design of steel structure beam

8/13/2019 Design of Steel Structure beam

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Introduction

Beams are an important class of structural element, and are normally horizontal.

The primary function of building structures is to support the major space enclosing

elements: commonly these are floors, roofs and walls. The total behaviour of anybuilding structure can be complicated but frequently two types of sub-structure can

be identified; vertical elements (associated with walls) and horizontal elements

(associated with floors and roofs).

Vertical elements are columns, walls and lift cores etc. Horizontal elements include

slabs, trusses, space frames and most importantly beams.


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What is a beam?

Beams support mainly vertical loads, and are small in cross-section compared with

their span. Engineering diagrams adopt simple conventions to represent beams,

supports and loads.

This section deals specifically with the engineering design of beams. Although

"beam" is a word in common usage for engineering design, it has a very particular

definition. A beamis a structural member which spans horizontally between supports

and carries loads which act at right angles to the length of the beam. Furthermore,

the width and depth of the beam are "small" compared with the span. Typically, the

width and depth are less than span/10.


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Use of BS 5950 - Part 1

BS5950 specifies rules for ensuring steel structures are safe

The current code of practice called "Structural Use of Steelwork in Building" is BS

5950 Part 1. This code gives specific guidance on the strength and stiffness of steelstructures for buildings to allow numerical calculations to be made.

Beam capacity is checked by comparing the ultimate strength with factored loadings.

It checks the strength of a structure by ensuring ultimate strength is not less than

working load x load factor

The load factor varies with the type of load.

Different load factors are applied to different types of load and load combinations.

This reflects the varying degree of confidence in the values of dead, imposed andwind loads used. Values of the load factors to be used are given in Table 2 of BS

5950.

The material strength is specified in relation to steel grade.

The ultimate strength is dependent on yield stress. Stresses are given for three

grades of steel called S275, S (These were formerly referred to as Grades 43, 50 and

55). Grade S275 (formerly Grade 43) is commonly used, although S355 is popular on

larger projects where it can offer significant economies. Higher grades are rarely

used, except for bridges, and special applications

The yield stresses pycorresponding to the different grades are given in BS 5950.

Specific guidance is given for determining the maximum moment and shear capacity

of a beam cross-section.

The maximum moment capacity is the lesser of:

Mc= py.Sx

and

Mc= 1.2 py.Zx

Sx is the plastic section modulus and Zx is the elastic section modulus.

The maximum shear capacity is

Pv= 0.6 pyAv

where Avis the shear area.

Cross-sections are classified according to their proportions.


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Open sections are classified as plastic, compact, semi-compact or slender. The

classification depends on the proportions of the webs and flanges. (Note that rolled

sections are seldom classified as slender).

The moment capacity of some sections may be reduced if shear forces are high.

The actual shear force (multiplied by the factor) is referred to by the symbol Fv. If Fv

exceeds 60% of the shear capacity of the cross-section, Pv, then this is defined as a

"high" shear load and the moment capacity for plastic and compact sections is

reduced.

For beams which are not fully restrained, bending strength may be reduced due to

lateral-torsional buckling; this is related to the slenderness ratio and cross-section

details of the beam.

If the compression side of a beam is not fully restrained against lateral torsional

buckling then the design stress py is reduced. This reduction depends on two factors

called the slenderness ratio and the D/T ratio.

The slenderness ratio l is given by:

l = LE/ry

LEis the effective length (Table 9 of BS5950).

ryis the radius of gyration = the square root of (I/A). Standard tables give values for

ry. The slenderness ratio may be reduced using the slenderness correction factor n

from table 20, to allow for the shape of actual bending moment.

The beam must be stiff enough to carry the working load without exceeding the

deflection limits specified.

Limiting deflections are given in Table 8 of BS 5950 as a proportion of the beam

span. These limiting values are compared with calculated deflections taking account

of the load, length, support conditions, and cross-section of the beam. In calculating

deflections it is normal to ignore any permanent loads, and to consider conditions in

service (ie without any load factors)


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Support conditions

Beam supports are generally classified as pinned, fixed or free.

Beams span between supports carrying the external load forces to the external

reaction forces.

The type of support influences the distribution of bending moments and shear forces.

For simple span beams the supports may bepinned, fixedor free.

A pinned support provides vertical but not rotational restraint.

A fixed support provides vertical and rotational restraint.

A free support provides no restraint which might seem to be a paradox (a free

support is often called a free end).

The type of support significantly influences the bending moments and shear forces.

