United StatesACI 318-19
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.
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
- Key Properties
- Design Criteria
- Longitudinal Reinforcement at Midspan
- Shear Reinforcement at Supports
- 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
Summary & Graphs
Access the full PDF file of the results of this calculation here: Task 1Method & scope
Design Criteria
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
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
1
Key Properties
- 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.
- 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.
2
Longitudinal Reinforcement at Midspan
Tension Bars vs. Compression BarsTension 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.)
- 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
- 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.
3
Shear Reinforcement at Supports
4
Loads
- 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.
US Concrete Beam: Overview
US Concrete Beam: Example
Common questions
What design method and standard does this calculator follow?
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.
What are the key inputs?
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.
What checks does it perform?
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.
How does ACI 318-19 shear differ from ACI 318-14?
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.
Does it support T-beams?
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.
Does this calculator support load linking with column and footing calculations?
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.
Next steps
Concrete Column Calculator to ACI 318-19 - Overview
Design rectangular concrete columns to ACI 318-19. Checks axial capacity, P-M interaction, biaxial bending and slender column moment magnification.