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From version < 27.1 >
edited by IwonaBudny
on 2018/09/06 15:36
To version < 27.2 >
edited by IwonaBudny
on 2018/09/06 15:36
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262 262  
263 263  == Combination rule, rotation and second order effects ==
264 264  
265 +(% style="text-align: justify;" %)
266 +According to EC8 4.3.3.5, the combination rule of x', y' and maybe Z direction effects, namely the seismic calculation of final results (Seismic max.), can be selected from the following two possibilities:
267 +
268 +[[image:1536240253862-277.png||height="109" width="120"]]
269 +
270 +(% style="text-align: justify;" %)
271 +The first rule which is called SRSS is implemented to all the other codes than EC8 and NS3491-12 and there is no possibility for rule selection.
272 +
273 +(% style="text-align: justify;" %)
274 +=== (% style="font-size:18px" %)**Torsional effect**(%%) ===
275 +
276 +(% style="text-align: justify;" %)
277 +According to EC8 4.3.2 the program gives possibility to take into account the accidental mass distribution of the structure by the calculation of the torsional effect. This means that from the horizontal seismic forces a Z directional torsional moment can be calculated according to EC8 4.3.3.3.3 (EC8 4.17 equation) as follows:
278 +
279 +(((
280 +(% style="text-align: justify;" %)
281 +(% class="mark" %)M,,ai ,,= e,,ai,, F,,i,,
282 +
283 +(% style="text-align: justify;" %)
284 +where:
285 +
286 +* M,,ai,, is the torsional moment applied at the mi point about the vertical axis,
287 +* e,,ai,, is the accidental eccentricity of mass i in accordance with expression (EC8 4.3 formulas) for all relevant directions:
288 +
289 +(% style="text-align: justify;" %)
290 +(% class="mark" %)e,,ai,, = ± 0,05 L,,i,,
291 +)))
292 +
293 +* L,,i,, is the floor-dimension perpendicular to the direction of seismic action (Lx',i or Ly',i),
294 +* F,,i,, is the horizontal force acting on the place of mi in x' or y' direction, when static method is used. In the modal analysis, this force is calculated, selecting the mode shape which gives the largest effective mass (fundamental shape). Using this mode shape this force is calculated according to static, mode shape. So, the total mass and not the effective mass of the structure is taken into account which belongs to this fundamental mode shape.
295 +
296 +The explanation of the floor-dimension (L,,x',i ,,and L,,y',i,,) on the ith storey:
297 +
298 +[[image:1536240529728-753.png||height="244" width="202"]] [[image:1536240543701-430.png||height="245" width="133"]]
299 +
300 +
301 +(% class="box warningmessage" style="text-align: justify;" %)
302 +(((
303 +Remarks:
304 +
305 +* To calculate the torsional effect, storey(s) should be defined.
306 +* The accidental eccentricity of the masses which are not laid on the storey will be considered on the nearest storey’s eccentricity.
307 +)))
308 +
309 +(% style="text-align: justify;" %)
310 +It was seen that the influence of uncertainties of mass position was modeled by the rotation effect. According to our experiment using the FE method, when a plate, a wall and beams are divided into several elements the accidental torsional effect is not reasonable.
311 +
312 +=== (% style="font-size:18px" %)**Second-order effects (P-∆ effects)**(%%) ===
313 +
314 +(% style="text-align: justify;" %)
315 +Only EC8 gives a possibility to calculate the second order effect which is done according to 4.4.2.2(2). The second order effect is ignored if the following condition is fulfilled in all storeys and all horizontal directions:
316 +
317 +(% style="text-align: justify;" %)
318 +[[image:1536240719142-621.png||height="56" width="151"]]
319 +
320 +(% style="text-align: justify;" %)
321 +where:
322 +
323 +* θ is the interstorey drift sensitivity coefficient,
324 +* P,,tot,, is the total gravity load at and above the storey considered in the seismic design situation. Remark: this total gravity load is calculated back from the nodal masses.
325 +* d,,r,, is the design interstorey drift, evaluated as the difference of the average lateral displacements ds (see Displacement calculation) at the top and bottom of the storey under consideration and calculated in accordance with EC8 4.3.4,
326 +* V,,tot,, is the total seismic storey shear force,
327 +* h is the interstorey height.
328 +
329 +If 0,1 < θ ≤ 0,2, the second order effect is taken into account by multiplying the relevant seismic action effects (the internal and reaction forces) by a factor equal to 1/(1-θ).
330 +
331 +[[image:1536240962810-689.png||height="218" width="186"]]
332 +
333 +(% style="text-align: justify;" %)
334 +According to EC8 4.4.2.2(4)P the θ coefficient shall not exceed 0,3. When θ >0.3, FEM-Design sends a warning message and continues the calculation using θ = 0,0.
335 +
336 +(% style="text-align: justify;" %)
337 +The 0,2-0,3 interval is missing in EC8. In this case FEM-Design sends a warning message and continues the calculation using calculated θ.
338 +
339 +(% class="box warningmessage" %)
340 +(((
341 +Remark: To calculate the second order effect, storey(s) should be defined.
342 +)))
343 +
265 265  == Displacement calculation ==
266 266  
267 267  (% style="text-align: justify;" %)
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