Appendix A Tables and Diagrams

Transcription

1 Appendix A Tables and Diagrams Table A1.1 Mechanical properties of steel reinforcing bars Type of steel Grade f y (ksi) e y Carbon, A Low alloy, A Stainless, A Rail, A Axle, A Low carbon chromium, A Table A1.2 Steel bar sizes Bar size #3 #4 #5 #6 #7 #8 #9 #10 #11 #14 #18 Diameter (in.) Area (in 2 ) Springer International Publishing Switzerland 2017 M. Setareh, R. Darvas, Concrete Structures, DOI /

2 608 Appendix A: Tables and Diagrams Table A2.1 ACI approximate design moments and shears for beams and one-way slabs Positive moment Negative moment End spans Discontinuous end unrestrained w u 2 n /11 Discontinuous end integral with support w u 2 n /14 Interior spans w u 2 n /16 At exterior face of the first interior support Two spans w u 2 n /9 More than two spans w u 2 n /10 At other faces of interior supports w u 2 n /11 At the face of all supports for SLABS with spans not exceeding w u 2 n /12 10 ft; and BEAMS where ratio of sum of column stiffnesses to beam stiffness exceeds 8 at each end of the span At interior face of exterior support for members built integrally with supports Where support is a spandrel beam w u 2 n /24 Where support is a column w u 2 n /16 Shear In end members at the face of the first interior support 1.15 w u n /2 At face of all other supports w u n /2 w u Spandrel beam Column w u n 2 n n n w u n w u n 2 2 w u n 2 (V u ) 1.15w u n 2 2 w u n (End unrestrained) 11 w u n 2 w u n 2 w u n 2 14 (End integral with support) w u n 2 16 w u n 2 16 (Spandrel beam) w u n 2 24 (Two spans) w u n 2 9 w u n 2 9 (Two spans) (M u ) (Column) w u n 2 16 (Others) 2 w u n 10 2 w u n 12 2 w u n w 2 u n 11 (Others) 11 w u n 2 12 w u n w u n 11 2 w u n 12 2 w u n 11 2 w u n 12 2 w u n 11 2 w u n 12 (Slabs, n 10', 3 or more spans) (Slabs, n 10', 3 or more spans) (Slabs, n 10', 3 or more spans)

3 Appendix A: Tables and Diagrams 609 Table A2.2a Values of A 1 and B 1 for commonly used reinforcing steels f y (psi) ε ty A 1 B 1 40, , , Table A2.2b Values of A 2 and B 2 for commonly used reinforcing steels f y (psi) d t /c b c b /d t A 2 B 2 40, , , Table A2.3 ρ max and ρ tc for common grades of steel and compressive strength of concrete (single layer of steel, i.e., d ¼ d t ) f y (psi) fc 0 ¼ 3,000 psi fc 0 ¼ 4,000 psi fc 0 ¼ 5,000 psi ϕ ρ max (ε t ¼ 0.004) 40, , , ρ tc (ε t ¼ 0.005) 40, , , Note: For multiple layers of reinforcements, multiply the table values by d t d Table A2.4 Minimum steel ratio (ρ min ) f y (psi) fc 0 ¼ 3,000 psi ρ min fc 0 ¼ 4,000 psi fc 0 ¼ 5,000 psi fc 0 ¼ 6,000 psi 40, , ,

4 610 Appendix A: Tables and Diagrams Table A2.5a Resistance coefficient R (in psi) versus reinforcement ratio (ρ); f c 0 ¼ 3,000 psi, f y ¼ 40,000 psi (for beams ρ min ¼ 0.005) ρ R ρ R ρ R ρ R ρ R ϕ ρ R ϕ ρ tc

5 Appendix A: Tables and Diagrams 611 Table A2.5b Resistance coefficient R (in psi) versus reinforcement ratio (ρ); f 0 c ¼ 4,000 psi, f y ¼ 40,000 psi (for beams ρ min ¼ 0.005) ρ R ρ R ρ R ρ R ρ R (continued)

6 612 Appendix A: Tables and Diagrams Table A2.5b (continued) ρ R ρ R ϕ ρ R ϕ ρ tc

