> ## Documentation Index
> Fetch the complete documentation index at: https://calcs.com/docs/llms.txt
> Use this file to discover all available pages before exploring further.

# Design a Concrete Beam to ACI 318-19

> Design rectangular concrete beams and T-beams to ACI 318-19 across unlimited spans. Checks flexure, shear, and short- and long-term deflection.

<div className="calc-details not-prose">
  <div className="calc-details-item">
    <div className="calc-details-chips"><span className="calc-chip calc-chip--region">United States</span><span className="calc-chip calc-chip--primary">ACI 318-19</span></div>
    <div className="calc-details-head"><span className="calc-card-icon">    <img src="https://mintcdn.com/clearcalcs/32krV4BnKnXD1TTf/images/calculator-icons/c13d03d78d6f21b804f0743278041598207e42bb8452434e80915ba312b22d24.svg?fit=max&auto=format&n=32krV4BnKnXD1TTf&q=85&s=9c912fd2614c8216c945f384ac511ed8" alt="" width="24" height="24" loading="lazy" data-path="images/calculator-icons/c13d03d78d6f21b804f0743278041598207e42bb8452434e80915ba312b22d24.svg" /></span><p className="calc-details-name">Concrete Beam</p><a className="calc-details-run" href="https://app.calcs.com/new/sheet/concreteBeamRectangularUSAACI318-19">Run the calc</a></div>
  </div>
</div>

<div className="calc-answer">
  Design rectangular concrete beams to ACI 318-19 with customizable top and bottom reinforcement across unlimited spans. Checks include flexural strength, shear capacity, and short- and long-term deflection. Supports T-beams. Beam reactions link to connected column and footing calculations so changes propagate automatically.
</div>

The Calcs.com Concrete Beam Calculator allows users to design concrete beams by specifying the desired load cases and dimensions of the beam. In this article, each section of the calculator will be explained followed by a few worked examples.

The Rectangular Concrete Beam Calculator has 4 main sections

1. Key Properties
2. Design Criteria
3. Longitudinal Reinforcement at Midspan
4. Shear Reinforcement at Supports
5. Loads

## Worked example

#### Task 1

Design a concrete beam with the following characteristics

* Dimensions: 30 feet in length, 24x12 in cross-section
* Pinned supports at each end
* Concrete cover of 1.5 in
* Normal-weight concrete with a strength of 3000 psi
* Reinforcement strength of 50 ksi
* 2 tension bars of size #8 at a depth of 20 in
* 2 compression bars of size #8
* Stirrups of size #3 with 4 legs per bundle, and a spacing of 4 in at supports
* An end-to-end distributed load: 10 psf dead load and 40 psf live load with a tributary width of 5 in
* Include self-weight
* Assume a sustained load duration factor of 5+ years

#### Method

<img src="https://mintcdn.com/clearcalcs/wCKMGQrVqWo51C47/images/migrated/b07dfe4af195-file-xxsl72pkyk.png?fit=max&auto=format&n=wCKMGQrVqWo51C47&q=85&s=ac2bb586ab727f15d9a65209bb5c55db" alt="" width="761" height="628" data-path="images/migrated/b07dfe4af195-file-xxsl72pkyk.png" />

<img src="https://mintcdn.com/clearcalcs/6PuU-K_D_MascHz6/images/migrated/ceddddfb2912-file-t8oij0qyfj.png?fit=max&auto=format&n=6PuU-K_D_MascHz6&q=85&s=5e9b9ded3e83a65fa6f0330e8710800b" alt="" width="691" height="263" data-path="images/migrated/ceddddfb2912-file-t8oij0qyfj.png" />

<img src="https://mintcdn.com/clearcalcs/XO7fzDjaQ7IYQ3qi/images/migrated/0fd3d97a129b-file-gkjsotchxa.png?fit=max&auto=format&n=XO7fzDjaQ7IYQ3qi&q=85&s=cb6da999cb22e20d9b8e98ba7bc20d9a" alt="" width="769" height="421" data-path="images/migrated/0fd3d97a129b-file-gkjsotchxa.png" />

<img src="https://mintcdn.com/clearcalcs/XO7fzDjaQ7IYQ3qi/images/migrated/0ebc52308cd2-file-f9ahpvm4vl.png?fit=max&auto=format&n=XO7fzDjaQ7IYQ3qi&q=85&s=eff4bc073609bbdaad490913c7099389" alt="" width="746" height="274" data-path="images/migrated/0ebc52308cd2-file-f9ahpvm4vl.png" />

