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Reinforced Concrete Beam Design:
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This design guide is intended to provide guidance for the safe design and economical
construction of reinforced concrete beams. This design guide and the corresponding
calculations are based on the requirements of ACI 318 and strength design method
where the capacity of the beam is designed to support factored loads.
All calculations cover the design of a typical simply supported, single span, flexural
reinforced concrete beam having a rectangular cross section.
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Iterative Design For Known Rectangular Beam Cross Section:
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1. Calculate the initial area
of tension steel, Asi using an estimated value for the distance from the centroid
of the compressed area to extreme compression fiber, dc, of dc = 0.1d.
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2. Calculate the area of compression,
Ac using the trial area of tension steel Asi.
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3. Calculate the depth of the
compression zone, t, and the distance from the centroid to the extreme compression
fiber, dc, from the area of compression, Ac.
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4. Calculate the nominal moment
capacity, Mn, of the design section using the trial area of tension steel,
Asi, and the calculated factor dc.
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5. Calculate the adjusted
area of steel, As, from the nominal moment capacity, Mn, and the maximum moment
load, Mu, on the beam.
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Beam Design For Unknown Rectangular Beam Cross Section:
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1. Select a value of the steel reinforcement ratio, p, between the minimum, pmin, and maximum, pmax, values. (Larger values will lead to
smaller concrete cross sections.) It is a commonly held opinion that values
of pfy/f'c near 0.18 lead to economical beams (or use p = 0.18f'c/fy to design an economical beam).
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2. Calculate the required beam dimensions,
bd^2, from the nominal moment, Mn, on the beam. The nominal moment,
Mn, is equal to the factored moment, Mu, divided by the factor 0.9.
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3. Choose appropriate values of b and d. A good choice is to keep the value
of d/b between 1.5 and 2.5. If the beam has a single layer of tension steel,
the value of d is approximately equal to h - 2.5 in. If the depth is chosen
that is larger than the fraction of the span in the table below deflection calculations
can be obviated.
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Minimum Beam Thickness Unless Deflections Are Computed
(fy = 60,000 psi)
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Construction
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Minimum h
(fraction of span length)
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Simply supported
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1/16
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One end continuous
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1/18.5
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Both ends continuous
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1/21
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Cantilever
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1/8
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The above table is for normal weight concrete reinforced with fy
= 60,000 psi (400 MPa) steel. For other steel strengths multiply the values
in the table by the following adjustment factors: 20 lb/cf (14.13 and 18.83
kN/m^3), multiply the table values by the following adjustment factors:
For SI: 1.65 - 0.0318w >= 1.09
For US: 1.65 - 0.005w >= 1.09
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4. Calculate the required steel area as As = pbd.
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5. Select the reinforcing steel bars to satisfy the distribution and placement requirements
of ACI 318.
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Minimum Beam Widths (Inches)
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Size of Bar, No.
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Number of bars in a single layer of reinforcement
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Add to width, b of beam for each additional
bar
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2
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3
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4
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5
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6
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7
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8
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no. 4
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6.1
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7.6
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9.1
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10.6
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12.1
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13.6
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15.1
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1.50
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no. 5
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6.3
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7.9
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9.6
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11.2
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12.8
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14.4
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16.1
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1.63
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no.6
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6.5
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8.3
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10.0
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11.8
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13.5
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15.3
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17.0
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1.75
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no. 7
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6.7
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8.6
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10.5
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12.4
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14.2
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16.1
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18.0
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1.88
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no. 8
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6.9
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8.9
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10.9
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12.9
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14.9
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16.9
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18.9
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2.00
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no. 9
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7.3
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9.5
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11.8
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14.0
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16.3
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18.6
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20.8
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2.26
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no. 10
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7.7
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10.2
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12.8
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15.3
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17.8
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20.4
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22.9
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2.54
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no. 11
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8.0
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10.8
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13.7
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16.5
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19.3
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22.1
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24.9
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2.82
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no. 14
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8.9
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12.3
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15.6
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19.0
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22.4
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25.8
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29.2
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3.39
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no. 18
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10.5
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15.0
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19.5
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24.0
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28.6
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33.1
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37.6
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4.51
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6. Design the shear reinforcment.
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- Calculate the shear envelope for the factored loads, calculating
the shear at any section, Vu.
- Calculate the concrete shear strength, Vc.
- Determine the portions of the beam where the factored shear is less <= 0.85Vc/2.
Stirrups are not required in these sections.
- Calculate the
required steel shear strength, Vs checking against maximum allowable steel shear
and maximum allowable total shear. If the maximum allowable steel shear or
the maximum total shear is to much, then the adequate shear strength cannot be achieved
with the steel, or the total shear cannot be achieved with the beam, in either case
the beam dimensions must be adjusted.
- Calculate the maximum stirrup spacing and the area of shear reinforcement
required, Av, for vertical
stirrups or if desired for
angled stirrups. Aternatively, if Av is to large with the maximum
spacing, s, choose a smaller Av and solve for the required stirrup spacing, s for vertical stirrups or required spacing s, for angled stirrups.
- Calculate the minimum steel shear strength, Vsmin for vertical stirrups, or Vsmin for angled stirrups, by setting Av to the minimum shear reinforcement, Av min, and again using the
maximum stirrup spacing,
s. Use this minimum reinforcement in areas where Vc/2 < Vu < Vc + Vsmin.
- Determine shear reinforcement embedment length. For U-shaped stirrups, ACI
318 requires that each end of the stirrup is bent around the longitudinal
steel, anchoring the ends for all no. 5 and smaller bars and no. 6, 7 and 8 bars
with fy <= 40,000 psi (276 MPa). For no 6, 7 and 8 bars where fy > 40,000
psi (276 MPa), both ends must be around longitudinal reinforcement, with one end
having an embedment distance between midheight of the member and the outside of
the hook equal to the
required embedment length.
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7. Check themaximum tension steel spacing,smax,
requirement for crack control.
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8. Check the deflection requirements per ACI 318 if the depth of the beam
is less than the minimum depth required in the table above, or the beam supports
nonstructural elements that are sensitive to deformations.
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