7 Appendix A: Tables and Diagrams 613 Table A2.5c Resistance coefficient R (in psi) versus reinforcement ratio (ρ); f 0 c ¼ 5,000 psi, f y ¼ 40,000 psi (for beams ρ min ¼ ) ρ R ρ R ρ R ρ R ρ R (continued)

8 614 Appendix A: Tables and Diagrams Table A2.5c (continued) ρ R ρ R ρ R ϕ ρ R ϕ ρ tc

9 Appendix A: Tables and Diagrams 615 Table A2.6a Resistance coefficient R (in psi) versus reinforcement ratio (ρ); f 0 c ¼ 3,000psi, f y ¼ 60,000 psi (for beams ρ min ¼ ) ρ R ρ R ρ R ρ R ϕ ρ tc

10 616 Appendix A: Tables and Diagrams Table A2.6b Resistance coefficient R (in psi) versus reinforcement ratio (ρ); f 0 c ¼ 4,000psi, f y ¼ 60,000 psi (for beams ρ min ¼ ) ρ R ρ R ρ R ρ R ρ R ϕ ρ tc

11 Appendix A: Tables and Diagrams 617 Table A2.6c Resistance coefficient R (in psi) versus reinforcement ratio (ρ); f c 0 ¼ 5,000psi, f y ¼ 60,000 psi (for beams ρ min ¼ ) ρ R ρ R ρ R ρ R ρ R ϕ ρ R ϕ ρ tc

12 618 Appendix A: Tables and Diagrams Table A2.7a Resistance coefficient R (in psi) versus reinforcement ratio (ρ); f 0 c ¼ 3,000 psi, f y ¼ 75,000 psi (for beams ρ min ¼ ) ρ R ρ R ρ R ϕ ρ tc

13 Appendix A: Tables and Diagrams 619 Table A2.7b Resistance coefficient R (in psi) versus reinforcement ratio (ρ); f 0 c ¼ 4,000 psi, f y ¼ 75,000 psi (for beams ρ min ¼ ) ρ R ρ R ρ R ρ R ϕ ρ tc

14 620 Appendix A: Tables and Diagrams Table A2.7c Resistance coefficient R (in psi) versus reinforcement ratio (ρ); f 0 c ¼ 5,000psi, f y ¼ 75,000 psi (for beams ρ min ¼ ) ρ R ρ R ρ R ρ R ϕ ρ R ϕ ρ tc

15 Appendix A: Tables and Diagrams 621 Table A2.8 b min and b max for reinforced concrete beams (in.) Number of bars in single layer #3 or #4 #5 #6 #7 #8 #9 #10 #11 b max b min Table A2.9 Areas of multiple reinforcing bars (in 2 ) Bar size Number of bars #3 #4 #5 #6 #7 #8 #9 #10 #

16 622 Appendix A: Tables and Diagrams Table A2.10 Areas of reinforcement in one-foot-wide sections Bar sizes Spacing (in.) #3 #4 #5 #6 #7 #8 #9 #10 # Areas of steel are given in square inches for one-foot-wide sections of concrete (slabs, walls, footings) for various center-to-center spacings of reinforcing bars

17 Appendix A: Tables and Diagrams 623 Table A3.1 Description of factors used in embedment length formulae Symbol Name Condition Value l d ψ t ψ e ψ s λ c b K tr Development length Reinforcement location factor Coating factor Reinforcement size factor Lightweight aggregate concrete factor Spacing or cover dimension, in. Transverse reinforcement index Excess reinforcement Note: ψ t ψ e not to exceed 1.7 As calculated, but not less than 12 in. Horizontal reinforcement placed so that more than 12 in. of fresh concrete is cast in the 1.3 member below the development length or splice Other reinforcement 1.0 Epoxy-coated or zinc and epoxy dual-coated reinforcement with cover less than 3d b or 1.5 clear spacing less than 6d b Epoxy-coated or zinc and epoxy dual-coated 1.2 reinforcement for all other conditions Uncoated or zinc-coated (galvanized) 1.0 reinforcement #6 and smaller bars and deformed wires 0.8 #7 and larger bars 1.0 When lightweight aggregate concrete is used 0.75 When normal-weight concrete is used 1.0 Use the smaller of either distance from the center of the bar to the nearest concrete surface, or one-half of the center-to-center spacing of the bars being developed. It is permitted to use K tr ¼ 0 as a design simplification, even if transverse reinforcement is present. (s ¼ spacing of the transverse reinforcement; and n ¼ number of bars being developed or lap spliced along the plane of splitting). Reinforcement in a flexural member is in excess of that required by analysis. 40A tr sn A s,required A s,provided

