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Concrete Rectangular Beam Calculator to ACI 318-19 (IMP)'s banner

Concrete Rectangular Beam Calculator to ACI 318-19 (IMP)

Verified by the CalcTree engineering team on June 27, 2024

This calculator performs the analysis and design of a reinforced concrete beam. It takes applied axial, shear and moments for several load types and checks all ULS and SLS load combinations to identify the critical design loads. It then checks the design loads against the moment and shear capacities, deflection limits and also checks the minimum depth, cover and reinforcement required. This calculator uses imperial units.
All calculations are performed in accordance with ACI 318-19 and ASCE7-22.

Code Calculation

Materials

Concrete


f'c
:{"mathjs":"Unit","value":4000.0000000000005,"unit":"psi","fixPrefix":false}​



Ec
:3604996.5325919534​

Reinforcement


fy
:{"mathjs":"Unit","value":60000.00000000001,"unit":"psi","fixPrefix":false}​



Es
:{"mathjs":"Unit","value":29000000,"unit":"psi","fixPrefix":false}​



n
:8 psi​

Where:
  1. 
    
    is the specified compressive strength of concrete in psi
  1. 
    
    is the specified strength for non-prestressed reinforcement in psi
  1. 
    
    
    
    f'c
    :{"mathjs":"Unit","value":4000.0000000000005,"unit":"psi","fixPrefix":false}​
    (19.2.2.1.b) is the Modulus of Elasticity for the concrete
  1. 
    
    is the Modulus of Elasticity for the reinforcement in psi.
  1. 
    
    is the modular factor, expressed as
    
    
    
    n
    :8.0 psi​


Cross Section

Geometry




Cross section



b
:{"mathjs":"Unit","value":14,"unit":"in","fixPrefix":false}​



cover
:{"mathjs":"Unit","value":1.4999999999999998,"unit":"in","fixPrefix":false}​



h
:{"mathjs":"Unit","value":23.999999999999996,"unit":"in","fixPrefix":false}​



C1
:{"mathjs":"Unit","value":11.999999999999998,"unit":"in","fixPrefix":false}​



L
:{"mathjs":"Unit","value":30,"unit":"ft","fixPrefix":false}​



C2
:{"mathjs":"Unit","value":11.999999999999998,"unit":"in","fixPrefix":false}​



Profile view


Reinforcement

Top


Ntop
:2​



Top rebar
:#3​

Bottom


Nbot
:4​



Bot rebar
:#7​

Stirrup


Legs
:2​



S1
:{"mathjs":"Unit","value":8,"unit":"in","fixPrefix":false}​



Stirrup rebar
:#3​



S2
:{"mathjs":"Unit","value":16,"unit":"in","fixPrefix":false}​

Where:
  1. Ntop: number of bars used as top reinforcement.
  1. Top rebar: diameter of the top reinforcement expressed as eighths of an inch.
  1. Nbot: number of bars used as bottom reinforcement.
  1. Bot rebar: diameter of the bottom reinforcement expressed as eighths of an inch.
  1. Legs: number of vertical bars used as transverse reinforcement, assuming two legs for a regular stirrup.
  1. Stirrup rebar: diameter of the transverse reinforcement expressed as eighths of an inch.
  1. S1/S2: Longitudinal spacing of the transverse reinforcement in the corner and the centre of the beam, respectively. Measured center to center.

Loads

Loads Entry

Following the above axis system, you can introduce the different beam solicitations for each load.
3D Axis

Where:
D: Dead Load.
E: Earthquake Load.
F: Fluids Load.
H: Earth Load.
L: Live Load.
Lr: Roof Live Load.
S: Snow Load.
R: Rain Load.
W: Wind Load.

👉 A(+) is compression


Ultimate Loads

Load Combinations

The full table of applied ultimate loads to the structure according to the combinations established in the ACI318-19 and ASCE7-22.

0.00 kips​
0.21 kips​
1.57 kips-ft​
0.00 kips​
0.79 kips​
10.70 kips-ft​
0.00 kips​
0.79 kips​
10.70 kips-ft​
0.00 kips​
0.79 kips​
10.70 kips-ft​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.00 kips​
0.18 kips​
1.34 kips-ft​
0.00 kips​
0.18 kips​
1.34 kips-ft​
0.00 kips​
0.18 kips​
1.34 kips-ft​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.00 kips​
0.14 kips​
1.01 kips-ft​
0.00 kips​
0.14 kips​
1.01 kips-ft​

Max/Min Loads

Resume of the max/min applied ultimate loads to the structure according to the combinations established in the ACI318-19 and ASCE7-22.

