Global Analysis (clause 5.2)
The EN 1993-1-1:2005 has prescribed use of the first order analysis if the buckling factor of the structure is greater than 10 if elastic analysis is employed (equation 5.1, clause 5.2.1). This has been specifically meant to ease the work of the structural engineers using manual methods for analysis and design.
While analyzing the structure with a computer, a designer can employ the second order analysis without verifying the aforementioned condition to generate more accurate analysis results. If the effect of deformed geometry is not supposed to be substantial the additional second order forces would be negligible from the analysis results.
However, if the user wishes to do this check and then employ a first order or second order elastic analysis, he can initially specify a PERFORM BUCKLING ANALYSIS. If the reported Buckling factors are reported as being bigger than 10, he can employ the first order analysis by specifying PERFORM ANALYSIS – else he can resort to using the second order analysis by specifying a PDELTA 30 ANALYSIS. The PDELTA 30 ANALYSIS calculates both the big delta and small delta effects.
A complete analysis needs to ensure that the Second Order effects and Imperfections are accounted for. STAAD can account for this as prescribed in clause 5.2.2 (3) b – that is, partially by global analysis and partially through the individual stability checks of members according to clause 6.3 of the code. Note that the Global Analysis in STAAD does not in itself accounts for Member Imperfections.
Imperfections:
When we talk about imperfections, we will only talk about global sway imperfections. The local bow imperfections are considered within capacity equations of buckling resistance of members.
Clause 5.3.2 (3) a of the code, equation 5.5 gives the equations for calculating the global sway imperfection in terms of Φ, the initial sway imperfection of the frame. One may choose to model the structure by incorporating this imperfection in the model. However, an easier way to model the initial sway imperfection is to replace the specified imperfection with a system of horizontal loads of value Φ*NED. NED is the vertical load on the column members of the frame.
These horizontal loads, called the notional loads, can easily be generated in STAAD using the Notional Load Command.
The use of Notional Loads to model the Sway Imperfection of the Frame is discussed in the following example.
Example of Global Analysis including Imperfections:
Let us consider the frame in the following example. The height of the frame is 10.5 metres and the width of the frame is 10.5 metres with four columns in each of the four rows on either side.
The Imperfection calculation is as below:
Φ = Φ0 αn αm
Φ0 = 1/200 = 0.005
αn = 2/(n)0.5 = 0.62 < 2/3
Thus, αn = 2/3 = 0.67
m = 4
αm = (0.5 (1+1/m))0.5
= (0.5 (1+1/4))0.5
= 0.79
Φ = 0.005 X 0.67 X 0.79
= 0.0026
Now, the imperfection can be modelled as horizontal load of magnitude 0.0026* NED. N is the axial load on the vertical members resulting from factored vertical dead and imposed load.
Now, the load items of the Dead Load Case and the Live Load case are specified as Reference Load Case as below:
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE Dead TITLE DEAD LOAD
SELFWEIGHT Y -1
JOINT LOAD
17 TO 48 FY -7
49 TO 64 FY -3.5
LOAD R2 LOADTYPE Live TITLE LIVE LOAD
17 TO 48 FY -4
49 TO 64 FY -1.5
END DEFINE REFERENCE LOADS
Now, let us assume a combination of Dead Load and Live of 1.35 DL + 1.5 LL. For imperfection consideration, appropriate Notional Load should also be considered alongside the combination of dead load and Live Load.
Now, the first primary load case defines the Factored Dead Load as below:
LOAD 1 LOADTYPE Dead TITLE DEAD LOAD
REFERENCE LOAD
R1 1.35
The second primary load case defines the factored Live Load:
LOAD 2 LOADTYPE Live TITLE LIVE LOAD
R2 1.5
The combination of Dead and Live Loads along with the appropriate Notional Loads in X direction can then be defined as follows:
LOAD 4 LOADTYPE None TITLE 1.35DL + 1.5LL + NOT_X
REPEAT LOAD
1 1.0 2 1.0
NOTIONAL LOAD
1 X 0.0026 2 X 0.0026
Similarly, the Notional Loads in Z direction can be specified as:
LOAD 5 LOADTYPE None TITLE 1.35DL + 1.5LL + NOT_Z
1 Z 0.0026 2 Z 0.0026
Now, let us specify the PERFORM BUCKLING ANALYSIS to determine the Buckling factors. The Buckling factors is to be determined under Vertical Load only. Thus, we have also specified a load case to determine the corresponding buckling factor.
LOAD 3 LOADTYPE TITLE LOAD CASE TO DETERMINE ALPHA_cr
This load case will not be required for subsequent analysis and can be de-activated after the Buckling factors have been determined.
Now the Output file Reports the Buckling factor for the first four modes as below:
CALCULATED BUCKLING FACTORS FOR LOAD CASE 3
MODE BUCKLING FACTOR
1 24.61027
2 37.93287
3 66.56160
4 88.10634
As we can see, the critical buckling mode has a buckling factor of greater than 10 and hence we can opt for an elastic analysis only.
