<
From version < 224.1 >
edited by Fredrik Lagerström
on 2020/03/30 16:24
To version < 224.2 >
edited by Fredrik Lagerström
on 2020/03/30 16:24
>
Change comment: (Autosaved)

Summary

Details

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Content
... ... @@ -502,103 +502,50 @@
502 502  
503 503  The calculation process is based on so-called buckling regions, which can be defined at //RC design/Surface reinforcement/Buckling length.//
504 504  
505 +(% style="text-align:center" %)
506 +[[image:1585577974695-846.png]]
505 505  
506 506  Each buckling region on the shell has a corresponding buckling factor (beta) and a direction vector in the plane of the shell. The former will be used to calculate the buckling length of the equivalent column, while the latter one specifies the x’ longitudinal axis of this column. By default, FEM-Design generates one buckling region on each RC wall and plate. Default buckling direction is vertical on walls, and parallel with the local x axis on plates**.  Buckling factor is set to 0.0 on all shells in order to let the User decide whether this calculation is needed or not, since it is quite time consuming**.
507 507  
508 -|[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image023.wmz||alt="MCj02990090000%5b1%5d"]]|Shells with zero buckling factor will not be considered for shell buckling calculation, but zero utilization is set for them.
510 +|[[image:light.png]]|Shells with zero buckling factor will not be considered for shell buckling calculation, but zero utilization is set for them.
509 509  
510 510  The default buckling regions can be modified by adding new regions to the shell. One shell may have more buckling regions with different beta factor and direction vector, but the shell must be completely covered by these regions.
511 511  
512 -[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image096.png]]
514 +[[image:1585578009012-980.png]]
513 513  
514 514  During the checking process, the program generates equivalent bar(s) from the shell based on its material, thickness and reinforcement. This bar is checked as an RC bar: Its utilization is calculated by determining its second order internal forces and resistance.
515 515  
516 516  The calculation process consists of the following steps:
517 517  
518 -1. [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image097.png]]
519 -As other shell design calculations, the shell buckling is also calculated in every node of the shell (only where there is a buckling region with non-zero beta value).
520 +1. As other shell design calculations, the shell buckling is also calculated in every node of the shell (only where there is a buckling region with non-zero beta value).
521 +[[image:1585578021942-234.png]]
522 +1. An equivalent bar is generated for the examined node as follows. The edges of the shell are intersected by the ray determined by the node and the direction vector of the corresponding buckling region. The two intersection points are taken as the start and the end point of the equivalent bars.(((
523 +|(% style="width:110px" %)[[image:warning.png]]|(% style="width:1340px" %)Note that this intersection is always made with the edges of the shell and not with the edges of the buckling region corresponding to the node! If a node is on the border of two or more buckling regions, it is calculated with both different beta values and direction vectors, and the higher utilization will be used.
520 520  
521 -1. An equivalent bar is generated for the examined node as follows. The edges of the shell are intersected by the ray determined by the node and the direction vector of the corresponding buckling region. The two intersection points are taken as the start and the end point of the equivalent bars.
522 -
523 -|[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image067.wmz||alt="MCj04113200000%5b1%5d"]]|Note that this intersection is always made with the edges of the shell and not with the edges of the buckling region corresponding to the node! If a node is on the border of two or more buckling regions, it is calculated with both different beta values and direction vectors, and the higher utilization will be used.
524 -
525 -|(((
526 -β=2
525 +[[image:1585578078770-899.png]]
526 +
527 527  )))
528 -
529 -|(((
530 -β=2
531 -)))
532 -
533 -|(((
534 -β=1
535 -)))
536 -
537 537  1. The cross section of the equivalent bar is 1 m wide and its height equals to the thickness of the shell. Along the bar, the applied reinforcement of the shell is transformed into the direction of the bar and placed into it.
538 -
539 -[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image099.png]]
540 -
529 +[[image:1585578130458-333.png]]
541 541  The checking process is executed section by section along the bar. The distance between these sections is given by //Division length of substitute column// parameter in Calculation parameter dialog (see the lower figure). Internal forces acting at these sections are calculated by transforming shell internal forces at the section point into the coordinate system of the column. As the buckling direction of shells is perpendicular to its plane, we need the equivalent bar’s normal force and moment vector in the plane of the shell for the calculation.
542 -
543 -[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image100.png]] [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image101.png]]
544 -
545 -|(((
546 -0.5 m
547 -)))
548 -
549 -|(((
550 -0.5 m
551 -)))
552 -
553 -|(((
554 -0.5 m
555 -)))
556 -
557 -|(((
558 -0.5 m
559 -)))
560 -
561 -|(((
562 -0.5 m
563 -)))
564 -
565 -|(((
566 -0.5 m
567 -)))
568 -
569 -|(((
570 -1.0 m
571 -)))
572 -
531 +\\[[image:1585578173612-713.png]]
573 573  1. Once the first order internal forces are obtained in every section, the second order internal forces are calculated based on the //nominal stiffness// or //nominal curvature// method, according to the configuration settings. The only difference in the checking process of a real bar and this equivalent bar is that now the eccentricity coming from the second order effects are applied only perpendicularly to the plane of the shell. In other words, the out-of-plane normal force has eccentricity only along the z’ axis of the shell. This modification is in harmony with the fact that the buckling direction of the shell is perpendicular to the plane.
574 -
575 -|(((
576 -NEd
577 -)))
578 -
579 -|(((
580 -MEd,I
581 -)))
582 -
583 -|(((
584 -NEd
585 -)))
586 -
587 -|(((
588 -MEd,II
589 -)))
590 -
533 +[[image:1585578216982-698.png]]
591 591  1. Finally, based on the second order internal forces, the utilization is calculated for every cross section of the equivalent bar (based on the interaction curve), and the highest section utilization is assigned to the node.
592 592  
536 +
537 +
593 593  Shell buckling calculations are available for //Load combinations//, //Maximum of load combinations// and //Maximum of load groups//. The utilization results can be displayed in the //New result/RC shell/Shell buckling/Utilization//
594 594  
595 -[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image104.png]]
540 +(% style="text-align:center" %)
541 +[[image:1585578251132-617.png]]
596 596  
597 597  Some details of the calculation can be obtained by listing //RC design/Load combinations/Shell, buckling //table. Also, wall buckling utilization appears in the //Shell, Utilization// list.
598 598  
599 -[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image106.png]]
545 +(% style="text-align:center" %)
546 +[[image:1585578261812-195.png]]
600 600  
601 -[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image107.png]]
548 +[[image:1585578266824-221.png]]
602 602  
603 603  Every plate and wall has one result, containing the coordinates of the dominant section, the corresponding reinforcement, first and second order internal forces together with the capacity and buckling factor.
604 604  
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