For the same span L and the same loading, say a uniformly distributed load of W, the

distribution of bending moments and shear forces is quite different.

In simple construction, beam supports are commonly assumed to be pinned.

Ideal pinned and fixed supports are rarely found in practice, but beams supported on

walls or simply connected to other steel beams are regarded as pinned. Where


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beams are continuous or part of complete frames (portal etc.) the distribution of

moments and shear forces is influenced by the behaviour of the complete structure.


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Summary

Beams are commonly found in many types of structure.

Beams carry load principally by bending.

The internal forces generated in beams under load are referred to as bending

moments and shear forces.

The support conditions influence the nature of the bending moments and

shear forces.

The strength of a beam is related to its section modulus.

The stiffness of a beam is related to its second moment of area.

Local buckling and shear forces can reduce the bending strength of a beam.

Lateral torsional buckling is possible in laterally unrestrained beams, in which

case the buckling strength is related principally to the slenderness of the

beam.


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Factors affecting the design

Beams must be both strong and stiff.

The objective of the engineering design of beams is to make a choice of a beam for a

particular purpose then test by established numerical procedures whether:

the beam is strongenough

the beam is stiffenough

The behaviour of a beam is principally affected by the span, loading, how it is

supported, its material and its cross-section.

For the same span and loading, three things affect the performance of a beam.

These are:

the way the beam is supported.

the properties of the material

the geometry of the beam cross-section


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Factors affecting beam strength

Bending strength may be limited by material strength, lateral-torsional buckling or

local buckling.

As was stated previously the strength of a beam depends on its maximum momentand shear capacities, and these depend on the relevant allowable stresses.

A beam may fail in one of three ways. The three types of failure are material failure

causing a plastic hinge to form, lateral-torsional buckling along the length of the

beam, and local buckling of the beam cross-section.

A plastic hinge forms when the bending stress reaches the material yield strength.

Collapse by formation of a plastic hinge. Where the stress in the beam reaches the

yield stress, the bending moment cannot be increased and the beam collapses as

though a hinge has been inserted into the beam.

Lateral-torsional buckling is associated with the compression developed in part of the

beam cross-section due to bending.

Bending moments cause a pair of internal horizontal forces, one force is a tension

force and the other a compression force. The tension force stretches one side of the

beam. This force, like pulling a string, tends to keep the tension side of the beam

straight between supports.

However, the compression force can buckle the compression side of the beam.

Because the tension force is keeping one side taut, the beam can only bucklesideways and twist the beam - hence lateral torsional buckling.


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Lateral-torsional buckling may be resisted by restraining the beam laterally.

This buckling may be prevented by adequate lateral restraint preventing sideways

movement of the beam. If this is at discrete points, the beam may buckle between

these points.

Steel floor beams are often adequately restrained by the floor slab.

In building structures the floor slab is often able to provide effective restraint to the

floor beams, preventing lateral-torsional buckling. In such cases the beams can be

designed on the basis of the full bending strength.


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Local buckling can occur if the beam cross-section is very slender.

If some part of the beam is very slender, then this may buckle locally. In practice,

standard steel sections are proportioned so that this is not a critical design

consideration.

The dominant failure mode depends on a number of factors.

Which type of failure occurs depends on four factors:

the slenderness ratio of the beam.

the shape of the bending moment diagram.

the proportions of the individual parts (webs, flanges etc.) of the beam cross-

section.

the presence of a "high" shear force.

Any of these factors may reduce the allowable stress to below the yield stress to

ensure that the beam is safe against any type of failure.


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Estimating sizes

Simplified procedures can be used to estimate the required size of beam section.

In many cases it is not necessary to perform detailed calculations to determine beam

sizes, and simpler methods can be adopted. These include rules of thumb whichenable a simple estimate of approximate section sizes, and safe load tables which

provide a rigorous alternative to design calculations for standard cases.

Rules of thumb provide an estimate of the required depth of different types of beam

in relation to span.

A typical structural frame may include both primary (main) and secondary beams.

Roof beams tend to be more lightly loaded than floor beams, and the required

section is therefore generally somewhat smaller. Some guidance on maximum beam

spans and the required provide depth (as a proportion of the beam span) is given inthe table below.

Supporting Floor Roof

max span depth max span depth

Primary beams

(conventional

composite deck orprecast floor)

15m span/20 15m span/25

Secondary beams

(conventional

composite deck

floor)

12m span/25 12m span/30

ASB beams

(conventional

composite deck

floor)

10m span/30

Safe load tables provide more rigorous guidance on required sizes.


