Design the flexural reinforcement for a rectangular section with a width of 10 in. and a total depth, h of 20 in. that is subjected to MD = 88 k-ft and ML = 70 k-ft. f’c = 6 ksi and fy = 80 ksi. BARSIZE#3#4#5#6Total Areas for Various Numbers of Reinforcing Bars#8#9#10NOMINALDIAMETER(in.)WEIGHT(lb/ft)120.3760.6681.0431.5022.0442.670 0.793.4004.303 1.27 2.545.3137.6513.6040.11 0.220.20 0.400.31 0.620.44 0.880.60 1.2030.330.440.550.880.60 0.801.001.201.40 1.600.931.241.551.862.172.481.32 1.762.202.64 3.08 3.521.802.403.003.604.204.803.163.95 4.745.53 6.321.58 2.371.00 2.00 3.004.00 5.00 6.00 7.00 8.003.81 5.08 6.35 7.62 8.89 10.161.56 3.124.68 6.24 7.80 9.36 10.92 12.482.254.506.75 9.00 11.25 13.50 15.7518.004.00 8.00 12.00 16.00 20.00 24.00 28.00 32.00 36.0020.25NUMBER OF BARS560.3750.5000.6250.7500.8751.0001.1281.270#111.410#14ª1.693#18ª2.257#14 and #18 bars are used primarily as column reinforcement and are rarely used in beams.70.66 0.778Minimum Width of Web for Multiple Bars, in., ACI 318-14a,b,c#3 "U" Shaped Stirrups#4 "U" Shaped StirrupsNumber of Bars in a Single Layer34562Number of Bars in a Single Layer3 49.00 10.50526.75 8.25 9.75 11.25 12.7567.5012.0013.506.8810.13 11.75 13.387.639.25 10.88 12.50 14.138.508.75 10.50 12.25 14.007.007.759.50 11.25 13.00 14.757.137.889.75 11.63 13.50 15.389.25 11.25 13.2510.00 12.00 14.00 16.007.257.51 9.76 12.02 14.279.00 10.88 12.75 14.6315.2516.5317.958.008.26 10.51 12.77 15.02 17.287.79 10.33 12.87 15.418.54 11.08 13.6216.16 18.7017.28 20.108.82 11.64 14.469.39 12.77 16.16 19.54 22.9310.77 15.29 19.80 24.31 28.839Bar SizeDesignation#4#5#6#7#8#9# 10# 11#14# 18*Minimum spacing and bend radii based on ACI 318-2014, Sections 25.2.1 and 25.3.2 (3/4 in. max agg. size).Bars are not lap-spliced or bundled.*Cover for stirrups assumed to be 1 1/2 in. (based on interior exposure).0.991.802.793.965.407.119.0011.4314.04Add for EachAdditional Bar(in.)1.501.631.751.882.002.262.542.823.394.51101.102.003.104.406.007.9010.0012.7015.6022.5040.00 Design of Singly-Reinforced Rectangular BeamsB. If section dimensions are restricted (given)1. Knowing h, determine an initial estimate for d:de h-2.5" if A, is placed in one layerde h-3.5" if A, is placed in two layers2. Use Equation (B) to determine p.Compute A₂ = p bd.✓lf A₂ ≤ ATC ⇒ Good.Select steel bars. If needed, revise d. Compare selected steel amountto steel limits set by the code.✓lf A₂ > ATC ⇒ N.G.Need compression steel3. Check that MM, where = 0.90Design of Singly-Reinforced Rectangular Beams.• Recommended practice for sizing beams- Use whole inch increments for beam dimensions.- Use stem width (b or b) in increments of 2" or 3" (e.g. do not useb = 5", 7", 11", etc.)- Maintain bar symmetry - use at least 2 bars in any one layer.- Use #11 or smaller bars. Larger bar sizes are used only in specialapplications.- Do not use more than two different bar sizes.-If two different bar sizes are used to provide required steel area, donot use bars that are more than two bar sizes apart.9

We are given MD = 88 K-ft ML = 70 K-ft Fcatored Moment Mu = 1.2*MD+1.6*ML Fcatored Moment Mu =…

Answered: Design the flexural reinforcement for a…

Design the flexural reinforcement for a rectangular section with a width of 10 in. and a total depth, h of 20 in. that is subjected to MD = 88 k-ft and ML = 70 k-ft. f’c = 6 ksi and fy = 80 ksi.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

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Design the flexural reinforcement for a rectangular section with a width of 10 in. and a total
depth, h of 20 in. that is subjected to MD = 88 k-ft and ML = 70 k-ft. f’c = 6 ksi and fy = 80 ksi.