<img src="https://mintcdn.com/clearcalcs/-3TA4BOzcQ3BrOZT/images/migrated/94babe1cc320-file-w9alxy2xxo.png?fit=max&auto=format&n=-3TA4BOzcQ3BrOZT&q=85&s=02ef38335feb3b9fa7a143926afcc602" alt="" width="661" height="391" data-path="images/migrated/94babe1cc320-file-w9alxy2xxo.png" />

<img src="https://mintcdn.com/clearcalcs/wCKMGQrVqWo51C47/images/migrated/a2e55af5a1c7-file-gadjigynn6.png?fit=max&auto=format&n=wCKMGQrVqWo51C47&q=85&s=146766f9cced1508e5c646dac4dc3993" alt="" width="721" height="203" data-path="images/migrated/a2e55af5a1c7-file-gadjigynn6.png" />

#### Summary & Graphs

Access the full PDF file of the results of this calculation here: [Task 1](https://s3.amazonaws.com/helpscout.net/docs/assets/5c09df402c7d3a31944ed720/attachments/5ff5137cfd168b7773531eac/US-Concrete-Beam---B1.pdf)

## Method & scope

| Property         | Detail                                                            |
| ---------------- | ----------------------------------------------------------------- |
| Design standards | ACI 318-19                                                        |
| Regions          | United States                                                     |
| What it checks   | Flexural capacity, Shear capacity (ACI 318-19 update), Deflection |

#### Design Criteria

<img src="https://mintcdn.com/clearcalcs/lchEzA4h00Mzlgpc/images/migrated/f88269e22d58-file-tljczm5vub.png?fit=max&auto=format&n=lchEzA4h00Mzlgpc&q=85&s=c9ed5c8a1da1216c12fb108a41c7ec7f" alt="" width="581" height="246" data-path="images/migrated/f88269e22d58-file-tljczm5vub.png" />

##### A. Absolute Deflection Limit

The hard maximum deflection allowed for the beam, regardless of span length. Normally, your local building code will dictate this. For the IBC, Table 1604.3 provides the limits.

##### B. Live/Short-Term Deflection Limit

Calculated independently for each span. For cantilevers, “L” is taken to be twice the length of the cantilever. Normally, your local building code will dictate this limit. For the IBC 2018, Table 1604.3 provides the limits.

##### C. Long-Term Deflection Limit

Long term deflection limit, including creep effects etc.

##### D. Simplified DL+LL Deflection Limit

Calculated independently for each span. For cantilevers, “L” is taken to be twice the length of the cantilever. Normally, your local building code will dictate this limit. For the IBC, Table 1604.3 provides the limits.

#### See the exact clause

<Tip>
  Every check in this calculator links back to its governing clause in ACI 318-14. Open the **Formula Reference** panel on any result and select the clause reference to read it. See [Viewing Clauses from Inside a Calculator](/docs/running-calculations/standards-and-codes/viewing-clauses-from-inside-calculator).
</Tip>

#### Calculation method

The Concrete Beam (ACI 318-19) calculator designs rectangular and T-beam sections per ACI 318-19 using LRFD. The same fundamental approach as the ACI 318-14 version applies, with updated shear provisions.

##### Flexural capacity

Positive and negative moment capacities **φMn** use the ACI rectangular stress block at εcu = 0.003. For T-beams, the effective flange width per ACI 318-19 Cl 6.3.2.1 engages the slab in compression for positive moments, increasing Mn relative to a rectangular section of the same web width.

**Mn = A\_s × fy × (d, a/2)** for singly reinforced rectangular sections

φ = 0.90 for tension-controlled sections (net strain εt ≥ 0.005).

##### Shear capacity (ACI 318-19 update)

ACI 318-19 introduced a table-based Vc (Table 22.5.5.1) that depends on three parameters: longitudinal reinforcement ratio ρw, the ratio of factored moment to shear at the critical section (Mu/Vud), and axial load Nu/Ag. This replaces the simpler simplified formula of 318-14 and can give different (higher or lower) Vc depending on the beam's reinforcement and loading.

**φVn = φ(Vc + Vs)** where Vs = Av × fy × d / s, and φ = 0.75.

The lightweight concrete modification factor λ is applied to Vc per ACI 318-19 Table 19.2.4.2.

##### Deflection

Cracked-section effective moment of inertia **Ie = Ig × (Mcr/Ma)³ + Icr × \[1, (Mcr/Ma)³]** is used for all three deflection checks: short-term, long-term (with creep/shrinkage multiplier), and simplified DL+(LL or SL). Results are checked against user-defined L/n deflection limits.