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The bending strength of a beam is related primarily to the material strength and the

section modulus, which itself depends on the size and shape of the cross-section. It

is therefore possible to calculate the maximum bending strength for any cross-

section, assuming that there is possibility of lateral-torsional buckling. Such tables

enable the section size required for a given bending moment to be read directly. In

using such tables, it is assumed that shear forces are relatively small (as is often the

case in practical design conditions), and some guidance is given in relation to

deflection control.


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Cross-section geometry

Cross-section size and shape influence beam

performance.

The performance of any beam is dependent upon thecross-sectional geometry, not only on the physical

dimensions, but also the shape. Steel beams are

available in a variety of cross-sectional shapes. These

include open sections and closed sections or tubes. In

practice I beams are most commonly used for the beams

in buildings. Rectangular hollow sections may be used

for edge beams where particular edge details are

required.

Beams may be standard sections or specially

manufactured.

Both open and closed sections are produced in a large variety of standard (serial)

sizes by a hot-rolling process. Standard sections are generally used because they

are readily available and are economic.

Variations on standard sections include castellated and cellform beams which are

efficient for very long spans, and provide for service runs.

Other sections can be fabricated from plate or by joining standard sections by boltingor welding.

Beams may be curved.

Beams may be curved to reduce overall deflections (precambering) or simply to

create more interesting shapes. This is achieved by a specialised bending process

which can be performed at a modest surcharge to fabrication costs. For small

degrees of curvature, the beam design calculations are no different from those for a

straight beam. However for significantly curved beams, the structural action becomes

that of an arch.

Bending behaviour is related to the moment of inertia and the section modulus of the

beam.

The main bending behaviour of a beam is determined by two geometric quantities.

These are the moment of inertiaand the section moduluswhich depend on the size

and shape of the cross-section. These quantities are given in standard tables for all

rolled sections.


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Beam strength

Beams must be sufficiently strong to carry the applied bending moments and shear

forces.

A primary concern of engineering design is to ensure that a chosen beam is strongenough to carry the load imposed on it safely. This simple concept is far from simple

to quantify.

The beam has to carry both the bending moment and the shear force.

The bending moment and shear force capacities are related to the physical

properties of the cross-section and material strength.

The bending moment capacity is expressed simply as:

moment capacity = allowable bending stress x section modulus

and the shear force capacity as:

shear capacity = allowable shear stress x shear area

The shear area for any section is calculated from the area of the vertical part of the

cross-section.

Note the maximum allowable stress is the stress of yield point and is called the yield

stress.

Provided

moment capacity / actual bending moment = adequate factor of safety

and

shear capacity / actual shear force = adequate factor of safety

everywhere along the beam then the beam is strong enough.


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Beam stiffness

Beams deflect when loaded and this must be limited to avoid damage and distress.

When a beam is loaded it will deflect. This deflection must be limited so that building

occupants are comfortable and that building materials are not damaged. Forinstance, large deflections in a steel beam supporting a partition could cause

unacceptable cracking in the plaster.

Beam deflections can be calculated and depend on the modulus of elasticity of the

material, and the moment of inertia of the cross-section.

In general, the calculation of deflection is not straightforward. However, algebraic

expressions are tabulated for many standard cases.

The deflection of a particular beam is inversely proportional to:

modulus of elasticity

moment of inertia

The modulus of elasticity is constant for all structural steels so the larger the moment

of inertia the smaller the deflection.


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Basic beam behaviour

Beam analysis is generally based on simplifying assumptions.

The detailed behaviour of a beam is complex and exact analysis requires

considerable mathematical sophistication. However, the vast majority of beams canbe designed using engineering beam theory. This is based on a number of

simplifying assumptions.

The structural action of a beam is represented by internal forces called bending

moments and shear forces.

A beam is subjected to two sets of external forces. These are the loads applied to the

beam and reactions to the loads from the supports. The beam transfers the external

load set to the external reaction set by a system of internal forces.

Engineering beam theory identifies two types of internal force bending moments

and shear forces. The behaviour of any beam is characterised by the magnitude and

distribution of these forces. At any point in the beam, the internal shear force and the

internal bending moment can be represented as pairs of forces.

The bending moment and shear forces vary along the beam length and are often

represented diagramatically.

These internal forces may vary along the length of the beam and are usually

represented as separate bending moment and shear force diagrams.

The calculation of bending moments and shear forces is traditionally part of structuralanalysis and is beyond the scope of this unit.

design of steel structure beam

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