Idea Transcript
CHAPTER
Reinforced Concrete Design
Fifth Edition
DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS • A. J. Clark School of Engineering •Department of Civil and Environmental Engineering
Part I – Concrete Design and Analysis
5b
FALL 2002
By
Dr . Ibrahim. Assakkaf
ENCE 355 - Introduction to Structural Design Department of Civil and Environmental Engineering University of Maryland, College Park
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Development Length: Compression Bars Q
Slide No. 1 ENCE 355 ©Assakkaf
Deformed Bars in Compression – The method for determining the development length in compression ld involves finding the the basic development length ldb and multiplying it by applicable modification factors. – The modification factors reflect special conditions. – Note: ld shall not be less than 8 in.
1
Slide No. 2
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Development Length: Compression Bars Q
ENCE 355 ©Assakkaf
Basic Development Length (compression) The basic development length in compression is given by
ldb = 0.02d b
fy f c′
(1)
But it shouldn’t be less than 0.0003fydb according to the ACI Code, Section 12.3.
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Development Length: Compression Bars Q
Slide No. 3 ENCE 355 ©Assakkaf
Modification Factors (Compression) – The following modification factors may be applied to the basic development length for compression bars: 1. Reinforcement in excess of that required: As required As provided
2. Bars enclosed within a spiral that is not less than ¼ in. in diameter and not more than 4 in. in pitch or within No. 4 ties and spaced at not more than 4 in. on center: USE 0.75
2
Slide No. 4
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Development Length: Compression Bars Q
ENCE 355 ©Assakkaf
Tables 1a through 1c gives values of the basic development length ldb for compression bars in inches for the following combinations of f c′ and fy: f c′ : 3000, 4000, 5000, and 6000 psi fy: 40,000, 50,000, and 60,000 psi
Slide No. 5
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Development Length: Compression Bars
ENCE 355 ©Assakkaf
Table 1a. Basic Development Length ldb for Compression Bars (in.) for fy = 40,000 psi Bar Size 3 4 5 6 7 8 9 10 11 14 18
f c′ (normal-weight concrete), psi 3000 5.5 7.3 9.1 11.0 12.8 14.6 16.5 18.5 20.6 24.7 33.0
4000 4.7 6.3 7.9 9.5 11.1 12.6 14.3 16.1 17.8 21.4 28.5
5000 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.2 16.9 20.3 27.1
6000 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.2 16.9 20.3 27.1
3
Slide No. 6
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
ENCE 355 ©Assakkaf
Development Length: Compression Bars
Table 1b. Basic Development Length ldb for Compression Bars (in.) for fy = 50,000 psi Bar Size 3 4 5 6 7 8 9 10 11 14 18
f c′ (normal-weight concrete), psi 3000 6.8 9.1 11.4 13.7 16.0 18.3 20.6 23.2 25.7 30.9 41.2
4000 5.9 7.9 9.9 11.9 13.8 15.8 17.8 20.1 22.3 26.8 35.7
5000 5.6 7.5 9.4 11.3 13.1 15.0 16.9 19.1 21.2 25.4 33.9
6000 5.6 7.5 9.4 11.3 13.1 15.0 16.9 19.1 21.2 25.4 33.9
Slide No. 7
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
ENCE 355 ©Assakkaf
Development Length: Compression Bars
Table 1c. Basic Development Length ldb for Compression Bars (in.) for fy = 60,000 psi Bar Size 3 4 5 6 7 8 9 10 11 14 18
f c′ (normal-weight concrete), psi 3000 8.2 11.0 13.7 16.4 19.2 21.9 24.7 27.8 30.9 37.1 49.4
4000 7.1 9.5 11.9 14.2 16.6 19.0 21.4 24.1 26.8 32.1 42.8
5000 6.8 9.0 11.3 13.5 15.8 18.0 20.3 22.9 25.4 30.5 40.6
6000 6.8 9.0 11.3 13.5 15.8 18.0 20.3 22.9 25.4 30.5 40.6
4
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 8 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Need for Hooks – In the event that the desired development length in tension cannot be furnished, it will be necessary to provide mechanical anchorage at the end of the bars
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 9 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Need for Hooks ld
ld
Hook
Column
Beam
Figure 1. 180°-Hook
5
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 10 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Types of Hooks
– Anchorage for main or primary reinforcement is usually accomplished by means of 90° or 180° hook. – The dimensions and bend radii for these hooks have been standardized by the ACI Code. – Standard reinforcement hooks are shown in Fig. 2.
