly interdependent.
It is usually necessary to make tentative cost estimates for several preliminary structural
layouts. Sometimes this may have to be carried out while the functional plan is being
developed; sometimes it can be done at a later stage. Selection of structural materials must
be based upon consideration of availability of specific materials and the corresponding
skilled labor, relative cost, and wage scales, and the suitability of the materials for the
structure.
The third stage of the design is a structural analysis. Although design specifications and
building codes usually describe the nature and magnitude of the loads to which the
structure may be subjected, at times the engineer must make the decision. Once the loads
are defined, a structural analysis must be made to determine the internal forces which will
be produced in the various members of the structure. Although this is a fairly routine
procedure, simplifying assumptions must invariably be made before the principles of
mechanics can be applied. The designer must be conscious of his or her assumptions to
ensure that the structure as designed can be expected to behave accordingly.
In the fourth phase of the design process, the engineer proportions the members of the
structural system. The latter must be chosen so that they will be able to withstand, with an
appropriate margin of safety, the forces which the structural analysis has disclosed.
Familiarity with the methods and processes of fabrication and their limitations and with the
techniques of constructions as well as their limitations is indispensable in the design
process.
The four steps in the structural design process discussed so far are seldom, if ever,
distinct, and in many cases they must be carried along more or less simultaneously.
Furthermore, they assume varying degree of importance relative to one another.
Design is necessarily a trial-and-error procedure. Most structures are statically
indeterminate and require that member properties be specified before the analysis for load
effects can be carried out. After the member forces have been determined, the validity of
the member selection must be evaluated. If changes in member properties are required, a
re-analysis must be carried out. The procedure must be repeated until the members
selected and resultant member forces are in acceptable arrangement. The development of
the computer has greatly facilitated this phase of the design process, but the judgment and
experience of the designer are impossible to build into a completely logical system as
required by the computer.
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Development of procedures for translating design specifications into computer programs
continues to receive the attention of engineers in all specialties. There are also a number of
specialized and industry-targeted such software products available nowadays. Many of such
software can now help the engineer from planning to analysis, design, detailing to quantity
estimations. Such programs, however, should be utilized only after the engineer has a
thorough understanding of the requirements of the specifications, the method of analysis
employed in the program, and the behavior of many types of structural members.
Design Philosophy
Structural design should be performed to satisfy three criteria: strength, serviceability,
and economy.
Strength pertains to the general integrity and safety of the structure under extreme load conditions. The structure is expected to withstand occasional overloads without severe
distress and damage during its lifetime.
Serviceability refers to the proper functioning of the structure as related to its appearance, maintainability, and durability under normal, or service load, conditions.
Deflection, vibration, permanent deformation, cracking, and corrosion are some design
considerations associated with serviceability.
Economy concerns the overall material and labor costs required for the design, fabrication, erection, and maintenance processes of the structure.
A structure should be designed and fabricated to fulfill the following conditions:
Remain fit for use during its intended life
Sustain the loads, which may occur during construction, installation and usage
Localize damage due to accidental overloads.
Have adequate durability in relation to maintenance costs.
The above requirements can be satisfied by using suitable materials, appropriate design and
detailing and specifying quality control procedures for construction and, if necessary, for
maintenance program.
Design Formats
The design of steel structures may be controlled by several criteria described as limits of
structural usefulness ". They are as follows:
Hypothetical attainment of yield point
Attainment of maximum plastic strength
Excessive deflections at service load and drift limitations
Instability
Fatigue
Fracture
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One or more of these conditions must form the basis for any rational design procedure and
their consideration enters into the subject matters to be presented in the subsequent-
sections for the design of several types of members and structural components.
As a result of the various design criteria, three major design methods and formats have
evolved in practice. At present, steel design can be performed in accordance with one of the
following three formats worldwide.
Al1owable Stress Design (ASD)
In the allowable stress design (ASD), a member is selected such that under expected loads,
known as service or working loads, the stress will not exceed one of the previously
described limits of usefulness. It is performed by specifying expected working design loads
and allowable stresses. The factor of safety is inherent, but usual1y not stated. Also, the
limit of usefulness is usual1y undesignated
This design methodology has been in use for decades for steel design of buildings and
bridges. It continues to enjoy popularity among structural engineers engaged in steel
building design. In allowable stress (or working stress) design, member stresses computed under the action of service (or working) loads are compared to some pre-designated stresses, called allowable stresses. The allowable stresses are usually expressed as a function of the yield stress (fy) or tensile stress (fu) of the material. To account for
overload, under-strength, and approximations used in structural analysis, a factor of safety is applied to reduce the nominal resistance of the structural member to a fraction of its
tangible capacity.
In so far as the method of analysis is concerned, allowable stress design is based on elastic
analysis to obtain the structural responses such as moments, shear and axial forces that a
member must be designed to carry.
The general formula for an allowable stress design has the form:
=
m
ii
s
n QFR
1
Where: Rn = nominal resistance of the structural component expressed in units of stress
Qi = service or working stress computed from the applied working load type i.
i = load type (dead, live, wind, etc.)
m = number of load types considered in the design
=
s
n
FR allowable stress of structural component
Plastic Design
Plastic design makes use of the fact that steel sections have reserved strength beyond the first yield condition, When a section is under flexure, yielding of the cross section occurs in
a progressive manner, commencing with the fibers farthest away from the neutral axis and
ending with the fibers nearest the neutral axis. This phenomenon of progressive yielding
referred to as plastification, means that the cross section does not fail at first yield. The additional moment that a cross section can carry in excess of the moment that corresponds
to first yield varies depending on the shape of the cross section. To quantify such reserved
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capacity, a quantity called shape factor, defined as the ratio of the plastic moment (moment that causes the entire cross section to yield, resulting in the formation of a plastic hinge) to the yield moment (moment that causes yielding of the extreme fibers only) is used.