BAR
SIZE
#3
#4
#5
#6
Total Areas for Various Numbers of Reinforcing Bars
#8
#9
#10
NOMINAL
DIAMETER
(in.)
WEIGHT
(lb/ft)
1
2
0.376
0.668
1.043
1.502
2.044
2.670 0.79
3.400
4.303 1.27 2.54
5.313
7.65
13.60
4
0.11 0.22
0.20 0.40
0.31 0.62
0.44 0.88
0.60 1.20
3
0.33
0.44
0.55
0.88
0.60 0.80
1.00
1.20
1.40 1.60
0.93
1.24
1.55
1.86
2.17
2.48
1.32 1.76
2.20
2.64 3.08 3.52
1.80
2.40
3.00
3.60
4.20
4.80
3.16
3.95 4.74
5.53 6.32
1.58 2.37
1.00 2.00 3.00
4.00 5.00 6.00 7.00 8.00
3.81 5.08 6.35 7.62 8.89 10.16
1.56 3.12
4.68 6.24 7.80 9.36 10.92 12.48
2.25
4.50
6.75 9.00 11.25 13.50 15.75
18.00
4.00 8.00 12.00 16.00 20.00 24.00 28.00 32.00 36.00
20.25
NUMBER OF BARS
5
6
0.375
0.500
0.625
0.750
0.875
1.000
1.128
1.270
#11
1.410
#14ª
1.693
#18ª
2.257
#14 and #18 bars are used primarily as column reinforcement and are rarely used in beams.
7
0.66 0.77
8
Minimum Width of Web for Multiple Bars, in., ACI 318-14a,b,c
#3 "U" Shaped Stirrups
#4 "U" Shaped Stirrups
Number of Bars in a Single Layer
3
4
5
6
2
Number of Bars in a Single Layer
3 4
9.00 10.50
5
2
6.75 8.25 9.75 11.25 12.75
6
7.50
12.00
13.50
6.88
10.13 11.75 13.38
7.63
9.25 10.88 12.50 14.13
8.50
8.75 10.50 12.25 14.00
7.00
7.75
9.50 11.25 13.00 14.75
7.13
7.88
9.75 11.63 13.50 15.38
9.25 11.25 13.25
10.00 12.00 14.00 16.00
7.25
7.51 9.76 12.02 14.27
9.00 10.88 12.75 14.63
15.25
16.53
17.95
8.00
8.26 10.51 12.77 15.02 17.28
7.79 10.33 12.87 15.41
8.54 11.08 13.62
16.16 18.70
17.28 20.10
8.82 11.64 14.46
9.39 12.77 16.16 19.54 22.93
10.77 15.29 19.80 24.31 28.83
9
Bar Size
Designation
#4
#5
#6
#7
#8
#9
# 10
# 11
#14
# 18
*Minimum spacing and bend radii based on ACI 318-2014, Sections 25.2.1 and 25.3.2 (3/4 in. max agg. size).
Bars are not lap-spliced or bundled.
*Cover for stirrups assumed to be 1 1/2 in. (based on interior exposure).
0.99
1.80
2.79
3.96
5.40
7.11
9.00
11.43
14.04
Add for Each
Additional Bar
(in.)
1.50
1.63
1.75
1.88
2.00
2.26
2.54
2.82
3.39
4.51
10
1.10
2.00
3.10
4.40
6.00
7.90
10.00
12.70
15.60
22.50
40.00

Design of Singly-Reinforced Rectangular Beams
B. If section dimensions are restricted (given)
1. Knowing h, determine an initial estimate for d:
de h-2.5" if A, is placed in one layer
de h-3.5" if A, is placed in two layers
2. Use Equation (B) to determine p.
Compute A₂ = p bd.
✓lf A₂ ≤ ATC ⇒ Good.
Select steel bars. If needed, revise d. Compare selected steel amount
to steel limits set by the code.
✓lf A₂ > ATC ⇒ N.G.
Need compression steel
3. Check that MM, where = 0.90
Design of Singly-Reinforced Rectangular Beams
.
• Recommended practice for sizing beams
- Use whole inch increments for beam dimensions.
- Use stem width (b or b) in increments of 2" or 3" (e.g. do not use
b = 5", 7", 11", etc.)
- Maintain bar symmetry - use at least 2 bars in any one layer.
- Use #11 or smaller bars. Larger bar sizes are used only in special
applications.
- Do not use more than two different bar sizes.
-If two different bar sizes are used to provide required steel area, do
not use bars that are more than two bar sizes apart.
9

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