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 11 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Types of Hooks
Figure 2a. Standard Hooks
6
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 12 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Types of Hooks
Figure 2b. Standard Hooks
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 13 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Types of Hooks
Figure 3. Standard Hooks
7
Slide No. 14
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
ACI Code Specifications – The ACI Code specifies that the development length ldh (see Fig. 2) for deformed bars in tension, which terminate in a standard hook, be computed as the product of a basic development length lhb and any applicable modification factors. – Mathematically, this may expressed as
ldh = lhb × MF
(2)
Slide No. 15
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
ACI Basic Development Length, lhb – For a hooked bar with fy = 60,000 psi,
lhb =
1200d b f c′
(3)
– Table 1 (Table A-13, Textbook) provides values for lhb.
8
Slide No. 16
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension ACI Modification Factors (MF)
Q
– Modification factors are to be used if applicable: 1. Bars with fy other than 60,000 psi, USE MF =
fy 60,000
(4)
2. Concrete cover for No. 3 through No. 11: Side cover (normal to the plane of the hook ) ≥ 2 ½ in. and, for 90° hooks, cover on bar extension beyond the bend ≥ 2 in.: USE 0.7 for MF
Slide No. 17
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
ACI Modification Factors, MF (cont’d) 3. Ties or stirrups: For No. 3 through No. 11 with hook enclosed vertically of horizontally within ties or stirrup ties spaced along the full development length ldh not greater than 3db: USE MF = 0.8. 4. Reinforcement in excess of that required, where anchorage or development for fy is not specifically required:
MF =
As required As provided
(5)
9
Slide No. 18
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension
ACI Modification Factors, MF (cont’d)
Q
5. Lightweight aggregate concrete: USE
MF = 1.3
(6)
6. Epoxy-coated reinforcement: USE
MF = 1.2
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
(7)
Slide No. 19 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
ACI Modification Factors, MF (cont’d) – The basic development length lhb must be multiplied by the application factors outlined in the previous viewgraphs. – In no case may ldb be less than 8db or 6 in., whichever is greater.
10
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 20 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 Determine the anchorage or development length required for f c′ the conditions shown in the figure. Use = 3,000 psi (normalweight concrete) and fy = 60,000 psi. The No. 8 bars may be categorized as top bars. Assume a side cover on the main bars of 2 ½ in. minimum. Bars are uncoated.
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 21 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 (cont’d) Column
ld (minimum)
14′′
ld (minimum)
3-#8 bars 2′′ clear
24′′
#8 bars
18′′
2′′ clear #4 stirrups @ 5′′ o.c.
Stirrups Beam
11
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 22 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 (cont’d) Anchorage into the exterior column: 1. Establish values for the multiplying factors α, β, γ, and λ: a. b. c. d.
α = 1.3 (the bars are top bars). β = 1.0 (the bars are uncoated). γ = 1.0 (the bars are No. 8) λ = 1.0 (normal-weight concrete used)
2. The product α ×β = 1.3 < 1.7 (OK)
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 23 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 (cont’d)
3. Determine c. Based on cover (center of bar to nearest concrete surface), consider the clear cover, the No. 4 stirrups diameter, and one-half the diameter of the No. 8 bar: c = 2.0 + 0.5 +
Based on bar spacing: c=
1.0 = 3.0 in. 2
14 − 2(2.0 ) − 2(0.5) − 2(0.5) Controls = 2.0 in. 2(2 )
Therefore, use c = 2.0 in (smallest)
12
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 24 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Table 2. ASTM Standard - English Reinforcing Bars Bar Designation #3 [#10] #4 [#13] #5 [#16] #6 [#19] #7 [#22] #8 [#25] #9 [#29] #10 [#32] #11 [#36] #14 [#43] #18 [#57]
Diameter in 0.375 0.500 0.625 0.750 0.875 1.000 1.128 1.270 1.410 1.693 2.257
Area in2 0.11 0.20 0.31 0.44 0.60 0.79 1.00 1.27 1.56 2.25 4.00
Weight lb/ft 0.376 0.668 1.043 1.502 2.044 2.670 3.400 4.303 5.313 7.650 13.60
Note: Metric designations are in brackets
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 25 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 (cont’d) 4. The figure shows stirrups in the beam. However, there are no stirrups in the column, and Ktr can be taken as zero for the column anchorage. 5. Check (c + Ktr)/db ≤ 2.5: c + K tr 2.0 + 0 = = 2.0 < 2.5 ⇒ USE 2.0 1.0 db