For an indeterminate structure, failure of the structure will not occur after the formation
of a plastic hinge. After complete yielding of a cross section, force (or, more precisely,
moment) redistribution will occur, in which the unfailed portion of the structure continues
to carry any additional loadings. Failure will occur only when enough cross sections have
yielded to render the structure unstable, resulting in the formation of a plastic collapse mechanism.
In plastic design the factor of safety is applied to the applied loads to obtain factored loads. A design is said to have satisfied the strength criterion if the load effects (i.e., forces, shears, and moments) computed using these factored loads do not exceed the
nominal plastic strength of the structural component. Plastic design has the form:
=
m
inin QR
1
Where: Rn = nominal plastic strength of the member
Qni = nominal load effects from the loads of type i.
i = load type (dead, live, wind, etc.)
m = number of load types considered in the design
= load factor
In steel building design the load factor is given by the AISC Specification as 1.7, if Qn consists of dead and live gravity loads only, and as 1.3, if Qn consists of dead and live gravity
loads acting in conjunction with wind or earthquake loads.
Limit State Design or Load and Resistance Factor Design
Limit state is a Probabilistic design procedure in which a structure, or part of a structure, is considered unfit for use when such a limiting condition exceed a particular state, called a
limit state, beyond which it infringes one of the criteria governing its performance thus
making the structure unable to meet design performance criteria. All relevant limit states
shall be considered in the design so as to ensure an adequate degree of safety,
serviceability and durability.
Three classes of limit states are recognized: ultimate limit states, serviceability limit states and durability limit states. Ultimate limit states are those which if exceeded can lead to collapse of part
or the whole of the structure, endangering safety of people. Serviceability limit states correspond to
states beyond which specified service criteria are no longer met. Durability limit states can be regarded as subsets of the ultimate and serviceability limit states depending on whether, for example,
the corrosion affects the strength of the structure or its aesthetic appearance. Structures should be designed by considering all relevant limit states.
A design is considered satisfactory according to the strength criterion if the resistance exceeds the
load effects by a comfortable margin. In actual design, a resistance factor m is applied to the nominal resistance of the structural component to account for any uncertainties associated with the
determination of its strength, and a load factor l is applied to each load type to account for the uncertainties and difficulties associated with determining its actual load magnitude. Different load factors are used for different load types to reflect the varying degree of uncertainty associated with
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the determination of load magnitudes. In general, a lower load factor is used for a load that is more
predictable and a higher load factor is used for a load that is less predictable.
Mathematically it can be expressed as:
=
m
iili
m
n QR1
Where:
=
m
nR
design strength
=
=
m
iiliQ
1 the required strength or load effects for a given load combination
Specifications and codes provide the values of pertaining to different loads and also outline the load combinations to be used on the right-hand side of the above equation. For a safe design, all load
combinations should be investigated, and the design is based on the worst-case scenario.
Although, allowable stress design has been used for decades, the world wide trend is to ward the limit
state approach to design. The national building codes, both EBCS 3 1995 far steel and EBCS 5 1995 far timber structures are also based on the concepts of the limit state design. In view of this trend
and in cognizance of the likelihood that limit state design/LRFD will be the mainstream design method henceforth, only limit state/LRFD provisions will be covered in this coursework. So, interested
readers on others are advised to refer to relevant literature.
1.3 Materials
Steel is one of the mast important structural materials. Properties of particular importance in structural usage are high strength compare to any other available material, and ductility (i.e., its
ability to deform substantially in either tension or compression before failure). The most important structural properties of steel are yield strength and ultimate strength, modulus of elasticity, shear
modulus, Poissons ratio, coefficient of thermal expansion, and its density.
Stress-strain Behavior of Structural steel
A schematic diagram of an engineering stress-strain curve of steel obtained from a simple
tension test is shown in Fig. 1.14.
Fig. 1.15 Idealized Stress-strain Curve
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Elastic region
In this region the stress is proportional to the strain, and Hooke's law applies. The constant
of proportionality is the modulus of elasticity or Youngs modulus, E. The modulus of elasticity for steel has values ranging from 190 - 210 GPa. The modulus of elasticity does
not vary appreciably for the different grades of steel used in construction, and a value of
200 GPa is often used for design. The elastic region ends when the stress reaches h" the yield stress. For stress below 1; no. plastic, or permanent, deformation will occur in the
steel section. Table 1.1 gives the yield point and the ultimate strength of several grades of
steel, classified according to ASTM designation, and of interest to the structural designer.
Inelastic Region
In this region the steel section deforms plastically under a constant stress, fy- The extent
of this deformation differs for different steel grades. Generally, the ductility (the ability
of a material to undergo plastic deformation prior to fracture) decreases with increasing
steel strength. Ductility is a very important attribute of steel. The ability of structural
steel to deform considerably before failure by fracture allows the structure to undergo
force redistribution when yielding occurs, and it enhances the energy absorption
characteristic of the structure
Strain-Hardening Region
In this region deformation is accompanied by an increase in stress. The peak point of the
engineering stress-strain curve is the ultimate stress, fu. fu is the largest stress the
material can attain under uniaxial condition. In a uniaxial tension test, the specimen
experiences non-uniform plastic deformation (necking) once the stress reaches fu. Beyond fu
deformation proceeds at a rapid rate and equilibrium can be maintained only by a reduction
in the applied load. For design purposes, fu is often regarded as the stress at which failure
is imminent.
Poissons Ratio
Poissons ratio, , is the absolute value of the ratio of the transverse strain to longitudinal
strain under axial load. In the idealized elastic range Poissons ratio for structural steels is
approximately 0.3 while in the plastic range it is about 0.5.
