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1 +Steel Design
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1 +Manuals.Theory Manual.WebHome
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1 +XWiki.StruSoft
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1 += General =
2 +
3 +(% style="text-align: justify;" %)
4 +The following design considers EC2 (standard) and the National Annex (NA) for Denmark, Finland, Germany, Hungary, Norway, Sweden and United Kingdom.
5 +
6 +(% style="text-align: justify;" %)
7 +With the steel module arbitrary structures in space can be designed with regard to a 1^^th^^ order or a 2^^nd^^ order analysis.
8 +
9 +(% style="text-align: justify;" %)
10 +In the **Code Check** all checks prescribed in the codes depending on section type, section class and acting section forces are displayed
11 +
12 += Limitations =
13 +
14 +== Torsion ==
15 +
16 +(% style="text-align: justify;" %)
17 +Only uniform torsion (St Venant torsion) is considered in the present version. For thin walled open sections the effect of warping torsion (Vlasov torsion) could be important and must then be considered separately.
18 +
19 +(% style="text-align: justify;" %)
20 +== Crushing of the web ==
21 +
22 +Crushing of an un-stiffened web due to a concentrated force is not checked in the present version.
23 +
24 += Global analysis =
25 +
26 +== General ==
27 +
28 +The design can be performed using either:
29 +
30 +* 1^^th ^^order analysis, using the initial geometry of the structure or,
31 +* 2^^nd^^ order analysis, taking into account the influence of the deformation of the structure.
32 +
33 +=== Choice between a 1^^th^^ order or a 2^^nd^^ order analysis ===
34 +
35 +For structures not sensitive to buckling in a sway mode a 1^^th^^ order analysis is sufficient. The design for member stability should then be performed with non- sway buckling lengths.
36 +
37 +In many cases it is easy to decide if a structure is sway or non-sway but in other cases it could be more difficult.
38 +
39 +One way to estimate if the non-sway condition is fulfilled is described in EC3 part 1-1 with the following criterion:
40 +
41 +α,,cr,, = F,,cr ,,/ F,,Ed,, > 10 => Non-sway
42 +
43 +where:
44 +
45 +**α,,cr,,** is the critical parameter meaning the factor by which the design loading would have to be increased to cause elastic instability in a global mode,
46 +**F,,Ed,,** is the design loading on the structure,
47 +**F,,cr,,** is the elastic critical buckling load for global instability mode based on initial elastic stiffness.
48 +
49 +An imperfection calculation in **FEM-Design** will display the critical parameters for the number of buckling shapes required by the user as shown below.
50 +
51 +[[image:1557408366029-104.png||height="377" width="563"]]
52 +
53 +//Critical parameter αcr displayed for the three first buckling shapes with regard to load combination L1.//
54 +
55 +
56 +(% style="text-align: justify;" %)
57 +As all critical parameters are > 10 a 1th order analysis and a design with non- sway buckling lengths would be sufficient in this case.
58 +
59 +(% style="text-align: justify;" %)
60 +If the criterion above is not fulfilled 2nd order effects must be considered but a 1^^th^^ order analysis could still be used in most cases. This could be done either by amplifying the 1^^th^^ order moments or by using sway-mode buckling lengths. In FEM-Design the latter method should be used.
61 +
62 +(% style="text-align: justify;" %)
63 +A full 2nd order analysis can be used for steel design in all cases.
64 +
65 +== Structural stability ==
66 +
67 +(% style="text-align: justify;" %)
68 +The calculations with regard to instability will be performed in different ways depending on the type of analysis.
69 +
70 +=== 1^^th^^ order theory ===
71 +
72 +For a 1^^th^^ order design the following apply:
73 +
74 +(% style="text-align: justify;" %)
75 +Both the flexural, lateral torsional and torsional buckling are calculated depending on the slenderness with respect to reduction factors specified in the appropriate code. The reduced slenderness for flexural and torsional buckling may be computed as:
76 +λ = [A f,,y,, / N,,cr,,]^^1/2^^
77 +
78 +(% style="text-align: justify;" %)
79 +The critical normal force for flexural buckling N,,cr,, will in this case be calculated using appropriate buckling lengths defined by the user in both directions for all members. The critical normal force Ncr for torsional buckling will be calculated according to support conditions defined by the user for all members. The reduced slenderness for lateral torsional buckling may be computed as:
80 +λ,,LT,, = [W fy / M,,cr,,]^^1/2^^
81 +
82 +(% style="text-align: justify;" %)
83 +The critical moment **M,,cr,,** will be calculated as buckling of the compressed flange with regard to a buckling length defined by the user.
84 +
85 +(% style="text-align: justify;" %)
86 +**Imperfections**
87 +Initial bow imperfections may be neglected as these effects are included in the formulas for buckling resistance of the members.
88 +
89 +(% style="text-align: justify;" %)
90 +For sway mode structures initial sway imperfections has to be considered. This could be done by changing the geometry before calculation or by defining systems of equivalent horizontal forces as described below
91 +
92 +=== 2^^nd^^ order theory ===
93 +
94 +A 2^^nd^^ order calculation produces the critical normal force **N,,cr,,** for flexural buckling and a corresponding stability check is not required. The critical normal force **N,,cr,,** for torsional buckling or the critical moment **Mcr** are not calculated since a basic finite element only contains the second order effects of the axial force and the effect of warping is neglected. The effect of the lateral torsional and torsional buckling will then have to be calculated as for 1^^th^^ order above.