6. The access reinforcement can be ignored and the factor applied can be omitted.
13
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 26 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 (cont’d)
7. Calculate ld:
3 f y αβγλ ld = db 40 f c′ c + ktr d b 3 60,000 1.3(1)(1)(1) (1.0) = 53.4 in. > 12 in. OK ld = 40 3,000 2.0
Since 53.4 in > 24 in. (column width), use a standard hook, either a 90° hook or a 180° hook.
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 27 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 (cont’d)
Anchorage using a standard 180° hook: 1. The basic development length lhb for the standard hook shown in the figure can be computed from lhb =
1200d b 1200(1) = = 21.9 in. (also check Table 1c) f c′ 3000
2. The only applicable MF is based on side cover of 2 ½ in. Therefore, USE MF = 0.7
14
Slide No. 28
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Table 1c. Basic Development Length ldb for Compression Bars (in.) for fy = 60,000 psi Bar Size 3 4 5 6 7 8 9 10 11 14 18
f c′ (normal-weight concrete), psi 3000 8.2 11.0 13.7 16.4 19.2 21.9 24.7 27.8 30.9 37.1 49.4
4000 7.1 9.5 11.9 14.2 16.6 19.0 21.4 24.1 26.8 32.1 42.8
5000 6.8 9.0 11.3 13.5 15.8 18.0 20.3 22.9 25.4 30.5 40.6
6000 6.8 9.0 11.3 13.5 15.8 18.0 20.3 22.9 25.4 30.5 40.6
Slide No. 29
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 (cont’d)
3. The required development length is then calculated from ldh = lhb × MF = 21.9(0.7 ) = 15.3 in. Check minimum : minimum ldh = 8d b ≥ 6 in. 8d b = 8 in. < 15.3 in.
OK
The minimum width of column required is 15.3 + 2.5 = 17.8 in. < 24 in. (column width)
OK
Therefore, the hook will fit into the column.
15
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 30 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 (cont’d)
Anchorage into beam: The development length required if bars are straight can be taken as 53.4 in. as determined previously. However, this number is conservative (Ktr = 0). To determine a more accurate value, we have to take into consideration the transverse reinforcement index Ktr because there are stirrups in the beam.
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 31 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 (cont’d) Area of 2 #4 stirrups Atr f yt 0.4(60,000) K tr = = = 1.067 1500sn 1500(5)(3)
c + K tr 2.0 + 1.067 = = 3.07 < 2.5 ⇒ USE 2.5 db 1.0 3 f y αβγλ ld = db 40 f c′ c + ktr d b
ld =
3 60,000 1.3(1)(1)(1) (1.0) = 42.7 in. > 12 in. OK 40 3,000 2.5
16
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 32 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Table 2. ASTM Standard - English Reinforcing Bars Bar Designation #3 [#10] #4 [#13] #5 [#16] #6 [#19] #7 [#22] #8 [#25] #9 [#29] #10 [#32] #11 [#36] #14 [#43] #18 [#57]
Diameter in 0.375 0.500 0.625 0.750 0.875 1.000 1.128 1.270 1.410 1.693 2.257
Area in2 0.11 0.20 0.31 0.44 0.60 0.79 1.00 1.27 1.56 2.25 4.00
Weight lb/ft 0.376 0.668 1.043 1.502 2.044 2.670 3.400 4.303 5.313 7.650 13.60
Note: Metric designations are in brackets
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
Slide No. 33 ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 (cont’d) Anchorage into beam (cont’d): – The development length required if bars are straight is 42.7 in. – Therefore, the bars must extend at least this distance into the span. – Figure 4 shows the detailed sketch for the development length.
17
Slide No. 34
CHAPTER 5b. DEVELOPMENT, SPLICES, AND SIMPLE SPAN BAR CUTOFFS
ENCE 355 ©Assakkaf
Development Length: Standard Hooks in Tension Q
Example 1 (cont’d) 2
″ 1 cover 2
ldb 180° Hook
Column
Required = 15.3′′ min. #8 bars
18′′
Beam 24′′
Figure 4. Detailed Sketch for Example 1
18