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From version < 40.1 >
edited by IwonaBudny
on 2018/09/10 11:17
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... ... @@ -256,6 +256,21 @@
256 256  
257 257  = **Calculations parameters and calculations steps** =
258 258  
259 +(% style="text-align: justify;" %)
260 +Calculation input parameters can be set in the Calculation dialog in Analysis/ Seismic analysis in the Setup as can be seen below.
261 +
262 +(% style="text-align: justify;" %)
263 +[[image:1536569776410-536.png||height="76" width="250"]]
264 +
265 +(((
266 +(% class="box warningmessage" %)
267 +(((
268 +Remarks:
269 +
270 +* Setup for the Seismic calculation can be done at any time, but the Seismic calculation could be performed only after Eigenfrequency calculation
271 +)))
272 +)))
273 +
259 259  == Calculation methods selection ==
260 260  
261 261  (% style="text-align: justify;" %)
... ... @@ -276,7 +276,8 @@
276 276  * Lateral force method, where the base shear force can be distributed in two ways (Static linear/mode shape),
277 277  * Modal response spectrum analysis (Modal analysis).
278 278  
279 -=== (% style="font-size:18px" %)Lateral force method(%%) ===
294 +(% id="H1.Lateralforcemethod" %)
295 +=== 1. Lateral force method ===
280 280  
281 281  In some codes called equivalent static analysis.EC8 as well NS3491-12 uses this method. The user may not use this method in other codes.
282 282  
... ... @@ -309,9 +309,10 @@
309 309  
310 310  (% style="text-align: justify;" %)
311 311  Distribution of the base shear force can occur in two ways which is described below.
328 +
312 312  )))
313 313  
314 -**a. Linear distribution of horizontal seismic forces (Static, linear shape)**
331 +==== a. Linear distribution of horizontal seismic forces (Static, linear shape) ====
315 315  
316 316  In this method the distribution of base shear force happens according to a simplified fundamental mode shape which is approximated by horizontal displacements that increased linearly along the height (see EC8 4.3.3.2.3(3)). The seismic action effects shall be determined by applying to the x' or y' direction. The horizontal forces are:
317 317  
... ... @@ -326,11 +326,129 @@
326 326  
327 327  According to NS3491-12 the distribution formula is:
328 328  
346 +(% class="MsoBodyText" style="margin-top:3.5pt; margin-right:5.2pt; margin-bottom:.0001pt; margin-left:18.0pt; text-align:justify; margin:0cm 0cm 0.0001pt 5.3pt" %)
347 +[[image:1536570150242-670.png||height="50" width="123"]]
329 329  
349 +where:
330 330  
351 +* k = 1 for T,,1,, ≤ 0,5 sec
352 +* k = 2 for T,,1,, ≥ 2,5 sec
331 331  
354 +In the 0,5-2,5 interval the value of the k is interpolated linearly.
332 332  
356 +(% style="text-align: justify;" %)
357 +As a matter of fact eigenfrequency calculation is not necessary for this method, because giving the base period time in x' and y' direction is enough for the calculation. Practically, eigenfrequency calculation is performed before setting this data, but these data can be defined using experimental formulas as well. Investigation can be done in x' or y' direction, or both together.
333 333  
359 +(% style="text-align: justify;" %)
360 +The user may set the calculation direction to be performed by selecting the desi- red direction. To set the desired x'-y' direction user should give the α angle (α is the angle between the global x and x'). α = 0,0 means x'-y' directions coincide with global x-y directions. More details can be found in Horizontal direction setting for seismic calculation to set the correct seismic effect direction (α).
361 +
362 +(% style="text-align: justify;" %)
363 +[[image:1536570274859-276.png||height="81" width="142"]]
364 +
365 +(% class="box errormessage" style="text-align: justify;" %)
366 +(((
367 +Some limitations of this method:
368 +
369 +* unusable if the whole foundation is not in the same plane,
370 +* unusable if the horizontal foundation is elastic
371 +)))
372 +
373 +== [[image:1536570428267-379.png||height="205" width="330"]] ==
374 +
375 +(% style="text-align: justify;" %)
376 +If any of the above mentioned situations happen, the static, mode shape or modal analysis should be used.
377 +
378 +
379 +==== b. Distribution of seismic forces according to fundamental mode shapes (Static, mode shape) ====
380 +
381 +(% style="text-align: justify;" %)
382 +In this method the distribution of base shear force happens according to the base vibration shape (see EC8 4.3.3.2.3(2)P). The horizontal forces acting on the place of mi are:
383 +
384 +(% style="text-align: justify;" %)
385 +[[image:1536570497215-808.png||height="62" width="122"]]
386 +
387 +(% style="text-align: justify;" %)
388 +where:
389 +
390 +* s,,i,,, s,,j,, are the horizontal displacements of masses
391 +* m,,i,,, m,,j,, in the fundamental mode shape.