Now, let us deactivate load case 3 and change the line PERFORM BUCKLING ANALYSIS to PERFORM ANALYSIS.
The final file input information is as below:
STAAD SPACE EXAMPLE PROBLEM FOR UBC LOAD
START JOB INFORMATION
ENGINEER DATE 19-May-15
END JOB INFORMATION
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 3.5 0 0; 3 7 0 0; 4 10.5 0 0; 5 0 0 3.5; 6 3.5 0 3.5;
7 7 0 3.5; 8 10.5 0 3.5; 9 0 0 7; 10 3.5 0 7; 11 7 0 7; 12 10.5 0 7;
13 0 0 10.5; 14 3.5 0 10.5; 15 7 0 10.5; 16 10.5 0 10.5; 17 0 3.5 0;
18 3.5 3.5 0; 19 7 3.5 0; 20 10.5 3.5 0; 21 0 3.5 3.5; 22 3.5 3.5 3.5;
23 7 3.5 3.5; 24 10.5 3.5 3.5; 25 0 3.5 7; 26 3.5 3.5 7; 27 7 3.5 7;
28 10.5 3.5 7; 29 0 3.5 10.5; 30 3.5 3.5 10.5; 31 7 3.5 10.5;
32 10.5 3.5 10.5; 33 0 7 0; 34 3.5 7 0; 35 7 7 0; 36 10.5 7 0;
37 0 7 3.5; 38 3.5 7 3.5; 39 7 7 3.5; 40 10.5 7 3.5; 41 0 7 7;
42 3.5 7 7; 43 7 7 7; 44 10.5 7 7; 45 0 7 10.5; 46 3.5 7 10.5;
47 7 7 10.5; 48 10.5 7 10.5; 49 0 10.5 0; 50 3.5 10.5 0; 51 7 10.5 0;
52 10.5 10.5 0; 53 0 10.5 3.5; 54 3.5 10.5 3.5; 55 7 10.5 3.5;
56 10.5 10.5 3.5; 57 0 10.5 7; 58 3.5 10.5 7; 59 7 10.5 7;
60 10.5 10.5 7; 61 0 10.5 10.5; 62 3.5 10.5 10.5; 63 7 10.5 10.5;
64 10.5 10.5 10.5;
MEMBER INCIDENCES
101 17 18; 102 18 19; 103 19 20; 104 21 22; 105 22 23; 106 23 24;
107 25 26; 108 26 27; 109 27 28; 110 29 30; 111 30 31; 112 31 32;
113 33 34; 114 34 35; 115 35 36; 116 37 38; 117 38 39; 118 39 40;
119 41 42; 120 42 43; 121 43 44; 122 45 46; 123 46 47; 124 47 48;
125 49 50; 126 50 51; 127 51 52; 128 53 54; 129 54 55; 130 55 56;
131 57 58; 132 58 59; 133 59 60; 134 61 62; 135 62 63; 136 63 64;
201 17 21; 202 18 22; 203 19 23; 204 20 24; 205 21 25; 206 22 26;
207 23 27; 208 24 28; 209 25 29; 210 26 30; 211 27 31; 212 28 32;
213 33 37; 214 34 38; 215 35 39; 216 36 40; 217 37 41; 218 38 42;
219 39 43; 220 40 44; 221 41 45; 222 42 46; 223 43 47; 224 44 48;
225 49 53; 226 50 54; 227 51 55; 228 52 56; 229 53 57; 230 54 58;
231 55 59; 232 56 60; 233 57 61; 234 58 62; 235 59 63; 236 60 64;
301 1 17; 302 2 18; 303 3 19; 304 4 20; 305 5 21; 306 6 22; 307 7 23;
308 8 24; 309 9 25; 310 10 26; 311 11 27; 312 12 28; 313 13 29;
314 14 30; 315 15 31; 316 16 32; 317 17 33; 318 18 34; 319 19 35;
320 20 36; 321 21 37; 322 22 38; 323 23 39; 324 24 40; 325 25 41;
326 26 42; 327 27 43; 328 28 44; 329 29 45; 330 30 46; 331 31 47;
332 32 48; 333 33 49; 334 34 50; 335 35 51; 336 36 52; 337 37 53;
338 38 54; 339 39 55; 340 40 56; 341 41 57; 342 42 58; 343 43 59;
344 44 60; 345 45 61; 346 46 62; 347 47 63; 348 48 64;
MEMBER PROPERTY EUROPEAN
101 TO 136 201 TO 236 PRIS YD 0.4 ZD 0.3
301 TO 348 TABLE ST IPEA400
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 2.5e+007
POISSON 0.156297
DENSITY 24
ISOTROPIC MATERIAL2
E 2.05e+008
POISSON 0.292124
DENSITY 77
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 MEMB 101 TO 136 201 TO 236
MATERIAL MATERIAL2 MEMB 301 TO 348
SUPPORTS
1 TO 16 FIXED
PERFORM ANALYSIS
FINISH