## How to use it

<Steps>
  <Step title="Key Properties">
    <img src="https://mintcdn.com/clearcalcs/E_1kb1vSSHohKQJH/images/migrated/55e3d073a904-file-gneoty9pgu.png?fit=max&auto=format&n=E_1kb1vSSHohKQJH&q=85&s=6f4647037bff6c03f2a27f3231e46601" alt="" width="595" height="584" data-path="images/migrated/55e3d073a904-file-gneoty9pgu.png" />

    **A. Beam Dimensions**

    The figure given below illustrates the three parameters that need to be specified in this section.

    <img src="https://mintcdn.com/clearcalcs/wCKMGQrVqWo51C47/images/migrated/b525454474c8-file-jg5cqcelhx.png?fit=max&auto=format&n=wCKMGQrVqWo51C47&q=85&s=a5af18c3597f962b0f764067bbe2a059" alt="" width="377" height="241" data-path="images/migrated/b525454474c8-file-jg5cqcelhx.png" />

    * Cross-section height (h) must be specified in inches.
    * Cross-section width (b) must be specified in inches.
    * Total length of the beam (L) must be specified in feet.

    **B. Concrete Strength**

    The strength of the concrete being used must be specified in Pounds per Square Inch (psi). Concrete strength cannot be less than 2500psi.

    **C. Concrete Weight Classification**

    The concrete weight classification needs to be selected from the drop-down menu shown below.

    <img src="https://mintcdn.com/clearcalcs/E_1kb1vSSHohKQJH/images/migrated/5d50f05fdf2b-file-jwbuenkdck.png?fit=max&auto=format&n=E_1kb1vSSHohKQJH&q=85&s=a1324602380655aeb1d55e3da0ca7f52" alt="" width="592" height="147" data-path="images/migrated/5d50f05fdf2b-file-jwbuenkdck.png" />

    Note that one can select 'custom' and input the concrete density and a lightweight concrete factor to create their own concrete weight classification.

    **D. Reinforcement Strength**

    Strength is limited to 80 ksi for regular columns, and 60 ksi in special seismic systems. This requirement is imposed to ensure steel yields before concrete crushes in the column.

    **E. Concrete Cover**

    Distance from concrete surface to edge of ties. Minimum cover: 1-1/2” for unexposed members, 2” for exposed members with bars >= #6, and 3” for any concrete cast against the ground.

    <img src="https://mintcdn.com/clearcalcs/5zVEHycKpm3vA7at/images/migrated/3d7360a14a87-file-pe9vgygwkk.png?fit=max&auto=format&n=5zVEHycKpm3vA7at&q=85&s=accc4cbc8f32b98ea096eb13d5b15a58" alt="" width="232" height="138" data-path="images/migrated/3d7360a14a87-file-pe9vgygwkk.png" />

    **F. Position of Supports from Left**

    <img src="https://mintcdn.com/clearcalcs/0BKfHfJWdoXOtU8o/images/migrated/e22f13987895-file-gnxhlvrncw.png?fit=max&auto=format&n=0BKfHfJWdoXOtU8o&q=85&s=6137ee3e88cd4cc0b46b68e8cbeaae07" alt="" width="570" height="134" data-path="images/migrated/e22f13987895-file-gnxhlvrncw.png" />

    For this section, the above table must be filled out as follows:

    * In the first column, the support type must be selected from the drop-down menu
    * In the second column, the location of the support must be specified in feet as measured from the left of the beam.
  </Step>

  <Step title="Longitudinal Reinforcement at Midspan">
    **<img src="https://mintcdn.com/clearcalcs/0BKfHfJWdoXOtU8o/images/migrated/e1624d064497-file-kpyintglll.png?fit=max&auto=format&n=0BKfHfJWdoXOtU8o&q=85&s=5d9b47d8828beaa8b082521751ee42e0" alt="" width="598" height="365" data-path="images/migrated/e1624d064497-file-kpyintglll.png" />Tension Bars vs. Compression Bars**

    Tension bars are the reinforcement bars which are in tension when the concrete beam is subjected to vertical loads. These are located towards the bottom of the cross-section (indicated in green in the figure below). Compression bars are the reinforcement bars which are in compression when the concrete beam is subjected to vertical loads. These are located towards the top of the cross-section (indicated in blue in the figure below.)