Sear modulus
Shear modulus, G, is the ratio of shear stress to shear strain. The shear modulus, G, is
presumed to be constant (= 80 GPa ) for all structural steels.
Thermal expansion
The design of structures to serve under atmospheric temperature rarely involves concern
about high temperature behavior. Knowledge of such behavior is desirable when specifying
welding procedures, and when concerned with the effects of fire as the modulus of
elasticity, yield strength and tensile strength all reduces with increase in temperature. The
coefficient of thermal expansion, , for structural steel is 12 x 10-6 per oc.
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Fatigue
Fatigue failure can occur in members or structures subjected to fluctuating loads such as
crane girders, bridges and offshore structures. Failure occurs through progressive growth
of a crack that starts at a fault and the failure load may be well below its static value.
Welded connections have the greatest effect on the fatigue strength of steel structures.
On the other hand, bolted connections do not reduce the strength under fatigue loading. To
avoid fatigue failure, detail should be such that stress concentrations and abrupt changes
of section are avoided in regions of tensile stress.
Brittle
Structural steel is ductile at temperatures above 10oC, but it becomes more brittle as the
temperature falls, and fracture can occur at low stresses below 0c. To reduce the
likelihood of brittle fracture, it is necessary to take care in the selection of the steel to be
used and to pay special attention to the design detail. Thin plates are more resistant than
thick ones, abrupt changes of section and stress concentration should be avoided. Fillets
welds should not be laid down across tension flanges and intermittent welding should not be
used.
Types of Steel
Structural steels used for construction purposes are generally grouped into several major
classifications according to national and international standards. The American Society for
Testing and Materials (ASTM) classifications are among such widely used standards. The
Ethiopian Building Code Standard EBCS 3 1995 also classifies according to their strength.
The following are per the ASTM classification
Carbon Steels (ASTM A36, ASTM A529, ASTM A709)
In addition to iron, the main ingredients of this category of steels are carbon (maximum
content 1.7%) and manganese (maximum content 0.65%), with a small amount (
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Fig. 1.16 Typical Stress-strain Curves
High-strength Low-alloy Steels (ASTM A441, ASTM A572)
These steels possess enhanced strength as a result of presence of one or more alloying
agents, such as chromium, copper, nickel, silicon, and vanadium; in addition to the basic
elements of iron, carbon, and manganese. Normally, the total quantity, of all the alloying
elements is below 5% of the total composition. This category includes steels having yield
stresses from 275 to 480 MPa with a well defined yield point (see Fig.). These steels
generally have higher corrosion resistance capacity than carbon steels.
Quenched and Tempered Alloy Steels (ASTM A852, ASTM A514)
The quantities of alloying elements used in these steels are in excess of those used in
carbon and low-alloy steels. In addition, they are heat-treated by quenching and tempering
to enhance their strengths. These steels do not exhibit well-defined yield points (see Fig.).
Their yield stresses are determined by the 0.2% offset strain method. These steels,
despite their enhanced strength, have reduced ductility (see Fig. ), and care must be
exercised in their usage, as the design limit state for the structure or structural elements
may be governed by serviceability considerations (e.g. deflection, vibration) or local buckling
(under compression).
Table1.1 gives a summary of the specified minimum yield stress (fy) and the specified
minimum tensile strengths (fu), and Table 1.2 gives the general usages for these various
categories of steel in accordance with ASTM designation.
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Table 1.1 Properties of Steels used for Buildings and Bridges
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Table 1.1 Continued
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Table 1.2 Uses of Various Structural Steels
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Table 1.3 Continued
EBCS 3, 1995 recognizes three grades of ordinary hot rolled steel as shown in Table 1.4.
Table 1.4 Nominal Values of fy and fu for Various Grades of Structural Steel (EBCS 3, 1995)
Nominal Steel
Grade
Thickness t (mm)
t 40mm 40mm < t 100mm fy (MPa) fu (MPa) fy (MPa) fu (MPa)
Fe 360 235 360 215 340
Fe 430 275 430 255 410
Fe 510 355 510 335 49
Note: t is the nominal thickness of the element
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Structural Steel Shapes
In general, there are three procedures by which steel shapes can be formed: hot-rolled, cold-formed, and combined. Most of the rolling is done on hot steel, with the product termed hot-rolled steel. Sometimes the thinner plates are further rolled or bent, after cooling, into cold-rolled or "cold-formed" steel products. Regardless of the manner by which
the steel shape is formed, it must be manufactured to meet certain international standards
such as ASTM or European standards. The commonly used standard hot rolled steel shapes
are as shown in Fig. 1.17
Cold formed steel shapes are formed in rolls or brakes from sheet or strip steel. Because
of the great variety which can be produced, shapes of this type, unlike hot rolled shapes,
have not been standardized (see Fig. 1.18).
Fig. 1.17 Standard Rolled Shapes
Fig. 1.18 Some Cold-formed Shapes
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Design of Steel and Timber Structures CE-519 Yibeltal T.
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The dimensions and geometric properties of the various hot rolled sections utilized in design
calculation are listed in the tables of manual (see Tables at the back which are obtained
from British Standards).
Structural Fasteners
Every structure is an assemblage of individual parts or members which must be fastened
together, usually at the ends of its members. The two main fastening means are bolting and
welding (with a few and isolated case also riveting and pins). Connections are structural
elements used for joining different members of a framework.
Bolts
Four basic types of bolts are commonly in use; they are designated by ASTM as A307,
A325, A490, and A449
A307 Bolts: These are called unfinished or ordinary bolts and are made from low-carbon steel. They are furnished in two grades, A and B, the former for the general purposes and
the latter for joints in pipe systems. They are available with several head and nut
configurations, but the hexagonal and square head are most commonly used.
