Aluminium Design and Construction John Dwight

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CHAPTER 9 Tension and compression members 9.1 GENERAL APPROACH 9.1.1 Modes of failure This chapter covers the static design of members subjected to axial force either in tension (‘ties’) or in compression (‘struts’). The basic requirement is that the factored resistance should not be less than the tensile or compressive force (action-effect) arising in the member under factored loading. The factored resistance is found by dividing the calculated resistance by the factor � m (Section 5.1.3). There are four possible modes of failure to consider in checking such members: 1. localized failure of the cross-section (Section 9.3); 2. general yielding along the length (Section 9.4); 3. overall column buckling (Section 9.5); 4. overall torsional buckling (Section 9.6). Check 1, which applies to both ties and struts, must be satisfied at any cross-section in the member. It is likely to become critical when a particular cross-section is weakened by HAZ softening or holes. Checks 2, 3 and 4 relate to the overall performance of the entire member. Check 2 is made for tension members, and checks 3 and 4 for compression members. Check 4 is not needed for hollow box or tubular sections. Most of the chapter is concerned with finding the calculated resistance P c to each mode of failure, when the force on the member acts concentrically, i.e. through the centroid of the cross-section. We then go on to consider the case of members which have to carry simultaneous axial load and bending moment (Section 9.7), one example of this being when an axial load is applied eccentrically (not through the centroid). Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
9.1.2 Classification of the cross-section (compression members) An early step in the checking of a compression member is to classify the section as compact or slender. If it is compact, local buckling is not a factor and can be ignored. If it is slender, local buckling will reduce the strength and must be allowed for. The classification procedure is first to classify the individual plate elements comprising the section, by comparing their slenderness ß with the limiting value ß s (Section 7.1.4). The classification for the section as a whole is then taken as that for the least favourable element. Thus for a section to be compact, all its elements must be compact. If one element is slender, then the overall cross-section is slender. Refer to Chapter 7 for the definition of the plate slenderness ß (Section 7.1.3 or 7.4.5), and also for the determination of ß s (Table 7.1). 9.2 EFFECTIVE SECTION 9.2.1 General idea It is important to consider three possible effects which may cause local weakening in a member, namely HAZ softening at welds, buckling of thin plate elements in compression and the presence of holes. These are allowed for in design by replacing the actual cross-section with a reduced or effective one (of area Ae ) which is then assumed to operate at full strength. Reference should be made to Chapter 6 in dealing with HAZ softening, and Chapter 7 for local buckling. Chapter 10 gives advice on the determination of section properties. 9.2.2 Allowance for HAZ softening Referring to Chapter 6, we assume that at any welded joint there is a uniformly weakened zone (HAZ) of nominal area Az , beyond which a step-change occurs to full parent properties. We take an effective thickness of kzt in this zone and calculate Ae accordingly, with the softening factor kz put equal to kz1 or kz2 depending on the type of resistance calculation being performed: Local failure of the cross-section kz =kz1 General yielding kz =kz2 Overall buckling kz =kz2 Alternatively a ‘lost area’ of Az (1-kz ) can be assumed at each HAZ, which is then deducted from the section area. This procedure is often preferable at a cross-section just containing small longitudinal welds, as it avoids the need to find the actual disposition of the HAZ material, Az for such welds being a simple function of the weld size (Section 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
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With MIG welding, an electrode-posi
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CHAPTER 7 Plate elements in compres
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(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
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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 and 192: Figure 8.23 Sections covered in Tab
Page 193 and 194: where: I yy , I vv =inertia about m
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Page 197: Figure 8.26 Components of deflectio
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
Page 243 and 244: 10.5.3 Evaluation of warping When t
Page 245 and 246: For sections where the position of
Page 247 and 248: (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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