18 624 Appendix A: Tables and Diagrams Table A3.2 Simplified expression of development length, d, for bars in tension based on ACI code Section #6 and smaller bars Conditions and deformed wires A. Clear spacing of bars or wires being developed or! spliced not less than d b, clear cover not less than f y ψ t ψ e d b, and stirrups or ties throughout d not less than pffiffiffiffi d b 25λ f 0 the ACI Code minimum; or clear spacing of bars c or wires being developed or lap spliced at least 2d b and clear cover at least d b! B. Other cases 3f y ψ t ψ e pffiffiffiffi d b 50λ f 0 c Note: The development length used may not be less than 12 in. #7 and larger bars! f y ψ t ψ e pffiffiffiffi 20λ f 0 c! 3f y ψ t ψ e pffiffiffiffi 40λ f 0 c d b d b Table A3.3 Development length for tension bars ( d ) with f y ¼ 60 ksi (ψ e ¼ ψ t ¼ λ ¼ 1.0) [in.] l d (in.) fc 0 ¼ 3 ksi fc 0 ¼ 4 ksi Bar size Condition A Condition B Condition A Condition B # # # # # # # # # Note: Conditions A and B are based on Table A3.2

19 Appendix A: Tables and Diagrams 625 Table A3.4 Factors for development of hooked bars in tension [ACI Section ] Symbol Name Condition Value ψ e Coating factor Epoxy-coated or zinc and epoxy dual-coated reinforcement 1.2 Uncoated or zinc-coated (galvanized) reinforcement 1.0 ψ c Cover factor #11 Bar and smaller hooks with side cover (normal to plane of hook) 2.5 in., and for 90 hook with 0.7 cover on bar extension beyond hook 2 in. Other 1.0 #11 Bar and smaller 90 hooks: (1) enclosed along dh within ties or stirrups perpendicular to dh at spacing 3d b,or (2) Enclosed along the bar extension beyond hook including the bend within ties or stirrups perpendicular to the hook extension at spacing ψ r Confining factor 0.8 3d b (3) #11 and smaller bars 180 hooks Enclosed along dh within ties or stirrups perpendicular to dh at spacing 3d b Other 1.0 λ Lightweight aggregate concrete factor Normal weight concrete 1.0 Lightweight concrete 0.75 Excess reinforcement Reinforcement used by excess of that required by analysis A s,required A s,provided Note: The development length used may not be less than the smaller of 8d b or 6 in. Table A3.5 Factors for development of bars in compression [ACI Section ] Symbol Name Condition Value ψ r λ Confining factor Lightweight aggregate concrete factor Excess reinforcement Reinforcement enclosed within one of the following: (1) A spiral (2) A circular continuously wound tie with 0.75 d b 1/4 in., and pitch 4 in. (3) #4 Ties spaced 4 in. on center (4) Hoops spaced 4 in. on center Other 1.0 Lightweight concrete 0.75 Normal-weight concrete 1.0 Reinforcement used in excess of that required by analysis Note: The development length used may not be less than 8 in. A s,required A s,provided

20 626 Appendix A: Tables and Diagrams Table A3.6 Development length for compression bars ( dc ) with f y ¼ 60 ksi and various fc 0 values (in.) ½λ ¼ ψ r ¼ 1:0 Bar size fc 0 ¼ 3 ksi fc 0 ¼ 4 ksi fc 0 5 ksi # # # # # # # # #

21 Appendix A: Tables and Diagrams 627 Table A4.1a Values of V c in kips ðf 0 c ¼ 3,000psiÞ [d ¼ h 2.5 in. (+/ )] (λ ¼ 1.0) fc 0 ¼ 3,000 psi b w (in.) h (in.) Table A4.1b Values of V c in kips ðf 0 c ¼ 4,000psiÞ [d ¼ h 2.5 in. (+/ )] (λ ¼ 1.0) fc 0 ¼ 4,000 psi b w (in.) h (in.)