1.2D+1.6L+0.5Lr​
0.79 kips​
10.70 kips-ft​
1.2D+1.6L+0.5Lr​
0.79 kips​
10.70 kips-ft​
0.9D+ 1.0W​
0.14 kips​
1.01 kips-ft​
0.9D+ 1.0W​
0.14 kips​
1.01 kips-ft​

Service Loads

The full table of applied service loads to the structure according to the combinations established in ASCE7-22.

1.00 kips​
1.00 kips​
1.00 kips​
1.00 kips-ft​
1.00 kips-ft​
1.00 kips-ft​
1.00 kips​
2.00 kips​
2.00 kips​
2.00 kips-ft​
2.00 kips-ft​
2.00 kips-ft​
1.00 kips​
3.00 kips​
3.00 kips​
3.00 kips-ft​
3.00 kips-ft​
3.00 kips-ft​
1.00 kips​
1.70 kips​
1.70 kips​
1.70 kips-ft​
1.70 kips-ft​
1.70 kips-ft​
1.00 kips​
2.00 kips​
2.00 kips​
2.00 kips-ft​
2.00 kips-ft​
2.00 kips-ft​
1.00 kips​
2.50 kips​
2.50 kips​
2.50 kips-ft​
2.50 kips-ft​
2.50 kips-ft​
1.00 kips​
2.28 kips​
2.28 kips​
2.28 kips-ft​
2.28 kips-ft​
2.28 kips-ft​
1.00 kips​
2.50 kips​
2.50 kips​
2.50 kips-ft​
2.50 kips-ft​
2.50 kips-ft​
1.00 kips​
1.60 kips​
1.60 kips​
1.60 kips-ft​
1.60 kips-ft​
1.60 kips-ft​
1.00 kips​
3.10 kips​
3.10 kips​
3.10 kips-ft​
3.10 kips-ft​
3.10 kips-ft​
1.00 kips​
2.88 kips​
2.88 kips​
2.88 kips-ft​
2.88 kips-ft​
2.88 kips-ft​
1.00 kips​
3.10 kips​
3.10 kips​
3.10 kips-ft​
3.10 kips-ft​
3.10 kips-ft​
1.00 kips​
1.20 kips​
1.20 kips​
1.20 kips-ft​
1.20 kips-ft​
1.20 kips-ft​

Elastic Deflections

In the following table, you can add the deflections for each type of load, in case of a required deflection analysis. These deflections must be the product of an elastic analysis of the beam for the correct use of this page.


Flexural Strength

The flexural strength of the beam is calculated according to the standard literature for prismatic and simple reinforced beams. The

factor of 0.90 corresponds to the established in the ACI318-19; it can be changed according to the necessity of the user.

Mn =ρbd2fy(1−0.59ρfyfc′)M_n\ =\rho bd^2f_y(1-0.59\rho \frac{f_y}{f'_c})


φf
:0.9​



Mn, Bot
:242.53681730479084​



φMn, Bot
:218.2831355743119​



Mn,Top
:24.0750032188715​



φMn,Top
:21.66750289698435​


Shear strength

The

factor of 0.75 corresponds to the established in the ACI318-19; it can be changed according to the necessity of the user.
22.5.1.1
Nominal one-way shear strength at a section

Vn =Vc + VsV_n\ = V_c\ +\ V_s


φs
:0.75​


(22.5.1.1)


Vn1
:49.852389621235396​



Vn2
:49.852389621235396​



φVn,1
:37.38929221592655​



φVn,2
:37.38929221592655​


Notice that two Shear Strengths are calculated in each section, each corresponding to the different spacings used in the beam.

Concrete Ultimate Design Shear



Vc1
:13.922724616984​



Vc2
:13.922724616984​

Vc shall not be taken greater than:

Vc, max= 5λfc′bwdV_{c,\ max}=\ 5\lambda\sqrt{f'_c}b_wd
(22.5.5.1.1)


Vc,max+
:96.0146554568624​



Vc,max-
:97.1214526379213​

For nonprestressed members, Vc shall be calculated by Table 22.5.5.1:
A complete revision for each load combination was made for the following calculation. The final value is taken as the minimum calculated value in the table below. Finally, the

condition can be checked in the code revision.
Table 22.5.5.1 - ACI 318-19



Vc_22.5.5.1-1
:13.922724616984​



Vc_22.5.5.1-2
:13.922724616984​


1.4D​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+1.6L+0.5Lr​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+1.6L+0.5S​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+1.6L+0.5R​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+ 1.6Lr+1.0L​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+ 1.6S+1.0L​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+ 1.6R+1.0L​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+ 1.6Lr+0.5W​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+ 1.6S+0.5W​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+ 1.6R+0.5W​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+ 1.0W+ 1.0L+0.5Lr​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+ 1.0W+ 1.0L+0.5S​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+ 1.0W+ 1.0L+0.5R​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
1.2D+ 1.0E+ 1.0L + 0.2S​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
0.9D+ 1.0W​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​
0.9D+ 1.0E​
0.00 kips​
38.41 kips​
38.85 kips​
30.62 kips​
13.92 kips​
24.33 kips​
11.02 kips​