A325 Bolts: The A325 bolt is made of medium carbon steel. It is also used in both hot-
rolled and cold-formed construction. e are called high-strength bolts. A325 bolts are made of medium-carbon steel. They are used in both hot-rolled and cold-formed construction. A490 bolts are made from quenched and tempered alloy steel and thus have higher strength, than A325 bolts. They are used for general construction purposes.
A449 Bolts: The A449 bolt also of medium carbon steel, is furnished in three ranges of
diameter.
490 Bolts: The A490 bolt is made of alloy steel in one tensile-strength grade.
Table 1.5 Properties of Structural Bolts (ASTM)
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Design of Steel and Timber Structures CE-519 Yibeltal T.
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Table 1.6 Nominal Values of Yield Strength fyb and Ultimate Tensile Strength fub for Bolts (EBCS 3, 1995)
Bolt Grade 4.6 4.8 5.6 5.8 6.8 8.8 10.9
fyb (MPa) 240 320 300 400 480 640 900
fub (MPa) 400 400 500 500 600 800 1000
Welding
Welding is the process of joining metal parts by means of heat and pressure, which cause
fusion of the parts (resistance welding), or by heating the metal to the fusion temperature,
with or without the addition of weld metal (fusion welding).
Welds are classified according to their type as groove, fillet, plug, and slot. The detailed
treatment of welding and the electrodes which are used as filler materials are specified in
different standards. The detail will be covered in chapter seven, the design of connections.
Specifications and Building Codes
Then design of steel structures is generally done within the framework of codes giving
specific requirements for materials, structural analysis, member proportioning, etc.
Specification serves as a guide for the engineer to arrive at a safe and acceptable design.
It is also a guarantee to the owner that the resulting structure will comply with basic
standards to ensure safety, utility and economy.
The designer doing steel structures in various disciplines, such as buildings, bridges, etc, will
have to follow closely the relevant design requirements in the appropriate specifications and
design codes as minimum requirements.
The following are some important specifications for concrete structures.
EBSC 1 Ethiopian Building Code Standard for Basis of Design and Actions on Structures.
EBCS 3 Ethiopian Building Code Standard for the Design of Steel Structures. EBCS 4 Ethiopian Building Code Standard for Design of Composite Steel and Concrete Structures.
EBCS 8 Ethiopian Building Code Standard for Basis Earthquake design of Structures.
EC 3 European Standards for the Structural Use of Steel AISC American Institute of Steel Construction, Steel Construction Manual
AWS American Welding Society, Structural Welding Code
AASHTO American Association of State Highway and Transportation Officials, Specification for Highway Bridges
BS 5950 British Standards for The Structural Use of Steel Works in Buildings AREA American Railway Engineering association, Specification for Steel Railway Bridges
ASTM American Society for Testing and Materials
DIN DIN V ENV 1993 German Standards for the Structural Use of Steel
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Chapter Two: Tension Members
Design of Steel and Timber Structures CE-519 Yibeltal T.
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Chapter Two: Tension Members
2.1 Introduction
Tension members are structural members that carry pure tension loads. They are efficient
carriers of load and are used encountered in most steel structures. The bottom chords of
roof and bridge trusses are c1assic examples of tension members. Steel cables in suspension
and cab1e-stayed bridges, cab1es-supported roofs, guyed microwave and radio
communication towers and power transmission towers, elevator cables and those cables in
parts of hoisting equipment are all examples of tension members.
Certain web members of a truss system may be in tension for certain loading condition and
in compression for other loading conditions. Wind bracing in an X configuration is frequently
used where the members are so flexible that "buckling" takes place under compression
stresses developed by wind in one direction but functions as a tension member for the
reversed wind.
Tension members frequently appear as secondary members, being used as tie rods to stiffen
a trussed floor system or to provide intermediate support for a wa1l girt system.
The selection of their cross section is one of the simplest and most straightforward
procedures encountered in the design of steel components. Since stability is of minor
concern with tension members, the process of designing such structural members is reduced
to:
selecting a section with sufficient cross-sectional area to carry the design load
without exceeding the design tensile stress as stipulated in relevant codes of
practice
proportioning connections so that all relevant design specifications are met with
regard to arrangement as well as stress limitations.
In all these, the tensile strength of steel is used. In this stress configuration, member
buckling or warping is not a matter of concern. However, specifications normally require a
minimum amount of member stiffness or rigidity with the view of preventing undue sagging,
deflection and vibration and, accordingly, slenderness ratio is 1imited by design
specifications in order to account for this requirement.
Tension members are frequently subjected to bending stresses in addition to the principal
tensile forces. These conditions occur when the cross section is acted upon by eccentric
forces. This calls for additional investigation of the member for proper design and members
subjected to such a condition of combined bending and tensile stresses will be discussed
later.
2.2 Types of Tension Members
Tension members may consist of a single structural shape or they may be built up from a
member of structural shapes as shown in Fig. 2. 2
The cross sectional arrangement of axially stressed tension members is structurally
unimportant so long as the net cross sectional are is sufficient to carry the design loads and
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Chapter Two: Tension Members
Design of Steel and Timber Structures CE-519 Yibeltal T.
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Fig. 2.1 Tension Members in Buildings and Bridges
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Chapter Two: Tension Members
Design of Steel and Timber Structures CE-519 Yibeltal T.
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the shape can be conveniently connected to other members in the structure. In view of this,
their form is governed largely by the type of structure of which they for parts and by the
method of joining them to the connecting portions of the structure. The only other
structural requirement is that they be sufficiently stiff to prevent harmful vibration,
unsightly sagging, or, where a member may resist a chance of reversal stress to compression
of small but indeterminate magnitude, to prevent buckling.
