Changes for page Concrete Design

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 ... ... @@ -466,7 +466,7 @@ 466 466 **Steel** 467 467 468 468 469 -[[image:1557394271242-563.png||height="333" width="484"]] 469 +[[image:1557394271242-563.png||height="311" width="452"]] 470 470 471 471 472 472 * **Ultimate limit states:** ... ... @@ -482,9 +482,158 @@ 482 482 483 483 According to EC2 5.8. 484 484 485 +* For calculation of 2nd order effect **Nominal curvature** method ((% style="color:#e74c3c" %)5.8.8(%%)) is used. 486 +* If there is no compression force in the section the eccentricity is equal to **0,0**. 487 +* Buckling lengths **l,,0x,,** and **l,,0y,,** are specified by the user. 488 +* Curvature: 485 485 490 +1 / r = kr kϕ 1 / r0 486 486 492 +where: 487 487 494 +**k,,r,,** is a correction factor depending on axial load, 495 + 496 +**κ,,ϕ,,** is a factor for taking account of creep, 497 + 498 +1 / r0 = ε,,yd,, / (0,45 d), 499 + 500 +**d** is the effective depth, 501 + 502 +d = (h / 2) + is 503 + 504 +where **i,,s,,** is the radius of gyration of the total reinforcement area. 505 + 506 +k,,r,, = (n,,u,, - n) / (n,,u,, - n,,bal,,) ≤ 1 507 + 508 +where: 509 + 510 +n = N,,Ed,, / (A,,c,, f,,cd,,), relative axial force, 511 + 512 +**N,,Ed,,** is the design value of axial force, n,,u,, = 1 + ω, 513 + 514 +**n,,bal,,** is the value of **n** at maximum moment resistance; the value 0,4 is used, 515 + 516 +ω = A,,s,, f,,yd,, / (A,,c,, f,,cd,,), 517 + 518 +**A,,s,,** is the total area of reinforcement, 519 + 520 +**A,,c,,** is the area of concrete cross section, 521 + 522 +k,,ϕ,, = 1 + β ϕ,,ef,, ≥ 1 523 + 524 +where: 525 + 526 +ϕ,,ef,, is effective creep ratio, defined by the user, 527 + 528 +β = 0,35 + fck /200 - λ / 150, 529 + 530 +λ is the slenderness ratio. 531 + 532 + 533 +* 2nd order effect is ignored, if: 534 + 535 +λ ≤ λ,,lim,, 536 + 537 +λ,,lim ,,= 20 A B C / √n 538 + 539 +where: A = 1 / (1 + 0,2 ϕ,,ef,,), 540 + 541 +B = √1 + 2 ω, 542 + 543 +C = 0,7 544 + 545 +ϕ,,ef,, is effective creep ratio, 546 + 547 +ω = A,,s,, f,,yd,, / (A,,c,, f,,cd,,), mechanical reinforcement ratio, 548 + 549 +**A,,s,,** is the total area of longitudinal reinforcement, 550 + 551 +n = N,,Ed,, / A,,c,, f,,cd,,), relative normal force, 552 + 553 +r,,m,, = M,,01,, / M,,02,,, moment ratio, 554 + 555 +**M,,01,,, M,,02,,** are the first order en moments |M,,02,,| ≥ |M,,01,,|. 556 + 557 + 558 +* Geometric imperfection (5.2 (7) a): 559 + 560 +e,,i,, = l,,0,, / 400 561 + 562 +* The minimum of all eccentricities (1st order + imperfection + 2nd order effect): max (20,0; h / 30,0). 563 +* Imperfection and 2nd order effect considered in both directions. 564 +* The eccentricity is calculated in four possible positions: 565 +** Stiff direction+, weak direction+ 566 +** Stiff -, weak+ 567 +** Stiff+, weak- 568 +** Stiff-, weak- 569 + 570 +**Torsion** 571 + 572 +* Necessary longitudinal reinforcement area (**A,,sl,,**): 573 +**T,,Ed,,** is the applied design torsion (see Figure 6.11): 574 + 575 +[[image:1557398781245-600.png||height="193" width="441"]] 576 + 577 +(% style="text-align: justify;" %) 578 +The required cross-sectional area of the longitudinal reinforcement for torsion** ΣA,,sl,,** may be calculated from: 579 + 580 +[[image:1557398836470-691.png||height="46" width="203"]] 581 + 582 +where: 583 + 584 +**u,,k,, **is the perimeter of the area **A,,k,,**, 585 + 586 +**f,,yd,,** is the design yield stress of the longitudinal reinforcement **A,,sl,,**, 587 + 588 +**θ** is the angle of compression struts, θ = 45 deg. 589 + 590 + 591 +(% style="text-align: justify;" %) 592 +Considering torsion in calculation of longitudinal bars: 593 + 594 +(% style="text-align: justify;" %) 595 +Calculation of torsional capacity by edges, considering all bars placed in tef strip. The minimum of capacities gives the torsional capacity of the section. Utilization for torsion calculated for all bars placed in the strip one by one. 596 + 597 +(% style="text-align: justify;" %) 598 +Area of these bars decreased in the calculation of axial effects (**N, My, Mz**) in proportion of utilization (see formula below): 599 + 600 +[[image:1557399352673-816.png||height="34" width="114"]] 601 + 602 +where: 603 + 604 +**A** is area of the bar, 605 + 606 +**A’** is decreased area used in calculation 607 + 608 + 609 +**ULS checking** 610 + 611 +[[image:1557399421450-202.png||height="263" width="441"]] 612 + 613 + 614 +**SLS checking** 615 + 616 +Crack width calculated according to EC2 7.3. 617 + 618 +• Crack width calculated as: 619 + 620 +w,,k,, = s,,r,max,, (ε,,sm,, - ε,,cm,,) 621 + 622 +where: 623 + 624 +**s,,r,max,,** is the maximum crack spacing, 625 + 626 +(% style="text-align: justify;" %) 627 +**ε,,sm,,** is the mean strain in the reinforcement under the relevant combination of loads, including the effect of imposed derforma- tions 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, 628 + 629 +(% style="text-align: justify;" %) 630 +**ε,,cm,,** is the mean strain in the concrete between cracks. 631 + 632 +(% style="text-align: justify;" %) 633 +ε,,sm,, - ε,,cm,, may be calculated from the expression: 634 + 635 + 636 + 488 488 == Stirrups == 489 489 490 490 === Shear ===