Transverse Reinforcement Ultimate Design Shear


Vs=AvfydsV_s=\frac{A_vf_yd}{s}
(22.5.8.5.3)


Vs1
:35.9296650042514​



Vs2
:35.9296650042514​



Effective Deflection

Cracking Moment


Mcr=frIgytM_{cr}=\frac{f_rI_g}{y_t}
(24.2.3.5)


Mcr
:53.12626469082875​



Cracked Moment of Inertia

The following calculation was made assuming a simple reinforced prismatic concrete beam.
Cracked Cross Section


Icr=b(kd)312+b(kd)22+nAs2(d−kd)I_{cr}=\frac{b{(kd)}^3}{12}+\frac{b{(kd)}^2}{2}+n{A_s}^2(d-kd)


Icr, Bot
:1319.6867570644195​



Icr, Top
:55.78928963530608​


Effective Moment of Inertia

Table 24.2.3.5 - ACI 318-19

Where:
  1. 
    
    is the moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement in
    
    .
  1. 
    
    is the moment of inertia of cracked section transformed to concrete (see chapter above) in
    
    E=mc^2
    .
  1. 
    
    is the cracking moment.
  1. 
    
    is the maximum moment in the member due to service loads at stage deflection is calculated.
A complete calculus for each combination of loads was made for the effective moment of inertia. (See the final chapter).


Time-dependent deflections

24.2.4.1.1
Additional time-dependent deflection resulting from creep and shrinkage of flexural members shall be calculated as the product of the immediate deflection caused by sustained load and the factor λΔ.
Table 24.2.4.1.3 - ACI 318-19

We use a time-dependent factor ξ of 2.0, corresponding to a sustained load duration of 60 or more months only for the dead loads, which are the one that remains sustained in time. A manual inclusion of this factor should be applied to the calculated deflection in case of a different condition.


ξBot
:2​



ξTop
:2​


λΔ=ξ1+50ρ′\lambda_\Delta=\frac{\xi}{1+50\rho'}
(24.2.4.1.1)


λΔ,Bot
:1.930573759831715​



λΔ,Top
:1.4325681149257323​

Where:
  1. 
    
    is the reinforcement ratio for the compressive reinforcement. We use the top ratio for positive flexural moments and the bottom ratio for negative flexural moments.

Service load calculated deflections

For immediate deflections, the dead load deflection is calculated first and then subtracted from the total combination deflection. The inmmediate deflection calculation is made only for live loads included combinations.

0.00 kips​
0.53 kips​
5.51 kips-ft​
1.00 in​
16128.00 in4​
1​
1.00 in​
2.00 in​
0.00 kips​
0.53 kips​
6.97 kips-ft​
2.00 in​
16128.00 in4​
1​
2.00 in​
1.00 in​
3.00 in​
0.00 kips​
0.15 kips​
1.12 kips-ft​
2.00 in​
16128.00 in4​
1​
2.00 in​
1.00 in​
3.00 in​
0.00 kips​
0.15 kips​
1.12 kips-ft​
1.70 in​
16128.00 in4​
1​
1.70 in​
2.70 in​
0.00 kips​
0.15 kips​
1.12 kips-ft​
2.00 in​
16128.00 in4​
1​
2.00 in​
3.00 in​
0.00 kips​
0.43 kips​
5.51 kips-ft​
2.50 in​
16128.00 in4​
1​
2.50 in​
1.50 in​
3.50 in​
0.00 kips​
0.43 kips​
5.51 kips-ft​
2.28 in​
16128.00 in4​
1​
2.28 in​
3.28 in​
0.00 kips​
0.43 kips​
5.51 kips-ft​
2.50 in​
16128.00 in4​
1​
2.50 in​
3.50 in​
0.00 kips​
0.15 kips​
1.12 kips-ft​
1.60 in​
16128.00 in4​
1​
1.60 in​
2.60 in​
0.00 kips​
0.43 kips​
5.51 kips-ft​
3.10 in​
16128.00 in4​
1​
3.10 in​
4.10 in​
0.00 kips​
0.43 kips​
5.51 kips-ft​
2.88 in​
16128.00 in4​
1​
2.88 in​
3.88 in​
0.00 kips​
0.43 kips​
5.51 kips-ft​
3.10 in​
16128.00 in4​
1​
3.10 in​
4.10 in​
0.00 kips​
0.09 kips​
0.67 kips-ft​
1.20 in​
16128.00 in4​
1​
1.20 in​
2.20 in​


Beam Properties

Geometry



Ag
:336​

Gross area of concrete section


Ig
:16128​

Moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement.


yt
:12​

Distance from centroidal axis of gross-section, neglecting reinforcement, to tensional face.