Fig. 2.2 Cross-sections of Typical Tension Members
Accordingly, if a member at the end is to be connected by bolts or rivets, the angle,
channel, or I section, single or built-up, will be better suited. The use a particular rolled or
built-up shape will be dictated, in addition to its capacity, by the remainder of the
structure; i.e., by the availability of sufficient space on the joint where the member will be
framed into. On the contrary, plates and angles are mostly used in welded structures. For
light trusses and for bracing systems, single angle sections are commonly used. The use of
double angles is generally preferred since the joint will be more symmetrical both in and out
of plane, as opposed to using a single angle, which will always have an out-of-plane
eccentricity.
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Chapter Two: Tension Members
Design of Steel and Timber Structures CE-519 Yibeltal T.
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Tension rods may be used as suspenders for suspension bridges and for smalls-pan roof
trusses. For heavy building trusses and long-span bridges, the eye bar is economical to use.
For latticed girders, the chord members are generally built-up sections .
For carrying greater tension the members have to provide larger net area and therefore
built up sections might be the only effective choice. Such members are also required when a
single or a pair of angles, or anyone of the standard rolled shapes does not have sufficient
rigidity (measured by L/r), or the joint will be impractical to fabricate. For long-span light
structures, tubular sections are ideally suited.
In general, therefore, the use of single structural shapes is more economical than built up
sections. However, the latter may be required under any of the following situations:
the tensile capacity of a single rolled section is not sufficient.
the L/r ratio (the ratio of the unbraced length to the minimum radius of gyration)
does not provide sufficient rigidity.
the effect of bending combined with the tensile behavior requires a large lateral
stiffness
usual connection details require a particular cross section
esthetic control
1.3 Design Consideration
Although the design of tension members is the simplest and most straight-forward one
compared to those for various other member types such as compression or bending. The
process nevertheless requires consideration of several factors. A member subject to axial
tension is supposed to develop a uniform tensile stress across the entire cross-sectional
area. The preconditions for such assumption are as follow:
Axial force is acting along the centroid of the cross section
No bending moment exists on the section
Inter-connections of members or joints are such that the center of gravity of the
member is collinear; that is, it has no eccentricity with the joint.
In order to fulfill these assumptions, due consideration need be given, among others, to
connection types and details, types of shapes available or required for the intended system,
and the effects of shear flow in the section.
Strength as a Design Criterion
The problem of designing a tension member is basically one of providing a member with
sufficient cross-sectional area to resist the applied loads with an adequate margin of safety against tensile failure. The controlling strength limit state for tension member will be either:
a) yielding of gross cross-sectional area of the member away from the joints, or
b) Fracture of the effective net sectional area through the holes at the joints.
Net Area:
For tension members having holes for rivets and bolts, the reduced cross section is
referred to as the net area. The determination of the net section involves the geometric
spacing of the holes made to accommodate the connecting bolts and rivets.
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Chapter Two: Tension Members
Design of Steel and Timber Structures CE-519 Yibeltal T.
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The net area of a cross-section or element section shall be taken as its gross area less
appropriate deductions for all holes and other openings. When the fastener holes are not
staggered the total area to be deducted should be the maximum sum of the sectional areas
of the holes in any cross-section perpendicular to the member axis.
Accordingly, the net area Aeff for the determination of section capacity will be given by:
=
=
on
iiiogeff tdAA
1, (2.1)
Where: Ag = gross cross sectional area
do,i = hole diameter at section i tj = thickness of the section at i
If the holes are not disposed symmetrically about the centerline of the section, an
effective net area, obtained by multiplying the net area by a reduction factor kA, should be
used. For a single hole, the reduction factor is given by:
=
be
bdK oA
211 (2.2)
where: do is the hole diameter,
e is edge distance ( from hole center to edge )
b is width of the section.
When the holes are staggered, the stress distribution is more complicated and an
approximation is allowed (Fig. 2.3a).
Fig. 2.3 Determination of Net Section
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Chapter Two: Tension Members
Design of Steel and Timber Structures CE-519 Yibeltal T.
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The almost universally adopted procedure is as follows:
Take any reasonable and possible path across a chain of holes and deduct one hole width for
each bolt hole encountered.
For each change in direction from hole to the next hole, add back the quantity
p
s
4
2
where s is
pitch or longitudinal distance between adjacent holes and g is gauge distance between adjacent holes across the width.
In general, the net sectional area Aeff can be determined from:
= =
+=
0
.01 1
2
4
n
i
n
i jgeff
p
jiit
gs
tdAA (2.3)
where
Ag is gross cross-sectional area
Do is nominal diameter of the ho1e (bolt cutout)
t is thickness of the component element (note that elements within cross section may have
different thickness, such as the webs and flanges in rolled sections)
S is the staggered pitch, the spacing of the centers of two consecutive holes in the chain measured
parallel to the member axis.
g is the gauge, the spacing of the centers of the same two holes measured perpendicularly to the
member axis.
In an angle, or other member, with holes in more than one plane, the gauge shall be measured along the
center of thickness of the material (Fig.2.3b).
Effective Net area
Then net area computed in the previous section may not correctly reflect the strength specially:
when the tension member has a profile consisting elements not in a common plane.
where the tensile load is transmitted at the end of the member by to some but not all of the
elements. Angle section having connection to one leg only is an example of such a situation.
due to shear lag effect (non uniformity of stresses in wide plates i.e. the shear transfer lags
or inefficient)
For such cases the tensile force is not uniformly distributed over the net area. To account for this,
LRFD provides for an effective area Aeff to be
computed as:
Aeff = U An (2.4)
where: U is a reduction coefficient
An is net area
Fig. 2.4 Eccentricity in Joints
gusset plateC.G. angle
x- x-
Gusset plates
Sym
x-
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Chapter Two: Tension Members
Design of Steel and Timber Structures CE-519 Yibeltal T.
