Steel and Timbe

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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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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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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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

Chapter Two: Tension Members


1


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



2

Fig. 2.1 Tension Members in Buildings and Bridges



3

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.



4

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.



5

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



6

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-



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)



8

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:


____________________________________________________________________________________


9

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.


____________________________________________________________________________________


10

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

Chapter Three: Compression Members

Design of Steel and timber structures (CE 519) Yibeltal Temesgen

1

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



2

Fig. 3.1b Tapered members

Fig. 3.1c Stepped columns

Fig. 3.1d Built up columns



3

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



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



5

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



6

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



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



8

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



9

The effect of end restraint is quantified by the two end restraint factors GA and GB where the su

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