    <img src="https://mintcdn.com/clearcalcs/5zVEHycKpm3vA7at/images/migrated/3b3a3b10381a-file-gvs3ovud1h.png?fit=max&auto=format&n=5zVEHycKpm3vA7at&q=85&s=8b68f710d1bd257a933afc21809091ff" alt="" width="121" height="161" data-path="images/migrated/3b3a3b10381a-file-gvs3ovud1h.png" />

    **A. Tension (Bottom) Bars**

    This section allows the user to add rows of tension bars using the following table. Each row in the table corresponds to a new row of tension bars.

    <img src="https://mintcdn.com/clearcalcs/wCKMGQrVqWo51C47/images/migrated/addafc6ed7f3-file-av2qwefgen.png?fit=max&auto=format&n=wCKMGQrVqWo51C47&q=85&s=4bee92b8a07442a80ba30539af698b6a" alt="" width="579" height="132" data-path="images/migrated/addafc6ed7f3-file-av2qwefgen.png" />

    * In the second column, the number of bars in the row must be specified.
    * In the third column, the size of the bars must be selected from a drop-down menu which has imperial sizes from #2-#18. For further information regarding Imperial dimensions of rebars visit: [https://www.engineeringtoolbox.com/reinforcing-bar-us-imperial-d\_1482.html](https://www.engineeringtoolbox.com/reinforcing-bar-us-imperial-d_1482.html)
    * In the fifth column, the depth corresponding to each row must be specified. Depth is the distance from the row to the top surface of the concrete beam.

    **B. Number of Compression (Top) Bars**

    The number of compression bars must be specified. The default has been set to two, to provide anchors for stirrups.

    **C. Compression Reinforcement Size**

    The size of the compression bars must be selected from a drop-down menu which has imperial sizes from #2-#18. For further information regarding Imperial dimensions of rebars visit: [https://www.engineeringtoolbox.com/reinforcing-bar-us-imperial-d\_1482.html](https://www.engineeringtoolbox.com/reinforcing-bar-us-imperial-d_1482.html)
  </Step>

  <Step title="Shear Reinforcement at Supports">
    <img src="https://mintcdn.com/clearcalcs/wCKMGQrVqWo51C47/images/migrated/b02f17630f87-file-rvn3wlusae.png?fit=max&auto=format&n=wCKMGQrVqWo51C47&q=85&s=2805dabe4f8d2dffbb4aa44bc82bd4cb" alt="" width="586" height="230" data-path="images/migrated/b02f17630f87-file-rvn3wlusae.png" />

    **A. Include Stirrups?**

    A Stirrup is a closed loop of reinforcement bar, which holds the main reinforcement bars in place. In this section, the user can specify whether or not to include stirrups in their design. Stirrups are required if more than half the concrete shear strength is utilized.

    **B. Stirrup Size**

    The size of stirrups must be selected from a drop-down menu which has imperial sizes from #2-#18. For further information regarding Imperial dimensions of rebars visit: [https://www.engineeringtoolbox.com/reinforcing-bar-us-imperial-d\_1482.html](https://www.engineeringtoolbox.com/reinforcing-bar-us-imperial-d_1482.html)

    **C. Number of Legs per Stirrup Bundle**

    The number of rebars per loop must be specified. Enter 0 if no stirrups are present. The default is set to two.

    **D. Stirrup Spacing at Supports**

    Spacing between stirrups at the supports. Note that as shear will typically be much lower at midspan under a UDL, this spacing may change. This sheet is intended to provide basic design info only, but the shear force diagram may be used to check additional spacings.
  </Step>

  <Step title="Loads">
    <img src="https://mintcdn.com/clearcalcs/wCKMGQrVqWo51C47/images/migrated/b0c2278b317d-file-necoafjh5i.png?fit=max&auto=format&n=wCKMGQrVqWo51C47&q=85&s=7d40af47692cd6cd015e5890feb82553" alt="" width="590" height="453" data-path="images/migrated/b0c2278b317d-file-necoafjh5i.png" />

    **A. Distributed Loads**

    The table in this section prompts the user to input distributed loads. For further instructions on how to fill out this table, check out our help article on how to input distributed loads.

    **B. Point & Moment Loads**

    In this section, the table must be filled out as follows:

    * In column 1, the user can name the load as they prefer.
    * In the second column, the location of the load must be specified in feet as measured from the left end of the beam.
    * The following table will appear when one clicks on the third column.

          <img src="https://mintcdn.com/clearcalcs/XO7fzDjaQ7IYQ3qi/images/migrated/10b404632cd0-file-lyhunwunon.png?fit=max&auto=format&n=XO7fzDjaQ7IYQ3qi&q=85&s=4458c5a45ec17165d2af7cf3d92cf76c" alt="" width="641" height="302" data-path="images/migrated/10b404632cd0-file-lyhunwunon.png" />

    The load type must be selected from the drop-down menu given. If it is a vertical load, its magnitude must be specified in pounds (lb). If it is a moment load, the magnitude must be specified in Pounds feet (lb.ft).

