Aluminium Design and Construction John Dwight

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Table 8.1 Lateral-torsional buckling of certain conventional sections—empirical formulae for X and Y in equation (8.32) Notes. 1. Refer to Figure 8.23 for section details. 2. Notation: �=D/B �=C/B �=T/t for PI, PC =1.0 for LI, LC. 3. The formulae are only valid when: 1.5��4.5 ��0.5 1��2 Figure 8.24 Lateral-torsional buckling, cases covered in Section 8.7.5 (2) and (3). expressions given below, in which the various section properties should generally be based on the gross section. (a) Bisymmetric section: (8.34) (b) Section symmetric about major axis: Same expression as for the bisymmetric section. (c) Section symmetric about minor axis: (8.35) (d) Skew-symmetric section: Equation (8.34) may be used, but with I yy changed to I vv . The value obtained for M cr relates to a moment acting about the major principal axis uu. Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
where: I yy , I vv =inertia about minor principal axis, �=St Venant torsion factor (Section 10.4.2), H=warping factor (Sections 10.4.5,10.5), ß x =special LT buckling factor (Section 10.4.6), E=modulus of elasticity=70 kN/mm 2 . 3. Hollow box-type sections These only need to be considered for LT buckling when they are especially deep in relation to their width (Figure 8.24(e)). Such sections have a very large torsion factor �, compared to an open section of similar size. It is therefore acceptable in their case to ignore warping effects and obtain M cr from the following simplified expression: (8.36) In order to obtain M cr (and hence �) for other section shapes the reader can refer to the book Flexural-torsional Buckling of Structures by Trahair [27]. 8.7.6 Beams with very slender compression flanges In considering the LT buckling of symmetrical I-beams and channels, in which the outstand element(s) forming the compression flange are very slender (Section 7.2.5), the question arises as to whether it is acceptable to exploit the post-buckled strength of such elements. There are two possible options: 1. Method A is effectively what BS.8118 does. Post-buckled strength is ignored in the determination of Mc , using expression (7.8) to obtain � for these elements. But in determining � (Section 8.7.5) we base ° Mcr in equation (8.33) on the gross section. This method tends to become over safe at low �. 2. Method B is more favourable when the lateral supports are close spaced (low �). Here Mc is based on an effective section in the compression flange that does take advantage of post-buckled strength, using expression (7.7) to � obtain . For convenience, the tension flange ° may be assumed to be reduced in the same way to preserve major axis symmetry. � Here is determined as in Section 8.7.5(1), with Iyy based on the same effective section as that used for finding Mc , but � with and H based on the gross section. 8.7.7 Effective length for LT buckling In any given bay, the effective length l would normally be taken equal to the actual distance L between points of lateral support to the Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
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Aluminium Design and Construction C
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First published 1999 by E & FN Spon
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2.2.1 Rolling mill practice 2.2.2 P
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5 Limit state design and limiting s
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8.2.6 Use of interpolation for semi
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10.3.2 Inertias for a section with
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Preface Aluminium is easily the sec
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List of symbols The following symbo
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uu, vv principal axes w effective s
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1.1.3 The industrial metal It is on
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where A is the section area (mm 2 )
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1.3.1. The good points about alumin
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Deflection Because of the lower mod
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1.4.4 Establishment of the alloys I
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1.5.2 New technology Most of alumin
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large span, where self-weight is a
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These tend to be in all-aluminium c
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Close-up of the M-dec system, which
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Aluminium glazing system for commer
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Nat West Media Centre, Lords Cricke
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The main requirements for the produ
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in which t and w are in mm. These a
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Figure 2.1 Extrusion process (direc
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Figure 2.2 Typical extrusion die. t
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Figure 2.6 ‘Semi-hollow’ profil
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especially the stronger alloys in t
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Figure 2.9 Conventional profiles. 2
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2.4 TUBES By tubes we mean hollow s
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CHAPTER 3 Fabrication 3.1 PREPARATI
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Figure 3.1 Alternative designs for
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Figure 3.2 Thread insert. a coil-sp
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3.3 ARC WELDING 3.3.1 Use of arc we
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adjusted. The technique is claimed
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For welds of minimum or fatigue qua
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Figure 3.5 Friction-stir welding: s
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are, and the designer/fabricator mu
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cartridge, and mixing takes place a
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3.7.4 Painting Alloys having durabi
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Where a range is given, as for the
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will be only slightly above that fo
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heating the metal to a temperature
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Table 4.4 Characteristics of differ
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softening in the heat-affected zone
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60 alloys, are: BSEN.485 plate and
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Firure 4.3 Nominal composition and
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popular alloys in the series are: 6
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Figure 4.6 Variation of tensile str
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undercarriages of aircraft. They ar
