<
From version < 60.1 >
edited by StruSoft Developers
on 2019/05/09 14:40
To version < 60.2 >
edited by StruSoft Developers
on 2019/05/09 14:54
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... ... @@ -226,7 +226,6 @@
226 226  1. If reinforcement is needed, it is designed to satisfy the detailing rules in (% style="color:#e74c3c" %)9.4.3(%%), if possible,
227 227  1. Design fails and a warning message is displayed if, **u,,out,,** is not found within 6 **d,,eff,,** distance from the column perimeter.
228 228  
229 -
230 230  **Comments, limitations**
231 231  
232 232  (% style="text-align: justify;" %)
... ... @@ -459,10 +459,9 @@
459 459  * **Ultimate limit states:**
460 460  Continuous line is used.
461 461  
462 -* **Servicibility limit states:**
461 +* **Servicibility limit states:**
463 463  Stage II is used (dashed line, without horizontal section).
464 464  
465 -
466 466  **Steel**
467 467  
468 468  
... ... @@ -472,10 +472,9 @@
472 472  * **Ultimate limit states:**
473 473  **B** graph with horizontal line is used.
474 474  
475 -* **Servicibility limit states:**
473 +* **Servicibility limit states:**
476 476  The same as ultimate but without safety factor.
477 477  
478 -
479 479  == Longitudinal reinforcement ==
480 480  
481 481  (% lang="EN-US" style="font-family:~"Times New Roman~",~"serif~"; font-size:12pt; letter-spacing:-0.05pt" %)**Analysis of second order effects with axial load**
... ... @@ -655,18 +655,245 @@
655 655  [[image:1557400792364-457.png||height="154" width="522"]]
656 656  
657 657  
658 -hc,ef = min (2,5 (h - d), (h - x) / 3, h / 2) sr,max = k3 c + k1 k2 k4 φ / ρp,eff
659 -where: φ is the bar diameter. Where a mixture of bar diameters is used in a section, an equivalent diameter, φeq, should be used. For a sec- tion with n1 bars of diameter φ1 and n2 bars of diameter φ2, the following expression should be used,
655 +h,,c,ef,, = min (2,5 (h - d), (h - x) / 3, h / 2)
660 660  
657 +s,,r,max,, = k,,3,, c + k,,1,, k,,2,, k,,4,, φ / ρ,,p,eff,,
661 661  
659 +where:
662 662  
661 +(% style="text-align: justify;" %)
662 +**φ** is the bar diameter. Where a mixture of bar diameters is used in a 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,
663 663  
664 +[[image:1557402498643-546.png||height="45" width="141"]]
665 +
666 +**c** is the cover to the longitudinal reinforcement,
667 +
668 +**k,,1,,** is a coefficient which takes account of the bond properties of the bonded reinforcement:
669 +
670 +**k,,1,, = 0,8** for high bond bars,
671 +
672 +**k,,1,, = 1,6** for bars with an effectively plain surface (e.g. prestressing tendons),
673 +
674 +**k,,2,,** is a coefficient which takes account of the distribution of strain:
675 +
676 +**k,,2,, = 0,5** for bending,
677 +
678 +**k,,2,, = 1,0** for pure tension
679 +
680 +For cases of eccentric tension or for local areas, intermediate values of k2 should be used which may be calculated from the relation:
681 +
682 +k,,2,, = (ε,,1,, + ε,,2,,) / 2 ε,,1,,,
683 +
684 +where: ε1 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.
685 +
686 +Recommended values of **k,,3,, = 3,4** and **k,,4,, = 0,425** are used.
687 +
688 +• Maximum crack spacing:
689 +
690 +s,,r,max,, = 1,3 (h - x)
691 +
692 +
693 +**Space between bars**
694 +
695 +* **Minimum distance:**
696 +The clear distance (horizontal and vertical) between individual parallel bars or horizontal layers of parallel bars should be not less than the maximum of k,,1,, bar diameter, (d,,g,, + k,,2,, mm) or 20 mm where d,,g,, is the maximum size of aggregate.
697 +
698 +
699 +* **Maximum distance:**
700 +The longitudinal bars should be so arranged that there is at least one bar at each corner, the others being distributed uniformly around the inner periphery of the links, with a spacing not greater than 350 mm.
701 +
702 +
703 +**Lengthening and anchorage**
704 +
705 +* **Because of shear effect (//shift rule//):**
706 +
707 +a,,i,, = 0,9 max (h, b)
708 +
709 +The code prescribes **d** instead of **h**, but the difference can be ignored.
