Aluminium Design and Construction John Dwight

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10.5.6 Skew-symmetric sections Figure 10.17(c) shows a skew-symmetric profile. For such a section, S again lies at the point of symmetry, and we take the start-point O for numbering the elements at the same position. But this is not now a point of zero warping and w o must be evaluated using equation (10.28), enabling w m to be found for each element. H is then calculated using equation (10.29). The summations in equations (10.28) and (10.29) may conveniently be made for the elements in one half of the section (as shown numbered), and then doubled. Skew-radial-symmetric sections are treated similarly (Figure 10.17(d)), the summations being made for the elements in one arm, and then multiplied by n (the number of arms). 10.5.7 Monosymmetric sections, type 1 The shear centre S always lies on the axis of symmetry ss for a monosymmetric section, but not generally at the same position as the centroid G. Before H can be calculated it is necessary to locate S, which involves taking a trial centre-of-twist B at a suitable point on ss. Firstly, we consider monosymmetric sections in which ss cuts across the section at its midpoint (Figure 10.18), referred to as type 1. For these, we take B at the point of intersection with ss, as shown, which coincides with the start-point O for the numbering of the elements. A quantity w b is introduced, analogous to w s , but based on rotation about the trial axis B instead of the true axis S (which has yet to be located). For element r we thus have: (10.30) where d b is the perpendicular distance from B to the median line of an element, using an equivalent sign convention to that employed for d (Section 10.5.3). The summation in the first term is for elements lying above ss, up to but not including the one considered. The location of S is then given by: Figure 10.18 Monosymmetric section, type 1. Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
(10.31) where: e=distance that S lies to the left of B, a=distance of midpoint of element from ss (taken positive), c=projection of b on an axis perpendicular to ss, taken positive if diverging from ss in the direction of flow, and negative if not, I ss =inertia of the whole section about ss. The summation is made for the elements lying above ss only. Having located S it is possible to find d and w m for the various elements, and hence obtain H from equation (10.29). Distance d is measured from the true axis of rotation (S), and w m is found from equation (10.26), putting w o =0. In calculating H the summation in equation (10.29) can be conveniently made for the elements on one side of ss and then doubled. Alternatively, H may be determined from the following equivalent expression, which avoids the need to find d and w m for the various elements: The summation is again just for the elements lying above ss. 10.5.8 Monosymmetric sections, type 2 (10.32) We now turn to monosymmetric sections in which the axis of symmetry ss lies along a central web (Figure 10.19), referred to as type 2. These require a modified treatment. The elements are again numbered on one side only Figure 10.19 Monosymmetric section, type 2. 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
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Table 7.1 Classification of element
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Figure 7.4 Slender internal element
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Figure 7.7 shows curves of � ° p
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(7.9a) (7.9b) The strain gradient c
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(through the centroid) for ß S . F
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Figure 7.13 Outstands under strain-
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Figure 7.15 Reinforced elements. Th
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Figure 7.18 Stiffener location for
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Figure 7.20 Slender reinforced inte
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CHAPTER 8 Beams 8.1 GENERAL APPROAC
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8.2.2 Section classification The di
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that for the gross section. It woul
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the usual manner. Line 1 in the fig
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1. Fully compact sections. The limi
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Figure 8.8 Transverse and longitudi
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8.3.4 Shear resistance of bars and
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Figure 8.12 Tension-field action. i
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Figure 8.14 Moment/shear interactio
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depending on the estimated degree o
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where a is the stiffener spacing an
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plates (if fitted), p v =limiting m
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ending moment diagram. Two cases ar
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Figure 8.23 Sections covered in Tab
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where: I yy , I vv =inertia about m
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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
Page 243 and 244: 10.5.3 Evaluation of warping When t
Page 245: For sections where the position of
Page 249 and 250: 10.5.9 Asymmetric sections Before s
Page 251 and 252: CHAPTER 11 Joints This chapter cons
Page 253 and 254: the use of limiting stresses taken
Page 255 and 256: and the summation is made for all t
Page 257 and 258: Figure 11.3 Interaction diagram for
Page 259 and 260: k in order to give a fair compariso
Page 261 and 262: 3. The design is satisfactory if fo
Page 263 and 264: When the method of surface preparat
Page 265 and 266: 11.3.3 Weld force arising In many c
Page 267 and 268: Table 11.6 Limiting stress p w (N/m
Page 269 and 270: where p a =limiting stress for unwe
Page 271 and 272: Figure 11.11 Interaction diagram fo
Page 273 and 274: Manufacturers of structural adhesiv
Page 275 and 276: 11.4.6 Creep Shear strength figures
Page 277 and 278: Figure 11.15 Effect of glue-line th
Page 279 and 280: Table 11.7 and Figure 11.17 provide
Page 281 and 282: 11.4.11 Resistance calculations for
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Page 285 and 286: therefore usually presented in term
Page 287 and 288: For example: The loading spectrum i
Page 289 and 290: act on the structure. However, BS.8
Page 291 and 292: Figure 12.4 Crack propagation: (a)
Page 293 and 294: 12.5 CLASSIFICATION OF DETAILS 12.5
Page 295 and 296: 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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