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 14:40
on 2019/05/09 14:40
edited by StruSoft Developers
on 2019/05/09 14:54
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="textalign: justify;" %) ... ... @@ 459,10 +459,9 @@ 459 459 * **Ultimate limit states:** 460 460 Continuous line is used. 461 461 462 * 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 * 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="ENUS" style="fontfamily:~"Times New Roman~",~"serif~"; fontsize:12pt; letterspacing:0.05pt" %)**Analysis of second order effects with axial load** ... ... @@ 655,18 +655,245 @@ 655 655 [[image:1557400792364457.pngheight="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="textalign: 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:1557402498643546.pngheight="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="textalign: 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="textalign: 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="textalign: justify;" %) 724 +η,,1,, = 0,7 725 + 726 +(% style="textalign: justify;" %) 727 +η,,2,, is related to the bar diameter: 728 + 729 +(% style="textalign: justify;" %) 730 +η,,2,, = 1,0 for φ ≤ 32 mm, 731 + 732 +(% style="textalign: justify;" %) 733 +η,,2,, = (132  φ) / 100 for φ > 32 mm 734 + 735 +(% style="textalign: justify;" %) 736 +l,,b,rqd,, = (φ / 4) (σ,,sd,, / f,,bd,,) 737 + 738 +(% style="textalign: justify;" %) 739 +where: 740 + 741 +(% style="textalign: justify;" %) 742 +σ,,sd,, = f,,yd,, (fully utilized bar supposed), 743 + 744 +(% style="textalign: justify;" %) 745 +l,,bd,, = α,,1,, α,,2,, α,,3,, α,,4,, α,,5,, l,,b,rqd,, ≥ l,,b,min,,, 746 + 747 +(% style="textalign: justify;" %) 748 +α,,i,, = 1,0 749 + 750 +(% style="textalign: 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:1557404124068157.pngheight="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:1557404308626814.pngheight="80" width="280"]] 795 + 796 +(% style="textalign: 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 crosssection 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 crosssection 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="textalign: 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:1557404927126189.pngheight="24" width="136"]] 811 + 812 +[[image:1557404943122538.pngheight="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 crosssectional 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="textalign: justify;" %) 831 +The recommended value of ν,,1,, is ν (see expression below). The recommended value of α,,cw,, is as follows:**1** for nonprestressed structures, 832 + 833 +[[image:1557405487679357.pngheight="82" width="120"]] 834 + 835 +Capacity of stirrups: 836 + 837 +[[image:1557405540899916.pngheight="37" width="170"]] 838 + 839 +where: 840 + 841 +**A,,sw,,** is the crosssectional 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:1557405627044695.pngheight="210" width="480"]] 853 + 854 + 855 +**A,,k,,** is the area enclosed by the centrelines 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 crosssection within the outer circumference, including inner hollow areas, 862 + 863 +**u** is the outer circumference of the crosssection, 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