710 +
711 +* **Anchorage:**
712 +
713 +f,,bd,, = 2,25 η,,1,, η,,2,, f,,ctd ,,
714 +
715 +where:
716 +
717 +(% style="text-align: justify;" %)
718 +**f,,ctd,,** is design value of concrete tensile strength. Due to the increasing brittleness of higher strength concrete, **f,,ctk,0,05,,** should be limited here to the value for **C60/75**, unless it can be verified that the average bond strength increases above this limit
719 +
720 +(% style="text-align: justify;" %)
721 +η,,1,, is a coefficient related to the quality of the bond condition and the position of the bar during concreting:
722 +
723 +(% style="text-align: justify;" %)
724 +η,,1,, = 0,7
725 +
726 +(% style="text-align: justify;" %)
727 +η,,2,, is related to the bar diameter:
728 +
729 +(% style="text-align: justify;" %)
730 +η,,2,, = 1,0 for φ ≤ 32 mm,
731 +
732 +(% style="text-align: justify;" %)
733 +η,,2,, = (132 - φ) / 100 for φ > 32 mm
734 +
735 +(% style="text-align: justify;" %)
736 +l,,b,rqd,, = (φ / 4) (σ,,sd,, / f,,bd,,)
737 +
738 +(% style="text-align: justify;" %)
739 +where:
740 +
741 +(% style="text-align: justify;" %)
742 +σ,,sd,, = f,,yd,, (fully utilized bar supposed),
743 +
744 +(% style="text-align: justify;" %)
745 +l,,bd,, = α,,1,, α,,2,, α,,3,, α,,4,, α,,5,, l,,b,rqd,, ≥ l,,b,min,,,
746 +
747 +(% style="text-align: justify;" %)
748 +α,,i,, = 1,0
749 +
750 +(% style="text-align: justify;" %)
751 +**l,,b,min,,** is the minimum anchorage length if no other limitation is applied:
752 +
753 +* for anchorages in tension:
754 +l,,b,min,, > max (0,3 l,,b,rqd,,; 10 φ; 100 mm),
755 +
756 +* for anchorage in compression:
757 +l,,b,min,, > max (0,6 l,,b,rqd,,; 10 φ; 100 mm),
758 +Rule given for compression is used.
759 +
760 +
664 664  == Stirrups ==
665 665  
666 666  === Shear ===
667 667  
765 +In Figure 6.5 below the following notations are shown:
766 +
767 +**α** is the angle between shear reinforcement and beam axis perpendicular to the shear force (measured positive as shown in Figure 6.5),
768 +
769 +**θ** is the angle between the concrete compression strut and the beam axis per- pendicular to the shear force,
770 +
771 +**F,,td,,** is the dessign value or the tensile force in the longitudinal reinforcement,
772 +
773 +**F,,cd,,** is the design value of the concrete compression force in the direction of the longitudinal member axis,
774 +
775 +**b,,w,,** is the minimum width between tension and compression chords,
776 +
777 +**z** is the inner lever arm, for a member with constant depth, corresponding to the bending moment in the element under consideration. In the shear analy- sis of reinforced concrete without axial force, the approximate value **z = 0,9 d** may normally be used.
778 +
779 +[[image:1557404124068-157.png||height="311" width="496"]]
780 +
781 +
782 +* **Member do not require shear reinforcement, if:**
783 +
784 +The design value for the shear resistance **V,,Rd,c,,** is given by:
785 +
786 +(% class="mark" %)V,,Rd,c,, = [C,,Rd,c,, k (100 ρ,,l,, f,,ck,,)1/3 + k,,1,, σ,,cp,,] b,,w,, d
787 +
788 +with a minimum of:
789 +
790 +(% class="mark" %)V,,Rd,c,, = (v,,min,, + k,,1 ,,σ,,cp,,) b,,w,, d
791 +
792 +where: **f,,ck,,** is in MPa
793 +
794 +[[image:1557404308626-814.png||height="80" width="280"]]
795 +
796 +(% style="text-align: justify;" %)
797 +**A,,sl,,** is the area of the tensile reinforcement, which extends: ≥ (**l,,bd,,** +** d**) beyond the section aonsidered (see Figure 6.3), **b,,w,,** is the smallest width of the cross-section in the tensile area [mm],
798 +
799 +σ,,cp,, = N,,Ed,, / A,,c,, < 0,2 f,,cd,, [MPa],
800 +
801 +**N,,Ed,,** is the axial force in the cross-section due to loading or prestressing [in N] (**N,,Ed ,,> 0** for compression). The influence of imposed deformations on **N,,E,,** may be ignored,
802 +
803 +**Ac** is the area of concrete cross section [mm2],
804 +
805 +**V,,Rd,c,,**,, ,,is [N]
806 +
807 +(% style="text-align: justify;" %)
808 +The recommended value for **C,,Rd,c,,** is **0,18 / γ,,c,,**, that for** v,,min,,** is given by the expression below and that for **k,,1,,** is **0,15**.