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Figure 4.11 Minimum stress-strain c
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AC.51400 This is another non-heat-t
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times that of the actual pits) prod
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The severity of bimetallic corrosio
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Nominal loading. Nominal loads are
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2. Material factor (� m ). In the
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design does not, because stress at
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Table 5.2 Summary of limiting stres
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Figure 5.4 Plastic strain at workin
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example, a reduced value might be t
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The parameter � depends purely on
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CHAPTER 6 Heat-affected zone soften
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area of softening. With 7xxx-type m
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Figure 6.3 Typical hardness plots a
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6.4 SEVERITY OF HAZ SOFTENING 6.4.1
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Figure 6.6 Categories of welded joi
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Figure 6.10 One-inch rule, extent o
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e allowed for in design by replacin
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Figure 6.13 Predicted area (A z ) o
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Figure 6.15 Overlapping HAZs. nomin
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In determining A zp , an appropriat
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failure plane in the HAZ, close to
Page 141 and 142: With MIG welding, an electrode-posi
Page 143 and 144: CHAPTER 7 Plate elements in compres
Page 145 and 146: (a) Compression member elements The
Page 147 and 148: Table 7.1 Classification of element
Page 149 and 150: Figure 7.4 Slender internal element
Page 151 and 152: Figure 7.7 shows curves of � ° p
Page 153 and 154: (7.9a) (7.9b) The strain gradient c
Page 155 and 156: (through the centroid) for ß S . F
Page 157 and 158: Figure 7.13 Outstands under strain-
Page 159 and 160: Figure 7.15 Reinforced elements. Th
Page 161 and 162: Figure 7.18 Stiffener location for
Page 163 and 164: Figure 7.20 Slender reinforced inte
Page 165 and 166: CHAPTER 8 Beams 8.1 GENERAL APPROAC
Page 167 and 168: 8.2.2 Section classification The di
Page 169 and 170: that for the gross section. It woul
Page 171 and 172: the usual manner. Line 1 in the fig
Page 173 and 174: 1. Fully compact sections. The limi
Page 175 and 176: Figure 8.8 Transverse and longitudi
Page 177 and 178: 8.3.4 Shear resistance of bars and
Page 179 and 180: Figure 8.12 Tension-field action. i
Page 181 and 182: Figure 8.14 Moment/shear interactio
Page 183 and 184: depending on the estimated degree o
Page 185 and 186: where a is the stiffener spacing an
Page 187 and 188: plates (if fitted), p v =limiting m
Page 189 and 190: ending moment diagram. Two cases ar
Page 191: Figure 8.23 Sections covered in Tab
Page 195 and 196: post (Section 8.6.4) or by some oth
Page 197 and 198: Figure 8.26 Components of deflectio
Page 199 and 200: 9.1.2 Classification of the cross-s
Page 201 and 202: hole. Alternatively, it might fail
Page 203 and 204: Figure 9.2 Limiting stress p b for
Page 205 and 206: The determination of l involves a c
Page 207 and 208: Figure 9.6 Monosymmetric section. I
Page 209 and 210: Figure 9.9 Limiting stress p b for
Page 211 and 212: where s=� s /� t s =slenderness
Page 213 and 214: Figure 9.11 Type-R sections covered
Page 215 and 216: Figure 9.14 Four standardized profi
Page 217 and 218: 9.7.2 Secondary bending in trusses
Page 219 and 220: Table 9.5 Necessary checks for memb
Page 221 and 222: Figure 9.18 Axial load with biaxial
Page 223 and 224: 1. Tension members. The localized f
Page 225 and 226: Figure 10.1 Symmetric plastic bendi
Page 227 and 228: We now turn to monosymmetric sectio
Page 229 and 230: distance of its centroid from the n
Page 231 and 232: Figure 10.6 Elements of sections. I
Page 233 and 234: 10.3.3 Product of inertia The produ
Page 235 and 236: Usually the conditions are such as
Page 237 and 238: Table 10.2 Torsion constant. Factor
Page 239 and 240: Figure 10.12 Warping. Conventional
Page 241 and 242: where b, t=element width and thickn
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10.5.3 Evaluation of warping When t
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For sections where the position of
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(10.31) where: e=distance that S li
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10.5.9 Asymmetric sections Before s
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CHAPTER 11 Joints This chapter cons
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the use of limiting stresses taken
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and the summation is made for all t
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Figure 11.3 Interaction diagram for
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k in order to give a fair compariso
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3. The design is satisfactory if fo
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When the method of surface preparat
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11.3.3 Weld force arising In many c
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Table 11.6 Limiting stress p w (N/m
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where p a =limiting stress for unwe
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Figure 11.11 Interaction diagram fo
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Manufacturers of structural adhesiv
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11.4.6 Creep Shear strength figures
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Figure 11.15 Effect of glue-line th
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Table 11.7 and Figure 11.17 provide
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11.4.11 Resistance calculations for
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high value reflects the various unc
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therefore usually presented in term
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For example: The loading spectrum i
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act on the structure. However, BS.8
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Figure 12.4 Crack propagation: (a)
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12.5 CLASSIFICATION OF DETAILS 12.5
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i.e. a joint extending in the same
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when the design life is low or when
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Methods (2) and (3) are difficult t
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it reverts to line 1. The slope s o
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Aluminium Design and Construction John Dwight

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