Aluminium Design and Construction John Dwight

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5.4.2 Construction of the design curves It is convenient to represent buckling design curves by means of an empirical equation, containing factors that enable them to be adjusted up or down as required. Here we follow BS.8118 by employing the modified Perry formula, which is a development of the original Perry strut-formula that was devised by Ayrton and Perry in 1886. The modified Perry formula is a quadratic in p b , the lower of the two roots being the one taken. It may be written as follows (valid for �>�1): where: p l =intercept on stress-axis, p E =‘ideal’ buckling stress (curve E)=� 2 E/� 2 �=slenderness parameter, � ° =intercept of plateau produced on curve � 1 =extent of plateau on design curve, c=imperfection factor, E=modulus of elasticity=70 kN/mm 2 . The solution to (5.6) is: where: (5.6) (5.7) Figure 5.6 shows the effect of c on the shape of the curve thus obtained, for given P 1 and � 1 . Figure 5.6 Modified Perry buckling formula, effect of c. Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
The parameter � depends purely on the geometry of the member. For ordinary column buckling (C) it is simply taken as effective length over radius of gyration (l/r). For the other buckling modes (T, LT) it is defined as follows: (5.8) where the ideal buckling stress p E is as given by standard elastic buckling theory. In other words, ? is taken in such a way that the ‘ideal’ curve (E) is always the same as the Euler curve, whatever buckling mode is considered. The stress p 1 at which the design curve intercepts the stress-axis would normally be put equal to the limiting stress p ° for the material (Section 5.3). However, a reduced value must be taken if the cross-section has reduced strength, due to either local buckling or HAZ softening at welds. 5.4.3 The design curves The exact shape of the curve for a given value of p 1 is controlled by two parameters: the plateau ratio � 1 /� ° and the imperfection factor c. In any buckling situation, these have to be adjusted to give the right shape of design curve. British Standard BS.8118 rationalizes overall buckling by adopting six series of design curves, with parameter values as given in Table 5.5. These are based on research by Nethercot, Hong and others [15–17]. The curves are compared in Figure 5.7 on a non-dimensional plot. Actual design curves of p b against � appear in Chapters 8 and 9, covering a range of values of p 1. Table 5.5 Overall buckling curves—parameter values Notes. 1. This table relates to equations (5.6), (5.7). 2. The resulting families of design curves are presented as follows: LT, Figure 8.22; C1, 2, 3, Figure 9.2; T1, 2 Figure 9.9. 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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Page 67 and 68: For welds of minimum or fatigue qua
Page 69 and 70: Figure 3.5 Friction-stir welding: s
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Page 73 and 74: cartridge, and mixing takes place a
Page 75 and 76: 3.7.4 Painting Alloys having durabi
Page 77 and 78: Where a range is given, as for the
Page 79 and 80: will be only slightly above that fo
Page 81 and 82: heating the metal to a temperature
Page 83 and 84: Table 4.4 Characteristics of differ
Page 85 and 86: softening in the heat-affected zone
Page 87 and 88: 60 alloys, are: BSEN.485 plate and
Page 89 and 90: Firure 4.3 Nominal composition and
Page 91 and 92: popular alloys in the series are: 6
Page 93 and 94: Figure 4.6 Variation of tensile str
Page 95 and 96: undercarriages of aircraft. They ar
Page 97 and 98: Figure 4.11 Minimum stress-strain c
Page 99 and 100: AC.51400 This is another non-heat-t
Page 101 and 102: times that of the actual pits) prod
Page 103 and 104: The severity of bimetallic corrosio
Page 105 and 106: Nominal loading. Nominal loads are
Page 107 and 108: 2. Material factor (� m ). In the
Page 109 and 110: design does not, because stress at
Page 111 and 112: Table 5.2 Summary of limiting stres
Page 113 and 114: Figure 5.4 Plastic strain at workin
Page 115: example, a reduced value might be t
Page 119 and 120: CHAPTER 6 Heat-affected zone soften
Page 121 and 122: area of softening. With 7xxx-type m
Page 123 and 124: Figure 6.3 Typical hardness plots a
Page 125 and 126: 6.4 SEVERITY OF HAZ SOFTENING 6.4.1
Page 127 and 128: Figure 6.6 Categories of welded joi
Page 129 and 130: Figure 6.10 One-inch rule, extent o
Page 131 and 132: e allowed for in design by replacin
Page 133 and 134: Figure 6.13 Predicted area (A z ) o
Page 135 and 136: Figure 6.15 Overlapping HAZs. nomin
Page 137 and 138: In determining A zp , an appropriat
Page 139 and 140: 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
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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
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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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post (Section 8.6.4) or by some oth
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Figure 8.26 Components of deflectio
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9.1.2 Classification of the cross-s
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hole. Alternatively, it might fail
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Figure 9.2 Limiting stress p b for
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The determination of l involves a c
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Figure 9.6 Monosymmetric section. I
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Figure 9.9 Limiting stress p b for
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where s=� s /� t s =slenderness
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Figure 9.11 Type-R sections covered
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Figure 9.14 Four standardized profi
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9.7.2 Secondary bending in trusses
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Table 9.5 Necessary checks for memb
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Figure 9.18 Axial load with biaxial
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1. Tension members. The localized f
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Figure 10.1 Symmetric plastic bendi
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We now turn to monosymmetric sectio
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distance of its centroid from the n
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Figure 10.6 Elements of sections. I
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10.3.3 Product of inertia The produ
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Usually the conditions are such as
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Table 10.2 Torsion constant. Factor
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Figure 10.12 Warping. Conventional
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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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