809 +
810 +[[image:1557404927126-189.png||height="24" width="136"]]
811 +
812 +[[image:1557404943122-538.png||height="192" width="607"]]
813 +
814 +* **Upper limit of shear:**
815 +
816 +(% class="mark" %)V,,Rd,max,, = α,,cw,, b,,w,, z ν,,1,, f,,cd,, / (cotθ + tanθ)
817 +
818 +where:
819 +
820 +**A,,sw,,** is the cross-sectional area of the shear reinfocement,
821 +
822 +**s** is the spacing of the stirrups,
823 +
824 +**f,,ywd,,** is the design yield strength of the shear reinforcement,
825 +
826 +**ν,,1,,** is a strength reduction factor for concrete cracked in shear,
827 +
828 +**α,,cw,, **is a coefficient taking account of the state of the stress in the compression chord.
829 +
830 +(% style="text-align: justify;" %)
831 +The recommended value of ν,,1,, is ν (see expression below). The recommended value of α,,cw,, is as follows:**1** for non-prestressed structures,
832 +
833 +[[image:1557405487679-357.png||height="82" width="120"]]
834 +
835 +Capacity of stirrups:
836 +
837 +[[image:1557405540899-916.png||height="37" width="170"]]
838 +
839 +where:
840 +
841 +**A,,sw,,** is the cross-sectional area of the shear reinforcement,
842 +
843 +**s** is the spacing of the stirrups,
844 +
845 +**f,,ywd,, **is the design yield strength of the shear reinforcement.
846 +
847 +
668 668  === Torsion ===
669 669  
850 +**T,,Ed,,** is the applied design torsion (see Figure 6.11)
851 +
852 +[[image:1557405627044-695.png||height="210" width="480"]]
853 +
854 +
855 +**A,,k,,** is the area enclosed by the centre-lines of the connecting walls, including inner hollow areas,
856 +
857 +**τ,,t,i,, **is the torsional shear stress in wall i,
858 +
859 +**t,,ef,i,, **is the effective wall thickness. It may be taken as A/u, but should not be taken as less than twice the distance between edge and center of the longitudinal reinforcement. For hollow sections the real thickness is an upper limit,
860 +
861 +**A** is the total area of the cross-section within the outer circumference, including inner hollow areas,
862 +
863 +**u** is the outer circumference of the cross-section,
864 +
865 +**z,,i,,** is the side length of wall i defined by the distance between the intersection points with the adjacent walls,
866 +
867 +θ = 45 deg, in all calculations.
868 +
869 +
870 +* **Member do not require torsional reinforcement, if:**
871 +
872 +(% class="mark" %)T,,Rd,c,, = f,,cd,, t,,ef,, 2 A,,k,, ≤ T,,Ed,,
873 +
874 +* **Upper limit of torsion:**
875 +
876 +T,,Rd,max,, = 2 ν α,,cw,, f,,cd,, A,,k,, t,,ef,i,, sinθ cosθ
877 +
878 +where ν and α,,cw,, are as above.
879 +
880 +* **Force in stirrups:**
881 +
882 +(% class="mark" %)T,,Rd,max,,=2να,,cw,,f,,cd,,A,,k,,t,,ef,i,,sinθcosθ
883 +
884 +The shear force **V,,Ed,i,,** in a wall **i** due to torsion is given by:
885 +
886 +(% class="mark" %)V,,Ed,i,, = τ,,t,i ,,t,,ef,i,, z,,i,,
887 +
888 +**z,,i,,** is section height used to be able to sum with shear.
889 +
890 +* **Capacity of stirrups:**
891 +
892 +See **Shear**.
893 +
670 670  === Shear and torsion ===
671 671  
672 672  
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