22 628 Appendix A: Tables and Diagrams Table A4.1c Values of V c in kips ðf 0 c ¼ 5,000psiÞ [d ¼ h 2.5 in. (+/ )] (λ ¼ 1.0) f 0 c ¼ 5,000 psi h (in.) b w (in.) Table A4.2a Values of V s in kips, with 2 legs of #3 stirrups (f yt ¼ 60,000 psi) #3 Stirrups 2 legs Spacing s (in.) h (in.) Note: Multiply table values by 2 for #3 stirrups with 4 legs

23 Appendix A: Tables and Diagrams 629 Table A4.2b Values of V s in kips, with 2 legs of #4 stirrups (f yt ¼ 60,000 psi) #4 Stirrups 2 legs Spacing s (in.) h (in.) Note: Multiply table values by 2 for #4 stirrups with 4 legs

24 630 Appendix A: Tables and Diagrams Table A5.1 Maximum number of bars in columns h h 1.5 in. for #5 to #8 1.5d b * for #9 to #11 (d b ¼ diameter of longitudinal bars) 1.5 in. for #5 to #8 1.5d b * for #9 to #11 Square tied column Round spiral column h (in.) #5 #6 #7 #8 #9 #10 #11 #5 #6 #7 #8 #9 #10 # Note: Values are based on 1 1 / 2 in. cover, #4 ties or spirals, with clear space of 1 1 / 2 in. for #5 to #8, and 1.5 times bar diameter for #9 to #11

25 Appendix A: Tables and Diagrams 631 a g 0.08 INTERACTION DIAGRAM R f c 4 ksi f y 60 ksi 0.6 h h K max e f s /f y 0 K n f c A g ε t = ε t = b R n e f c A g h 0.4 K n f c A g g Figure A5.1 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

26 Appendix A: Tables and Diagrams a g 0.08 INTERACTION DIAGRAM R f c f y 4 ksi 60 ksi 0.7 h h 1.6 K max e f s /f y 0 K n f c A g ε t = ε t = b R n e f c A g h K n f c A g g Figure A5.2 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

27 Appendix A: Tables and Diagrams 633 a g 0.08 INTERACTION DIAGRAM R f c 4 ksi f y 60 ksi 0.8 h h 1.6 K max e f s /f y 0 K n f c A g ε t = ε t = b R n e f c A g h K n f c A g 0.2 g Figure A5.3 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

28 634 Appendix A: Tables and Diagrams a g 0.08 INTERACTION DIAGRAM R f c 4 ksi f y 60 ksi 0.9 h h K max f s /f y 0 e K n f c A g ε t = ε t = R n e f c A g h b K n f c A g 0.2 g Figure A5.4 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

29 Appendix A: Tables and Diagrams 635 a g 0.08 INTERACTION DIAGRAM L f c 4 ksi f y 60 ksi 0.6 h h 1.6 K max e f s /f y 0 K n f c A g ε t = ε t = b R n e f c A g h 0.45 K n f c A g g Figure A5.5 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

30 636 Appendix A: Tables and Diagrams a g 0.08 INTERACTION DIAGRAM L f c 4 ksi f y 60 ksi 0.7 h h 1.6 K max e f s /f y 0 K n f c A g ε t = ε t = b R n e f c A g h 0.4 K n f c A g 0.2 g Figure A5.6 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

31 Appendix A: Tables and Diagrams 637 a g 0.08 INTERACTION DIAGRAM L f c 4 ksi f y 60 ksi 0.8 h h 1.6 K max e f s /f y 0 K n f c A g ε t = ε t = b e R n f c A g h g K n f c A g Figure A5.7 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

