Changes for page Concrete Design
Last modified by Iwona Budny Bjergø on 2022/01/18 12:23
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edited by StruSoft Developers
on 2019/05/09 11:15
on 2019/05/09 11:15
edited by StruSoft Developers
on 2019/05/09 11:25
on 2019/05/09 11:25
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... ... @@ 222,11 +222,207 @@ 222 222 223 223 === Design === 224 224 225 +1. Check, if reinforcement is needed at all, 226 +1. If reinforcement is needed, it is designed to satisfy the detailing rules in (% style="color:#e74c3c" %)9.4.3(%%), if possible, 227 +1. Design fails and a warning message is displayed if, **u,,out,,** is not found within 6 **d,,eff,,** distance from the column perimeter. 228 + 229 + 230 +**Comments, limitations** 231 + 232 +(% style="textalign: justify;" %) 233 + openings are not considered when control perimeters are generated. 234 + the position of the column relative to the plate is considered only in the generation of control perimeter. It means, (user or program defined) reinforcement may be partly out of the plate, but it won't affect the calculation. 235 + If ”Calculate β automatically” is set in the calculation parameter, β is calculated according to equation (% style="color:#e74c3c" %)6.4.3 (6.39)(%%). 236 + 237 + 225 225 == Serviceability limit state == 226 226 227 227 241 +**Method of solution** 228 228 243 +(% style="textalign: justify;" %) 244 +The program performs crack and deflection control for all load combinations according to EC2 7.3 and 7.4. Two limiting conditions are assumed to exist for the calculations: **Stadium I **(the uncracked condition) and **Stadium II **(the fully cracked condition). 229 229 246 + 247 +**Stadium I Uncracked condition** 248 + 249 +If the user does not activate the option **Cracked section analysis**, the calculation will be performed with respect to the total stiffness of the slab. 250 + 251 + 252 +**Stadium II Fully cracked condition** 253 + 254 +(% style="textalign: justify;" %) 255 +If the option **Cracked section analysis**, is activated the program will consider the decrease in slab stiffness on behalf of cracking. This means an iterative calculation where the slab in the beginning is assumed to be uncracked when the section forces are calculated. Sections which are not loaded above the level which would cause the tensile strength of the concrete to be exceeded will be considered to be uncracked (**Stadium I**). Sections which are expected to crack will behave in a manner intermediate between the uncracked and fully cracked conditions and an adequate prediction of behavior used in the program is shown below. 256 + 257 +(% style="textalign: justify;" %) 258 +The stiffness calculation is performed considering the required or the applied reinforcement depending on what option has been selected. If applied reinforcement has been selected this is used in all load combinations. If applied reinforcement is not present or not selected the required reinforcement is used instead. In the latter case the required reinforcement in every element is calculated as the maximum value from all load combinations, which means that all calculations of serviceability limit values are performed with the same reinforcement. 259 + 260 +(% style="textalign: justify;" %) 261 +In the next step a new calculation based on the new stiffness distribution is performed and so on. When the deflection values resulting from two calculations does not differ more than a defined percentage of the first one or the maximal number of allowed calculations has been reached the calculation is stopped. 262 + 263 + 264 +**Crack width** 265 + 266 +Crack width is according to EC2 7.3.4 calculated as: 267 + 268 +(% class="mark" %)w,,k,, = S,,r,max,, (ε,,sm,,  ε,,cm,,) 269 + 270 +where: 271 + 272 +(% style="textalign: justify;" %) 273 +**S,,r,max,,** is the maximum crack spacing, 274 + 275 +(% style="textalign: justify;" %) 276 +**ε,,sm,,** is the mean strain in the reinforcement under the relevant com bination of loads, including the effect of imposed deformations and taking into account the effects of tension stiffening. Only the additional tensile strain beyond the state of zero strain of the concrete at the same level is considered, 277 + 278 +(% style="textalign: justify;" %) 279 +**ε,,cm,,** is the mean strain in the concrete between cracks. 