7
The reduction coefficient is given by:
9.01
lx (2.4a)
where: l is the length of the connection
x is the connection eccentricity (distance from centroid of element being
connected eccentrically to plane of load transfer as shown in Fig; 2.4.)
U should be calculated using the maximum value of x.
1.4 Limit State Design of Tension Members
Limit state design of tension members calls for verification of the member to withstand
various kinds of failures related to tensile strength both in gross cross section and in effective net section as well as block shear with respect to tension fracture and shear fracture.
Ethiopian Building Code Standard EBCS 3, 1995
According to the EBCS 3 Specification, axially loaded tension members designed to resist a
factored axial force of Nt,Sd, calculated using appropriate load combinations, must satisfy
the condition:
RDLsdt NN ,. < where:
Nt, Rd = design tension resistance capacity of the cross-section, taken as a smaller of
either the design plastic resistance Npl,RD of the gross section or the design ultimate resistance Nu,Rd of the net section at the bolt hole where, again, Npl,Rd and Nu.Rd are determined as in the fol1awing expressions:
MO
ygRDPi
fxAN
=
, (2.5a)
2,
9.0
M
UeffRDU
fxAxN
= (2.5b)
The partial safety factor MO = 1.1 and while M2 = 1.25 represents resistance of the net
section at bolt holes.
AISC-LRFD Specification
According to the AISC-LRFD Specification, tension members designed to resist a factored
axial force of Pu, calculated using the appropriate load combinations, and must satisfy the
condition:
t Pn Pu (2.6)
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Chapter Two: Tension Members
Design of Steel and Timber Structures CE-519 Yibeltal T.
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Where:
Pn = the design tensile strength of the cross section and it is evaluated based on three limit states: yielding in gross section, fracture in effective net section,
and block shear.
t = 0.9 is the appropriate resistance factor in tension.
Yielding in the cross section away from the joint should be avoided to prevent excessive deformation that results when steel yields. The design strength for this limit state is
evaluated from the equation:
t Pn = t x fy x Ag (2.6a)
where
t = 0.9 = resistance factor for tension fy = specified minimum yield stress of steel
Pn = nominal axial strength
Fracture in effective net section or fracture of the net section the joint should be avoided, to prevent the loss of load-carrying capacity of the member. The design strength for this
limit state is evaluated from the equation:
t Pn t x fu x Ae (2.6b)
where:
t = 0.75 = resistance factor for fracture in tension Fu = specified minimum tensile strength of the material
Ae= effective net cross-sectional area of the member
Pn = nominal axial strength
For members without holes, fu11y connected by welds, both Aeff in EBCS 3 and Ae in AISC-
LRDF specifications are the smal1er of the gross area of the member and the effective
area of the welds.
As it can be seen from both EBCS 3 and AISC-LRDF specifications, the concept of net
section forms one of the criteria for the determination of limiting strength of the cross
section.
Block Shear
Block shear failure or rupture along a block shear failure path occurs when a segment of the
connecting member is torn out as a result of the combined effects of tension and shear.
Block shear must be checked if the load is transmitted by some but not all of the
component elements of the cross section.
Ethiopian Building Code Standard EBCS 3, 1995
The design value of the effective resistance Veff,Rd for rupture along a block shear failure
path shall be determined from:
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Chapter One: Introduction, Material and Design Concepts
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Design of Steel and Timber Structures CE-519 Yibeltal T.
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MO
efvyRDeff
fAxfxV
.
.
6.0=
(2.7)
Where MO = 1.1 = partial safety factor f = specified minimum yield stress of steel Av,eff = effective shear area subject to block shear
The effective shear area Av,eff for block shear, Fig. 2.5, is determined from:
Av,eff = t (Lv + L1 + L2 ndo) (2.7 a)
in which L1 and L2 are given by:
L1 = 5.0d0 a1 L1 = 2.5d0 a2 and n = the number of fastener holes in the block shear failure path
do = hole diameter
T = thickness of the web or bracket
Fig. 2.5 Net Shear Area for Block Shear.
.
AISC-LRFD Specification
According to the AISC-LRFD Specification, the design strength for block shear is
determined from the following two conditions:
Tension Fracture Shear Yield: t Pn = 0.75 x (0.60 x fy Agv + fuAnt) (2.8a) Shear Fracture Tension Yield: t Pn = 0.75 x (0.60 x fu Anv + fyAgv) (2.8b)
Where
0.75 = resistance factor for block shear
fy, fu = specified minimum yield stress and tensile strengths, respectively Agv = gross area of the torn-out segment under shear Ant = net area of the torn-out segment under tension Anv = net area of the torn-out segment under shear Agt = gross area of the torn-out segment under tension
Normally, it is necessary to investigate both the tension fracture - shear yield and the
shear fracture-tension yield criteria. The larger of the two values calculated is to be used
for tPn.
Slenderness Ratio
In al1 tension members, minimum amount of member stiffness or rigidity is required with
the view of preventing undue sagging, deflection and vibration. This is accomplished by
limiting the slenderness ratio given by L/r where L is the length of the member and r is the
list radius of gyration.
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AISC specifies an upper limit of 300 on r
L
Adequacy of the Connection
Connections must also be carefully designed and detailed. This topic will be discussed in
detail in Structural Connections and Design of Joints.
Longitudinal Spacing of Connectors
The spacing of connectors in built-up tension members consist of elements in continuous
contact shall conform to the spacing requirements for fasteners. Details of this will be
presented in Structural Connections and Design of Joints.