32 638 Appendix A: Tables and Diagrams a g 0.08 INTERACTION DIAGRAM L f c 4 ksi f y 60 ksi 0.9 h h 1.6 K max e 1.2 f s /f y K n f c A g ε t = ε t = b K n f c A g R n e f c A g h g Figure A5.8 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

33 Appendix A: Tables and Diagrams 639 a g 0.08 INTERACTION DIAGRAM C f c 4 ksi f y 60 ksi 0.60 h h K max e f s /f y 0 K n f c A g ε t = ε t = b R n e f c A g h 0.4 K n f c A g 0.2 g Figure A5.9 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

34 Appendix A: Tables and Diagrams a g 0.08 INTERACTION DIAGRAM C f c 4 ksi f y 60 ksi 0.7 h h K max f s /f y 0 e K n f c A g ε t = ε t = b e R n f c A g h g 0.01 K n f c A g Figure A5.10 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

35 Appendix A: Tables and Diagrams 641 a g 0.08 INTERACTION DIAGRAM C f c 4 ksi f y 60 ksi 0.8 h h K max f s /f y 0 e K n f c A g ε t = ε t = b R n e f c A g h K n f c A g g Figure A5.11 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

36 642 Appendix A: Tables and Diagrams a g 0.08 INTERACTION DIAGRAM C f c 4 ksi f y 60 ksi 0.9 h h K max f s /f y 0 e K n f c A g ε t = ε t = b R n e f c A g h K n f c A g g Figure A5.12 (a) ACI column interaction diagram [SP-17(11)], Courtesy of American Concrete Institute. (b) K n versus ϕ relationship

37 Appendix B Concrete Structure and Construction Images Figure B1.1 Boston city Hall, Boston, Massachusetts Springer International Publishing Switzerland 2017 M. Setareh, R. Darvas, Concrete Structures, DOI /

38 644 Appendix B: Concrete Structure and Construction Images Figure B1.2 Women Psychiatric Hospital, Chicago, Illinois

39 Appendix B: Concrete Structure and Construction Images 645 Figure B1.3 Concrete placement by pump Figure B1.4 Concrete placement by chute and test cylinders in preparation

40 Figure B West Washington Street, Naperville, Illinois Figure B2.2 An exposed reinforced concrete beam Courtesy of Professor Jack Davis, Virginia Tech

41 Appendix B: Concrete Structure and Construction Images 647 Figure B2.3 Beams supporting a one-way slab Figure B5.1 Lyon Train Station, Lyon, France Courtesy of Professor Jack Davis, Virginia Tech

42 648 Appendix B: Concrete Structure and Construction Images Figure B5.2 Main reinforcements and Ties for a column with 8 bars (see Figure 5.12e) Figure B5.3 Reinforcements in a reinforced concrete column

43 Appendix B: Concrete Structure and Construction Images 649 Figure B6.1 A high-rise building with flat plate floor system

44 650 Appendix B: Concrete Structure and Construction Images Figure B6.2 Forming for flat slab with drop panels Figure B6.3 An exposed waffle slab floor system

45 Appendix B: Concrete Structure and Construction Images 651 Figure B6.4 Construction of a waffle slab floor system Figure B6.5 Forming of a one-way joist floor

46 652 Appendix B: Concrete Structure and Construction Images Figure B6.6 An exposed one-way joist system Figure B7.1 A large square spread footing under construction

47 Appendix B: Concrete Structure and Construction Images 653 Figure B8.1 Large wall forming Courtesy of Mr. Doug Peters PE, President, Christman Constructors, Inc. Figure B8.2 Column forming

48 654 Appendix B: Concrete Structure and Construction Images Figure B8.3 Beam and slab forming Courtesy of Mr. Doug Peters PE, President, Christman Constructors, Inc. Figure B9.1 Prestressed I-Section concrete beams Courtesy of the William G. Godden Collection, NISEE-PEER, University of California, Berkeley

49 Appendix B: Concrete Structure and Construction Images 655 Figure B9.2 End anchor for a post-tensioned concrete beam Courtesy of the William G. Godden Collection, NISEE-PEER, University of California, Berkeley Figure B9.3 Post-tensioned concrete beams Courtesy of the William G. Godden Collection, NISEE-PEER, University of California, Berkeley