    **C. Include Self-Weight?**

    The user can choose whether or not they include the self-weight of the beam in their calculations. The calculator is set to include the self-weight by default unless the user specifies otherwise.

    **D. Use Reduced Companion Live Load?**

    The user can select whether reduced companion live load is used in their calculations or not. For live loads under 100 psf which are not in a garage or a place of public assembly, a 50% reduction in the live load is allowed when it is used as a companion load.

    **E. Sustained Duration Factor**

    A factor which accounts for the effects of creep in concrete. In most structures, the design life should conservatively remain at 5+ years. Sustained duration factor must be selected from the drop-down menu given below.

    <img src="https://mintcdn.com/clearcalcs/E_1kb1vSSHohKQJH/images/migrated/5895cb52a290-file-6ntaztx4kv.png?fit=max&auto=format&n=E_1kb1vSSHohKQJH&q=85&s=6944046925d8ea10369f9b9e557a3814" alt="" width="593" height="241" data-path="images/migrated/5895cb52a290-file-6ntaztx4kv.png" />
  </Step>
</Steps>

#### US Concrete Beam: Overview

<iframe src="https://www.youtube.com/embed/1w_h2DCyj_w" title="US Concrete Beam: Overview" className="w-full h-96 rounded-xl" allowFullScreen allow="autoplay; fullscreen" />

#### US Concrete Beam: Example

<iframe src="https://www.youtube.com/embed/ERJPo6hASFc" title="US Concrete Beam: Example" className="w-full h-96 rounded-xl" allowFullScreen allow="autoplay; fullscreen" />

<iframe src="https://fast.wistia.net/embed/iframe/ivzzwejnt3?videoFoam=true" title="Concrete Beam video walkthrough" className="w-full h-96 rounded-xl" allowFullScreen allow="autoplay; fullscreen" />

## Common questions

<AccordionGroup>
  <Accordion title="What design method and standard does this calculator follow?">
    Strength Design Method (LRFD) per ACI 318-19. Factored loads from ASCE 7 LRFD combinations are compared to reduced nominal capacities using ACI 318-19 strength reduction factors.
  </Accordion>

  <Accordion title="What are the key inputs?">
    Cross-section dimensions (bw and h, in inches), section type (rectangular or T-beam), flange width for T-beams, concrete compressive strength f'c (psi, minimum 2500 psi), concrete weight class (normalweight or lightweight), reinforcement yield strength fy (40-80 ksi), clear cover, positive and negative longitudinal reinforcement (bar size and count), stirrup size and spacing, span geometry, supports, and factored loads by type.
  </Accordion>

  <Accordion title="What checks does it perform?">
    Positive flexural capacity φMn+ ≥ Mu+, negative flexural capacity φMn- ≥ Mu-, shear capacity φVn ≥ Vu (ACI 318-19 table-based Vc plus stirrup Vs), short-term deflection, long-term deflection, and simplified DL+(LL or SL) deflection. Minimum cover and bar spacing requirements are also flagged.
  </Accordion>

  <Accordion title="How does ACI 318-19 shear differ from ACI 318-14?">
    ACI 318-19 introduced a more precise table-based Vc formula (Table 22.5.5.1) that is a function of the longitudinal reinforcement ratio, axial load, and the moment-to-shear ratio at the critical section. The 318-14 simplified Vc formula is more conservative for lightly reinforced sections; 318-19 can give higher or lower Vc depending on the section properties.
  </Accordion>

  <Accordion title="Does it support T-beams?">
    Yes, a T-beam option is available. When selected, the effective flange width is computed per ACI 318-19 Cl 6.3.2.1 based on span length and slab thickness, increasing the positive moment capacity by engaging the compression flange.
  </Accordion>

  <Accordion title="Does this calculator support load linking with column and footing calculations?">
    Yes, beam support reactions link directly to connected column and footing calculations in the same project. When any load or geometry changes, all linked calculations update automatically.
  </Accordion>
</AccordionGroup>

## Next steps

<CardGroup cols={2}>
  <Card title="Concrete Column Calculator to ACI 318-19 - Overview" icon="calculator" href="/docs/calculators/us/columns/concreteColumnUSAACI318-19">
    Design rectangular concrete columns to ACI 318-19. Checks axial capacity, P-M interaction, biaxial bending and slender column moment magnification.
  </Card>
</CardGroup>