_______________________________ ADDITIONAL READING
E.H. Gayloard and J.E. Stalmeyer
Chapter 3
Charles G. Salmon and Johne E. Johnson
Chapters 3
Robert Englekirk
Chapter 1
EBSC 3 and EC 3
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Chapter Three: Compression Members
Design of Steel and timber structures (CE 519) Yibeltal Temesgen
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pChapter Three: Compression Members
3.1 Introduction
Compression members are perhaps the most common structural elements in an ordinary structure and are variously termed as columns, posts, struts or stanchions, etc. A structural member is considered to be a compression member if it is designed primarily to resist axial compression, though some bending may also be present and accounted for in the design. If the bending action is quite significant, the member is termed as a beam-column and designed in a different way as will be shown later in Chapter Five.
Structural action of columns, stanchions, struts and posts is identical; but due to difference in their usage different names are used. Columns are ordinarily used in buildings, are vertical and transmit some actual load or beam reaction to another column or foundation. Stanchions are steel columns made of rolled steel sections (usually built up) and carry heavy loads. Struts on the other hand are not necessarily vertical and are used as compression members in roof trusses and bridge trusses. The term post is loosely used for a column but the end member of a bridge truss is known as the end-post. Similarly, the main compression members of a roof truss are known as rafters.
Under the general category of compression members could be included columns, compression members in a trussed structure, component parts of frames such as compression flanges of beams or plate girders.
The two main differences between tension and compression members are:
A. Tension members are held straight by means of tensile loads, while in the case of compression members, the compressive loads tend to bend the member out of the plane of loading.
B. For riveted or bolted connections, the net area will govern the strength of a tension member, while for compression members the rivets are assumed to fill the holes.
This Chapter will present the assessment and design of structural members that are acted upon by pure compression forces; i.e., direct loads with no moments acting simultaneously. The main kinds of compression members are as shown in Fig. 3.1.
Fig. 3.1a Simple compression members
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Chapter Three: Compression Members
Design of Steel and timber structures (CE 519) Yibeltal Temesgen
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Fig. 3.1b Tapered members
Fig. 3.1c Stepped columns
Fig. 3.1d Built up columns
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Chapter Three: Compression Members
Design of Steel and timber structures (CE 519) Yibeltal Temesgen
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Compression members can fail by yielding, inelastic buckling, or elastic buckling depending on the slenderness ratio of the members as well as in local buckling that is usually influenced by the relative thickness of the component elements that constitute the cross section. Members with low slenderness ratios generally tend to fail by yielding, whereas members with high slenderness ratios tend to fail by elastic buckling. Most compression members used in construction have intermediate slenderness ratios, and so the predominant mode of failure is inelastic buckling.
Member buckling can occur in one of three different modes: flexural, torsional, and flexural-torsional.
Flexural buckling occurs in members with doubly symmetric or doubly anti-symmetric cross sections such as I and Z sections, and in members with singly symmetric sections such as C, T, equal-legged L and double L.
Torsional buckling occurs in members with very thin walls.
Flexural-torsional buckling occurs in members with singly symmetric cross sections such as C, T, equal-legged L, double L.
Normally, torsional buckling of symmetric shapes and flexural-torsional buckling of un symmetric shapes are not important in the design of hot-rolled compression members; either they do not govern or their buckling strengths do not differ significantly from the corresponding weak-axis flexural buckling strengths. However, torsional and flexural-torsional buckling modes may govern for sections that have relatively thin component plates.
In addition to slenderness ratio and cross-sectional shape, the behavior of compression members is affected by the relative thickness of the component elements that constitute the cross section. The relative thickness of a component element is qualified by the width-to-thickness
Fig.3.1e Built up members
Fig. 3.1f Perforated plate columns
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Chapter Three: Compression Members
Design of Steel and timber structures (CE 519) Yibeltal Temesgen
4
ratio (b/t) of the element. The width-to- thickness ratios of some selected steel shapes are shown in Fig. 3.2. If the width-to-thickness ratio falls within a limiting value stipulated by relevant codes and specifications, local buckling of the component element will not occur. However, if the width-thickness ratio exceeds these stipulated values, consideration of local buckling in the design of the compression member is required.
3.2 Classification of Sections
Classification of sections of compression members depends on their failure modes under load. Different standards and codes stipulate various classification although they generally coverage to two main modes of classification-either into four classes (as in, for example, the EBCS3 1995) or into three classes (as in, for example, the AISC Standard).
Fig. 3.2 Dimensions of sections
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Chapter Three: Compression Members
Design of Steel and timber structures (CE 519) Yibeltal Temesgen
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The EBCS 3 1995 classifies sections into four categories. Accordingly, the design strength of a cross-section subject to compression depends on its classification as Class 1 (Plastic), Class 2 (Compact), Class 3 (Semi-compact), or Class 4 (thin-walled) according to their capacity in the following manner.
Class 1 cross sections, also known as plastic sections can develop their plastic moment resistance (fy times plastic modulus) with the rotation capacity required for plastic analysis. Only cross sections falling in this class may only be used for plastic design.
Class 2 cross sections can develop their plastic moment resistance but with limited rotation capacity. Cross-sections falling in this group are also known as compact sections.
Class 3 cross sections are those which can reach their yield moment (fy times elastic modulus) but local buckling prevents the development of the plastic moment resistance. In Class 3 sections, the stress in the extreme fibers should be limited to the yield stress because local buckling prevents development of the plastic moment capacity. Cross-sections falling in this group are also known as semi-compact sections.
Table 3.1. Classification of Compression Sections According to EBCS 3 1995 (Modified to meet latest Euro code Standard).