Reinforcement

Top Rebar


Øtop rebar
:0.375​



As, top_rebar
:0.110446616727766​



AsT, top_rebar
:0.220893233455532​



ρTop
:0.0007192290873603009​



dtop
:21.9375​

Bottom Rebar


Øbot rebar
:0.875​



As, bot_rebar
:0.60132046885117​



AsT, bot_rebar
:2.40528187540468​



ρBot
:0.00792188349248143​



dbot
:21.6875​

Transverse Rebar


Øst rebar
:0.375​



As, st_rebar
:0.110446616727766​



AsT, st_rebar
:0.220893233455532​



Design Check

In the following tables, the "Check" condition corresponds to a failure of accomplishment in the checked state.

Minimum Depth and Cover

Select the correct support condition for the current analysed beam:


Support
:Simply supported​


22.50 in​
Ok​
Table 9.3.1.1 - ACI 318-19

Select the correct exposure condition for the concrete:


Condition
:Cast against and permanently in contact with ground​


3.00 in​
Check​
Table 20.5.1.3.1 - ACI 318-19


Strength

Max/Min


1.2D+1.6L+0.5Lr​
0.79 kips​
10.70 kips-ft​
0.49​
N/A​
0.02​
0.02​
0.04​
OK​
1.2D+1.6L+0.5Lr​
0.79 kips​
10.70 kips-ft​
0.49​
N/A​
0.02​
0.02​
0.04​
OK​
0.9D+ 1.0W​
0.14 kips​
1.01 kips-ft​
0.05​
N/A​
0​
0​
0.01​
OK​
0.9D+ 1.0W​
0.14 kips​
1.01 kips-ft​
0.05​
N/A​
0​
0​
0.01​
OK​

Ultimate Combinations


0.00 kips​
0.21 kips​
1.57 kips-ft​
0.07​
N/A​
0​
0​
0.01​
OK​
0.00 kips​
0.79 kips​
10.70 kips-ft​
0.49​
N/A​
0.02​
0.02​
0.04​
OK​
0.00 kips​
0.79 kips​
10.70 kips-ft​
0.49​
N/A​
0.02​
0.02​
0.04​
OK​
0.00 kips​
0.79 kips​
10.70 kips-ft​
0.49​
N/A​
0.02​
0.02​
0.04​
OK​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.33​
N/A​
0.01​
0.01​
0.03​
OK​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.33​
N/A​
0.01​
0.01​
0.03​
OK​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.33​
N/A​
0.01​
0.01​
0.03​
OK​
0.00 kips​
0.18 kips​
1.34 kips-ft​
0.06​
N/A​
0​
0​
0.01​
OK​
0.00 kips​
0.18 kips​
1.34 kips-ft​
0.06​
N/A​
0​
0​
0.01​
OK​
0.00 kips​
0.18 kips​
1.34 kips-ft​
0.06​
N/A​
0​
0​
0.01​
OK​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.33​
N/A​
0.01​
0.01​
0.03​
OK​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.33​
N/A​
0.01​
0.01​
0.03​
OK​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.33​
N/A​
0.01​
0.01​
0.03​
OK​
0.00 kips​
0.56 kips​
7.19 kips-ft​
0.33​
N/A​
0.01​
0.01​
0.03​
OK​
0.00 kips​
0.14 kips​
1.01 kips-ft​
0.05​
N/A​
0​
0​
0.01​
OK​
0.00 kips​
0.14 kips​
1.01 kips-ft​
0.05​
N/A​
0​
0​
0.01​
OK​


Minimum Reinforcement

Longitudinal Reinforcement

According to 9.6.1.2 As shall be the larger of:

As,min=3fc′fybwdA_{s,min}=\frac{3\sqrt{f'_c}}{f_y}b_wd

As,min=200fybwdA_{s,min}=\frac{200}{f_y}b_wd

1.02 in²​
Check​
Ok​


Transversal Reinforcement

According to 9.6.3.4 If shear reinforcement is required... Av shall be the greater of:

Av,min=0.75fc′fybwA_{v,min}=\frac{0.75\sqrt{f'_c}}{f_y}b_w

As,min=50fybwA_{s,min}=\frac{50}{f_y}b_w


0.012 in²/in​
Ok​


Deflection Checks

The following deflections and deflection limits were calculated according to table 24.2.2 of ACI 318-19. The deflection limit can be changed in the table below according to the actual case for the current calculation.
Table 24.2.2 - ACI 318-19


1.50 in​
1.00 in​
Check​
4.10 in​
0.75 in​
Check​
Where "Check" means the beam isn't accomplishing the code requirements.

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