Aluminium Design and Construction John Dwight

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estimate for the resistance M c of the section, since element X can just reach a stress p ° before it buckles. Line 1 in the figure, on which equation (8.2) is based, approximately represents the stress pattern for this case when failure is imminent. (We say ‘approximately’ because it ignores the rounded knee on the stress-strain curve.) Now consider semi-compact sections generally, again taking the type of beam in Figure 8.3 as an example. For these, the critical element X will have a ß-value somewhere between ß f and ß s , and some degree of plastic straining can therefore take place before failure occurs. This leads to an elasto-plastic stress pattern at failure such as line 2 in the figure, corresponding to a bending moment in excess of the value Zp ° . In the extreme case when element X is almost fully compact (ß only just greater than ß f ) the stress pattern at failure approaches line 3, corresponding to an ultimate moment equal to the fully compact value Sp ° which can be as much as 15% above that based on Z. It is thus seen that the use of the value Zp ° tends to underestimate M c , increasingly so as ß for the critical element approaches ß f . It is therefore suggested that interpolation should be used for semicompact sections, with M c found as follows: (8.4) This expression, in which the ß’s refer to the critical element, will produce higher values of M c closer to the true behaviour. 8.2.7 Semi-compact section with tongue plates Figure 8.4 shows a section with tongue plates, in which the d/t of the web (between tongues) is such as to make it semi-compact when classified in Figure 8.4 Elastic-plastic method for beam with tongue plates. Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
the usual manner. Line 1 in the figure indicates the (idealized) stress pattern on which M c would be normally based, corresponding to expression (8.2). Clearly this fails to utilise the full capacity of the web, since the stress at its top edge is well below the value p ° it can attain before buckling. Equation (8.2) therefore underestimates M c . An improved result may be obtained by employing an elasto-plastic treatment, in which a more favourable stress pattern is assumed with yield penetrating to the top of the web (line 2). The moment calculation is then based on line 2 instead of line 1. If the web is only just semicompact, M c is taken equal to the value M c2 calculated directly from line 2, while, in the general semi-compact case, it is obtained by interpolation using equation (8.4), with the quantity Zp ° replaced by M c2 . When operating this method we allow for HAZ softening by using the gross section and reducing the stress in any HAZ region to k z2 p ° . 8.2.8 Local buckling in an understressed compression flange Figure 8.5 shows a type of section in which the distance y c from the neutral axis to a slender compression flange X is less than the distance y t to the tension face. For such sections, local buckling in the compression flange becomes less critical because it is ‘understressed’, and the normal method of calculation will produce an oversafe estimate of M c . An improved result can be obtained by replacing the parameter � (=�(250/ p ° )) in the local buckling calculations by a modified value �’ given by: (8.5) This may make it possible to re-classify the section as semi-compact, or, if it is still slender, a more favourable effective section will result. In either case, M c is increased. Note, however, that such a device should not be employed as a means for upgrading a section from semi-compact to fully compact. 8.2.9 Biaxial moment We now turn to the case of asymmetric bending, when the applied moment has components about both the principal axes of the section. Figure 8.5 Understressed compression flange (X). 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
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
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: that for the gross section. It woul
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
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
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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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