(Refer to fig. 3.2 for the various parameters under ratio checked)
Limiting Width-Thickness Ratios for Compression Elements (those exceeding these limits are taken as Class 4 section)
Section Element Ratio Checked Class 1 Class 2 Class 3
General - None Assumed Class 3
Rectangular - None Assumed Class 2
I - shape
Web d/tw (rolled)
33 44 51 d/tw (welded)
Flange c/tf (rolled) 10 11 15
c/tf (welded) 9 10 15
Box
Web d/tw 33 38 42
Flange (b-3tf)/tf (rolled) 42 42 42
b/tf (welded) 42 42 42
Channel Web d/tw 33 38 42
Flange b/tf 10 11 15
T-Shape
Web h/tw 33 38 42
Flange b/2tf (rolled) 10 11 15
b/2tf (welded) 9 10 14
Angle - h/t
NA NA 15.0
(b+h)/(2t) 11.5
Round Bar - None Assumed Class 1
Pipe - d/t 502 702 902
Double Angle - h/t
NA NA 15.0
(b+h)/(2t) 11.5
NA = Not Applicable
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Chapter Three: Compression Members
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Class 4 cross sections, also known as thin-walled cross-sections, are those in which local buckling is liable to prevent the development of the yield moment; i.e., premature buckling occurs before yield is reached.
According to EBCS 3 1995, the classification of sections depends on the classification of flange and web elements. The classification also depends on whether the compression elements are in pure compression, pure bending or under the influence of combined axial force and bending. The latter two conditions will be discusses in subsequent chapters. This Chapter presents classification of compression elements for only pure compression according to Table 3.1.
The section dimensions used in the tables are given in Fig. 3.2. If the section dimensions satisfy the limits shown in the tables, the section is classified as Class 1, Class2, or Class3 as applicable. A cross-section is classified by reporting the highest (least favorable) class of its constituent compression elements that are partially or wholly in compression. If a section fails to satisfy the limits for class 3 sections, it is classified as Class 4.
One of the major factors in determining the limiting width-thickness ratio is the parameter . This parameter is used to reflect the influence of yield stress on the section classification.
(3.1)
The properties of Class 4 cross-sections may be established by calculation using the effective widths of the component elements in compression. The later may be obtained from Table 3.2 both for internal and outstand elements. The effective widths of flange elements may be based on the stress ratio determined for the gross cross-section. The effective width of a web element should be based on the stress ratio determined for a cross-section comprising the effective area of the compression flange but the gross area of the web and tension flange. In Table 3.2, it is recommended to determine the reduction factor as follows:
Where is the element slenderness defined as:
Parameter Steel Grade
Fe 360 Fe 430 Fe 510
fy 235 275 355 1 0.92 0.81
>
=
673.022.0
673.01
2 pp
p
forp
for
2/1235
=
yf
Fig. 3.3 Gross and effective cross sections of class 4 section subjected to compression
p
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Chapter Three: Compression Members
Design of Steel and timber structures (CE 519) Yibeltal Temesgen
7
(3.2b)
t = the relevant thickness k = the buckling factor corresponding to the stress ratio from Table 3.2.
b = the relevant width (see Fig 3.2) and given as follows:
Webs
b = d
Internal flanges
b = d
Box elements:
b = b-3t
Outstand flanges
b = c
Equal-legged angle:
b = (b + h)/2
Unequal-legged angle:
b = h or (b + h)/2
Table 3.2 Effective width of Class 4 cross-sections. Generally, the neutral axis of the effective section will shift by a dimension e compared to the neutral axis of the gross section as shown in fig. 3.3. This should be taken into account when calculating the properties of the effective cross-section.
RADII OF GYRATION OF COMMON SECTIONS
Whatsoever the section may be for design purposes, its radii of gyration about the principal axes are required so that the least radius of gyration may be obtained and used to find slenderness ratio. Table 3.3 Approximate radii of gyration for different sections.
Radii of gyration of single sections can be found generally with less computational effort. These properties are also given along with manufacturers manuals for standard sections. But for built up sections made of two or more components with or without the cover plates, the calculation work for radii of gyration becomes very tedious. The design of compression members is a a process of a trail and error which means that if first trial is not satisfactory, the next trails will have to be made. In every trail the radii of gyration are to be necessarily calculated. It becomes customary for a designer to have an idea of approximate radii of gyration of various commonly used sections so that much of the calculation work is reduced. The radii of gyration of commonly used sections are given in Table 3.3
Generally, the neutral axis of the effective section will shift by a dimension e compared to the neutral axis of the gross section as shown in fig. 3.3. This should be taken into account when calculating the properties of the effective cross-section.
ktbf
cr
yp
4.28/
==
a) Internal compression element
b) Outstand compression element
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Chapter Three: Compression Members
Design of Steel and timber structures (CE 519) Yibeltal Temesgen
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Radii of Gyration of Common Sections
Whatsoever the section may be for design purposes, its radii of gyration about the principal axes are required so that the least radius of gyration may be obtained and used to find slenderness ratio.
Radii of gyration of single sections can be found generally with less computational effort. These properties are also given along with manufacturers manuals for standard sections. But for built up sections made of two or more components with or without the cover plates, the calculation work for radii of gyration becomes very tedious. The design of compression members is a process of a trail and error which means that if first trial is not satisfactory, the next trails will have to be made. In every trail the radii of gyration are to be necessarily calculated. It becomes customary for a designer to have an idea of approximate radii of gyration of various commonly used sections so that much of the calculation work is reduced. The radii of gyration of commonly used sections can be obtained from any standard books.
Effective Length Factor
The effective length factor K is a factor which, when multiplied by the actual unbraced length L of an end-restrained compression member, will yield an equivalent pinned-ended member whose buckling strength is the same as that of the original end-restrained member. For a prismatic member, the effective length factor can be determined from Fig. 3.4 or Fig. 3.5
Figure 3.4 is used when the support conditions of the compression members can be closely represented by those shown in the figure. On the other hand, Fig. 3.5 is used for members that are parts of a framework.
Fig. 3.4 K factor table
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Chapter Three: Compression Members
Design of Steel and timber structures (CE 519) Yibeltal Temesgen
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The effect of end restraint is quantified by the two end restraint factors GA and GB where the su