Chapter 2 Member Design

Chapter 2 : MEMBER DESIGN Summary:

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Section needs to be be classified classified to avoid local plate buckling

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A variety of section shapes are available for beams, choice depends on local and span.

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Beams may often be designed designed on basis basis of bending moment resistance. Stiffness under serviceability loads is an important consideration. Beams which are unable to move laterally are termed restrained . Moment resistance is dependent on section classification. Co-existent shear forces below 50% of the plastic shear resistance do not affect moment resistance. Beams bent about the major axis may fail by buckling in a more flexible plane This form of buckling involves both lateral deflection and twisting - lateral-torsional buckling The applied moment at which which a beam buckles by deflecting laterally laterally and twisting reached is the elastic critical moment  A design approach for beams prone to failure by lateral-torsional buckling buckling must account for a large number of factors - including section shape, the degree of lateral restraint , type of loading, residual stress pattern and initial imperfections Stocky beams beams are unaffected by lateral torsional buckling buckling and capacity is governed by the plastic resistance moment of the cross section Slender beams have capacities close to the theoretical elastic critical moment Many practical beams are significantly adversely affected by inelasticity and geometrical imperfections, hence elastic theory provides an upper band solution. A design expression linking the plastic capacity of stocky beams with the elastic behaviour of slender beams is provided by a reduction factor  for  for lateral torsional buckling Structural members subjected to axial compression and bending are known as beam columns. The interaction of normal force and bending may be treated elastically or plastically using equilibrium equilibrium for the classification of cross-section. The behaviour and design of beam-columns are presented within the context of members subjected to uniaxial bending, whose response is such that deformation takes place only in the plane of the applied moments. In the case of beam-columns which are susceptible to lateral-torsional lateral-torsional buckling, the out-of-plane flexural  buckling of the the column has has to be combined combined with the the lateral-torsional lateral-torsional buckling of of the beam using the relevant interaction formulae. • For beam-columns with biaxial bending, the interaction formula is expanded by the addition of an additional term.

• Objectives:

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explain the procedure for section classification explain the procedures used to design restrained beams, design a beam for bending resistance, check a beam for compliance with serviceability criteria, describe how to reduce the bending bending resistance resistance of a beam to allow for high shear loads. describe the difference in behaviour of stocky and slender columns recognise the sources of imperfection in real columns and the need for a probabilistic approach to design compare the ECCS column curves calculate the non-dimensional slenderness of a column calculate the reduction reduction factor for the relevant relevant buckling modes for columns columns of different cross-sectional shapes calculate the in-plane bending and axial compression force for beam-columns calculate the lateral-torsional buckling of beam-columns calculate the biaxial bending and axial compression force for beam-columns

References:

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Eurocode 3 Design of steel structures Part 1.1 General rules and rules for b uildings

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The Behaviour and Design of Steel Structures, N S Trahair and M A Bradord, E & F Span, 1994. Galambos, T.V., Structural Members and Frames, Prentice-Hall, 1968  Narayanan, R., Beams and Beam Beam Columns Columns - Stability Stability and Strength, Applied Science, Science, London, 1983

Contents:

1. 2. 3. 4. 5.

Section classification Compression members Restrained beams Unrestrained beams Members subjected to axial force and moments

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The Behaviour and Design of Steel Structures, N S Trahair and M A Bradord, E & F Span, 1994. Galambos, T.V., Structural Members and Frames, Prentice-Hall, 1968  Narayanan, R., Beams and Beam Beam Columns Columns - Stability Stability and Strength, Applied Science, Science, London, 1983

Contents:

1. 2. 3. 4. 5.

Section classification Compression members Restrained beams Unrestrained beams Members subjected to axial force and moments

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Chapter 2 Member Design 1

Local Buckling and Section Classification

1.1

Introduction.

Local buckling is a phenomena which affects all thin materials when subjected to a compressive force. Its effect is to cause wide plate elements within a member to buckle before they reach the design strength. A typical pattern of local buckling in the outstand flange of a  beam in bending is shown in figure figure 1.1.

Figure 1.1 typical pattern of local buckling in outstand flange:

1.2

Section Classification.

BS 5950 prevents local buckling of the various elements of the cross section by classifying each element according to its b/t or d/t ratio, then designing the cross section accordingly. It is therefore necessary to define the parts of the cross section which are to be considered. Figure 5 of BS 5950- 1 defines the various elements in a number of cross sections. For the  purpose of this lecture two particular shapes shapes will be considered, a universal beam and and a hot finished hollow section as shown in Figure 1.2:

2- 3

 b

T

 b

Outstand

Flange

r  D

Web

Web

t

D

t d

d

B

B

Universal Beam

For a Hot finished hollow section

d=D-2(T + r)

b = B/2

b=B-3t

d=D-3t

Figure 1.2 Section shapes The classification of sections is carried out according to tables 11 and 12 of the code parts of which are shown in Table 1.1 of these notes.

Table 1.1 - Limiting width to thickness ratios for H- or I-section or sections other than CHS and RHS

Compression element

Ratio

Outstand element of Rolled compression flange section Web (Neutral axis at mid depth) Web generally If r 1 is  positive (compression)

Limiting values Class 2 Class 3 Compact Semi-compact 10ε 15ε

 b/T

Class 1 Plastic 9ε

d/t d/t

80ε 80ε 

100ε 100

120ε 120ε 

1 + r 1

1 + 1.5r 1

1 + 2r 2

 but ≥ 40ε 

 but ≥ 40ε 

 but ≥ 40ε 

If the b/t or the d/t for class 3 (semi-compact) semi compact sections is exceeded then the element is class 4 (slender). i.e., it will buckle locally before full axial load is achieved.  Notes to tables: 1. 2. 3.

The term ε=(275/py)1/2 is used to accommodate varying design strengths. F c F c For I and H sections r 1 = but –1