392 +
393 +(% style="text-align: justify;" %)
394 +The following table shows how to select the base vibration shape. The table contains all mode shapes (No.), the vibration time (T(s)) and effective masses of the mode shapes in x' and y' directions (mx~(%) and my~(%)). As you can see the effective masses are given in a relative form to the total or reduced mass of the structure. The reduced mass means the total mass above the foundation or above the rigid basement. The value of the effective mass is referred to how the mode shape respond to a ground motion direction, so the effective mass shows the participation weight of the mode shape.
395 +
396 +(% style="text-align: justify;" %)
397 +It is recommended to select that mode shape which gives the largest effective mass as the fundamental mode shape. The method allows to Select one mode shape in x´ or/and y´ direction(s).
398 +
399 +(% style="text-align: justify;" %)
400 +[[image:1536570577597-259.png||height="191" width="233"]]
401 +
402 +
403 +(% class="box warningmessage" style="text-align: justify;" %)
404 +(((
405 +Remarks:
406 +
407 +* The calculation of base shear force is performed according to the total mass of the structure and not the effective mass, as was introduced earlier in Lateral force method.
408 +)))
409 +
410 +=== 2. Modal response spectrum analysis (modal analysis) ===
411 +
412 +(% style="text-align: justify;" %)
413 +This method can be used in all national codes. The essence of the method is the calculation of the structural response for different ground motions by the sufficient summation of more vibration shapes. Method gives possibility to take into account full x, y and z direction investigation. In the table below, more vibration mode shape could be selected in x', y' and z' directions if necessary. The last row of the table shows that in a given ground motion direction how large is the sum of the considered effective masses compared to the total or reduced mass of the structure.
414 +
415 +(% style="text-align: justify;" %)
416 +According to EC8 4.3.3.3.1(3) and NS3491-12 sum of the effective mass of the chosen mode shapes - at least in horizontal direction - should reach 90% of total mass. Additionally every mode shape has to be taken into account which effective mass is larger than 5%.
417 +
418 +(% style="text-align: justify;" %)
419 +[[image:1536570931469-309.png||height="183" width="222"]]
420 +
421 +(% class="box warningmessage" %)
422 +(((
423 +Remarks:
424 +
425 +* If the sum of the effective mass is much smaller than 90%, eigenfrequency calculation should be done for more shapes in order to reach 90%.
426 +* In vertical direction lots of mode shapes should be ensured to reach the 90% of total mass; highly recommended to check the national code whether it is necessary to examine the vertical effect.
427 +* (((
428 +The mode shapes which have small effective mass may be neglected, because their effect in result is very small but the calculation time increases.
429 +)))
430 +)))
431 +
432 +According to the EC8 and NS3491-12 the summation rule in the individual directions can be selected in the lower part of the seismic analysis setup dialog. In all other codes there is no possibility to choose, the SRSS rule is used for summation. According to EC8 4.3.3.3.2, the summation rule possibilities are the following:
433 +
434 +(% class="wikigeneratedid" %)
435 +[[image:1536570957782-355.png||height="54" width="141"]]
436 +
437 +(% class="wikigeneratedid" %)
438 +where:
439 +
440 +* E,,E,, is the seismic action effect under consideration (force, displacement, etc.),
441 +* E,,Ei,, is the value of this seismic action effect due to the vibration mode i,
442 +* r,,ij,, is the interaction between two vibration periods taking into ac- count the declining ratio:
443 +
444 +(% class="wikigeneratedid" %)
445 +== [[image:1536571049986-697.png||height="63" width="395"]] ==
446 +
447 +(% style="text-align: justify;" %)
448 +The **CQC **(Complete Quadratic Combination) summation rule might be adopted when individual direction, two vibration modes are dependent to each other if they satisfy the following condition:
449 +
450 +T,,j ,,/ T,,i ,,> 0,9 with T,,j ,,≤ T,,i,,
451 +
452 +(% style="text-align: justify;" %)
453 +
454 +
455 +FEM-Design always applies the selected rule for the summation except if the **Automatic **is highlighted. If the **Automatic **is selected then the rule selection procedure is as follows:
456 +
457 +* (((
458 +(% style="text-align: justify;" %)
459 +Always three directions (if there were more than one mode shape selected in that column) is investigated weather all mode shapes are independent from each other or not.
460 +)))
461 +* (((
462 +(% style="text-align: justify;" %)
463 +If at least one dependent situation exists in a direction, the program automatically uses the CQC rule for all mode shapes in that direction, otherwise SRSS rule is used.
464 +)))
465 +
466 +----
467 +
468 +(% class="wikigeneratedid" %)
334 334  == Other setting possibilities ==
335 335  
336 336  (% style="font-size:18px" %)Horizontal direction setting for seismic calculation
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