280 + 281 + 282 +ε,,sm,,  ε,,cm,, may be calculated from the expression: 283 + 284 +[[image:1557391677004144.pngheight="67" width="337"]] 285 + 286 +where: 287 + 288 +**σ,,s,, **is the stress in the tension reinforcement assuming a cracked section. For pretensioned members, σ,,s,, may be replaced by Δσ,,p,, the stress variation in prestressing tendons from the state of zero strain of the concrete at the same level, 289 + 290 +**α,,e,,**= is the ratio** Es / Ecm** 291 + 292 +**A,,p,,** and **A,,c,eff,,** are as defined in (% style="color:#e74c3c" %)7.3.2 (3)(%%), 293 + 294 +**ξ,,1,,** according to Expression (% style="color:#e74c3c" %)(7.5)(%%), 295 + 296 +**k,,t,,** is a factor dependent on the duration of the load. 297 + 298 + 299 +**k,,t,, = 0,6** for short term loading 300 + 301 +**k,,t,, = 0,4** for long term loading. For long term loads (**k,,t,, = 0,4**): 302 + 303 +**Ap´ = 0,0** (pre or posttensioned tendons) 304 + 305 +**Ac,eff:** 306 + 307 +[[image:1557392170606753.pngheight="170" width="449"]] 308 + 309 +[[image:1557392181561817.pngheight="172" width="541"]] 310 + 311 + 312 +(% class="mark" %)h,,cef ,,= min (2,5 * (h  d), (h  x) / 3, h / 2 ) 313 + 314 +(% class="mark" %)s,,r,max,, = k,,3,,c + k,,1,, k,,2,, k,,4,,φ /ρ,,p,eff,, 315 + 316 + 317 +where: 318 + 319 +(% style="textalign: justify;" %) 320 +**φ** is the bar diameter. Where a mixture of bar diameters is used in a 321 +section, an equivalent diameter, **φ,,eq,,**, should be used. For a section with **n,,1,,** bars of diameter **φ,,1,,** and **n,,2,,** bars of diameter **φ,,2,,**, the following expression should be used, 322 + 323 +[[image:1557392495138639.pngheight="66" width="164"]] 324 + 325 +**c **is the cover to the longitudinal reinforcement, 326 + 327 +**k,,1,,** is a coefficient which takes account of the bond properties of the bonded reinforcement: 328 + 329 + 330 +**k,,1,,** =** 0,8 **for high bond bars, 331 + 332 +**k,,1,,** **= 1,6** for bars with an effectively plain surface (e.g. prestressing tendons), 333 + 334 +**k(% style="fontsize:10.5px" %)2(%%)** is a coefficient which takes account of the distribution of strain: 335 + 336 +**k(% style="fontsize:10.5px" %)2(%%)** **= 0,5 **for bending, 337 + 338 +**k(% style="fontsize:10.5px" %)2(%%)** **= 1,0 **for pure tension, 339 + 340 +(% class="mark" %)k,,2,, = (ε1 + ε,,2,,) / 2ε,,1,, 341 + 342 +where ε,,1,, is the greater and ε,,2,, is the lesser tensile strain at the boundaries of the section considered, assessed on the basis of a cracked section. 343 +Recommended values of **k,,3,, = 3,4** and **k,,4,, = 0,425** are used. 344 + 345 + 346 +**Maximum crack spacing:** 347 + 348 +s,,r,max,, = 1,3 (h  x) 349 + 350 +**Equivalent quantities perpendicular to crack direction:** 351 + 352 +* **Reinforcement area:** 353 + 354 +[[image:1557393319443687.pngheight="31" width="274"]] 355 + 356 +* **Number of bars:** 357 + 358 +[[image:1557393330997858.pngheight="107" width="168"]] 359 + 360 +* **Diameter:** 361 + 362 +[[image:1557393343977995.pngheight="47" width="301"]] 363 + 364 + 365 +**Deflections** 366 + 367 +The calculations is performed according to EC2 7.4.3. 368 + 369 + 370 +**Stadium I Uncracked condition** 371 + 372 +Load depended curvature is calculated as: 373 + 374 +(% class="mark" %)1 / r,,f,, = M / E,,c,ef,, I,,1,, 375 + 376 + 377 +where: 378 + 379 +**M** is current moment, 380 + 381 +**I,,1,,** is Moment of Inertia in **Stadium I**, 382 + 383 +**E,,c,ef,,** is the modulus of elasticity with respect to creep. 384 + 385 + 386 +The modulus of elasticity is calculated as: 387 + 388 +(% class="mark" %)E,,c,eff,, = E,,cm,, / (1 + φ) 389 + 390 +where φ is the creep coefficient. 391 + 392 +Curvature with respect to shrinkage is considered according to (% style="color:#e74c3c" %)2.2.2(%%) above. 393 + 394 + 395 +**Stadium II Fully cracked condition** 396 + 397 +Load depended curvature is calculated as: 398 + 399 +(% class="mark" %)1 / r,,f,, = M / E,,c,ef,, I,,2,, 400 + 401 + 402 +where: 403 + 404 +**E,,c,ef,,** is the modulus of elasticity as shown above, 405 + 406 +**I,,2,,** is the moment of Inertia in Stadium II, 407 + 408 +**M** is current moment. 409 + 410 + 411 +Curvature with respect to shrinkage is considered according to 2.2.2 above. 412 + 413 + 414 +(% style="textalign: justify;" %) 415 +Sections which are expected to crack will behave in a manner intermediate between the uncracked and fully cracked conditions and an adequate prediction of this behavior is given by: 416 + 417 +(% style="textalign: justify;" %) 418 +α = ζ α,,II,, + (1  ζ) α,,I,, 419 + 420 +(% style="textalign: justify;" %) 421 +where: α is in this case the curvature calculated for the uncracked and fully cracked conditions, 422 + 423 + 424 + 425 + 230 230 ((( 231 231  232 232 )))