Changes for page Seismic analysis

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 ... ... @@ -227,7 +227,7 @@ 227 227 (% style="text-align: justify;" %) 228 228 In FEM-Design, we assume, the spectrum is constant for periods over 4 seconds and equal to the value of S,,d,,(T = 4). 229 229 230 -[[image:1536238500410-574.png||height="195" width="479"]] 230 +[[image:1536238500410-574.png||height="154" width="378"]] 231 231 232 232 where: 233 233 ... ... @@ -264,7 +264,69 @@ 264 264 (% style="text-align: justify;" %) 265 265 As an example in Norwegian code NS3491-12, seismic calculation is not necessary if the acceleration from the design spectrum is (% class="mark" %)S,,d,,(T,,1,,) ≤ 0,5 m/s^^2^^(%%) where T,,1,, is the base vibration period. In EC8 3.2.1 some criteria can be found. 266 266 267 +(% style="text-align: justify;" %) 268 +FEM-Design provides three types of calculation methods in harmony with EC8 and NS3491-12. 267 267 270 +(% style="text-align: justify;" %) 271 +[[image:1536241835290-794.png||height="105" width="297"]] 272 + 273 +(% style="text-align: justify;" %) 274 +These three methods really cover two basic concepts: 275 + 276 +* Lateral force method, where the base shear force can be distributed in two ways (Static linear/mode shape), 277 +* Modal response spectrum analysis (Modal analysis). 278 + 279 +=== (% style="font-size:18px" %)Lateral force method(%%) === 280 + 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 + 283 +This method can be used to calculate the seismic effect in horizontal plan, x' and/or y' direction. The main point of this method is to calculate base shear force taking into account the base vibration period and design spectrum in x' or y' direction which is distributed into those nodes of the structure where there are nodal masses. The base shear force formula is taken from EC8 4.3.3.2.2(1)P: 284 + 285 +(% class="mark" %)F,,b,, = S,,d,,(T,,1,,) m λ 286 + 287 +((( 288 +(% style="text-align: justify;" %) 289 +where: 290 + 291 +* S,,d,,(T,,1,,) is the value of design spectrum at T1 (means the acceleration of the structure), 292 +* T1 is the fundamental period of vibration of the building for lateral motion in the direction considered, 293 +* m is the total mass of the building, above the foundation or above the top of a rigid basement. Remark: the FEM-Design always ta- kes into account the total mass of the structure including the base- ment, 294 +* λ is the correction factor, the value of which is equal to: 0,85 if 295 +* T^^1^^ ≤ 2 TC and the building has more than two storeys, or λ = 1,0 otherwise. 296 +))) 297 + 298 +(% style="text-align: justify;" %) 299 +From this formula it can be seen that the base shear force is nothing else than the total seismic force of inertia (from second Newton’s law) which acts between the ground and the structure. 300 + 301 +((( 302 +(% class="box warningmessage" %) 303 +((( 304 +Remarks for NS3491-12: 305 + 306 +* There is no λ (λ = 1,0). 307 +* According to the code, if S,,d,,(T,,1,,) ≤ 0,5 m/s2, seismic analysis can be suspended, so when the above condition is fulfilled, it is not necessary to incorporate seismic loads in the design. 308 +))) 309 + 310 +(% style="text-align: justify;" %) 311 +Distribution of the base shear force can occur in two ways which is described below. 312 +))) 313 + 314 +**a. Linear distribution of horizontal seismic forces (Static, linear shape)** 315 + 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 + 318 +(% style="text-align: justify;" %) 319 +[[image:1536242331763-898.png||height="51" width="116"]] 320 + 321 +where: 322 + 323 +* F,,b,, is the seismic base shear force, 324 +* F,,i,, is the horizontal force acting on the place of mi, 325 +* z,,i,,, z,,j,, are the heights of the masses m,,i,,, m,,j ,,above the foundation level. 326 + 327 + 328 + 329 + 268 268 == Other setting possibilities == 269 269 270 270 (% style="font-size:18px" %)Horizontal direction setting for seismic calculation