95 +
96 +
97 +**Imperfections**
98 +For all structures initial local bow imperfections should be considered.
99 +
100 +As the flexural buckling design is based on the 2^^nd^^ order effects of the bending moments it is vital that there is a moment distribution in all members. By considering local bow imperfections this is ensured also for hinged members without lateral load.
101 +
102 +For sway mode structures also initial sway imperfections has to be considered. This could be done in the conventional way by changing the geometry before calculation or by defining systems of equivalent horizontal forces as described in the section below.
103 +
104 +(% style="text-align: justify;" %)
105 +In **FEM-Design** both initial bow imperfections and initial sway imperfections are considered automatically by using an alternative method presented in EC3 1-1 as described below in the section below. The user has to connect each load combination to one of the calculated buckling shapes and the program will then calculate imperfections with regard to this shape. It is up to the user to decide how many buckling shapes that has to be considered and to which load combinations these shapes should be connected to receive an adequate result. No design based on a 2^^nd^^ order analysis for compressed members can be performed without considering imperfection for one of the available buckling shapes. Some examples describing this process are presented in the manual Useful examples.
106 +
107 +(% class="box warningmessage" style="text-align: justify;" %)
108 +(((
109 +Note! When performing a 2nd order calculation a division of the members in more than one finite element could strongly influence the result. See chapter
110 +(% style="color:#e74c3c" %)2.3.3.4 (%%)for more information.
111 +)))
112 +
113 +
114 +== Imperfections for global analysis of frames ==
115 +
116 +The following imperfections should be taken into account:
117 +
118 +1. Global imperfections for the structure as a whole.
119 +1. Local imperfections for individual members.
120 +
121 +The assumed shape of global imperfections and local imperfections may be derived from the elastic buckling mode of a structure in the plane of buckling considered.
122 +
123 +Both in and out of plane buckling including torsional buckling with symmetric and asymmetric buckling shapes should be taken into account in the most unfavorable direction and form.
124 +
125 +For frames sensitive to buckling in a sway mode the effect of imperfections should be allowed for in frame analysis by means of an equivalent imperfection in the form of an initial sway imperfection and individual bow imperfections of members.
126 +
127 +
128 +=== Conventional method ===
129 +
130 +
131 +Global initial sway imperfections
132 +This effect could be considered in two ways.
133 +
134 +1. By changing the frame geometry before analysis with the slope as shown below. The slope φ will be calculated according to the relevant code.
135 +1. By defining a system of equivalent horizontal forces as shown below:
136 +
137 +[[image:1557409785741-586.png||height="234" width="217"]][[image:1557409850477-241.png||height="245" width="530"]]
138 +
139 +
140 +(% style="text-align: justify;" %)
141 +Where, in multi-storey beam and column building frames, equivalent forces are used they should be applied at each floor and roof level.
142 +
143 +(% style="text-align: justify;" %)
144 +These initial sway imperfections should apply in all relevant horizontal directions, but need only be considered in one direction at a time.
145 +
146 +(% style="text-align: justify;" %)
147 +The possible torsional effects on a structure caused by anti-symmetric sways at the two opposite faces, should also be considered
148 +
149 +[[image:1557410319017-185.png||height="259" width="597"]]
150 +
151 +
152 +* **Relative initial local bow imperfections of members for flexural buckling**
153 +Equivalent horizontal forces introduced for each member as shown below could consider this effect.
154 +The value **e,,o,,** considering initial bow as well as residual stresses is calculated according to the relevant code.
155 +
156 +=== Alternative method ===
157 +
158 +As an alternative to the methods described above for calculating imperfections the shape of the
159 +elastic critical buckling mode **η,,cr,,** of the structure may be applied as a unique global and local imperfection according to EC3 1-1. This method is used in **FEM-Design** when a 2^^nd^^ order analysis together with imperfection for one of the available buckling shapes is chosen.
160 +
161 +The amplitude of this imperfection may be determined from:
162 +
163 +[[image:1557767003804-873.png||height="51" width="205"]]
164 +
165 +
166 +
167 +== Division of members ==
168 +
169 +
170 += EuroCode(EC3) =
171 +
172 +
173 +== Classification of cross-sections ==
174 +
175 +
176 +== Axial force capacity ==
177 +
178 +
179 +=== Tension force ===
180 +
181 +
182 +=== Compression force ===
183 +
184 +
185 +== Bending moment capacity ==
186 +
187 +
188 +
189 +== Shear capacity ==
190 +
191 +
192 +
193 +== Shear and Torsion ==
194 +
195 +
196 +== Warping torsion (Vlasov torsion) ==
197 +
198 +
199 +
200 +
201 +
202 +
203 +
204 +{{box cssClass="floatinginfobox" title="**Contents**"}}
205 +{{toc /}}
206 +{{/box}}
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