Concrete Beam Shear Capacity Calculator

Introduction to one-way shear in reinforced concrete beams

A reinforced concrete beam that is perfectly safe in bending can still fail suddenly in shear. Diagonal tension cracks form in the web near the supports, where the shear force is largest, and once such a crack crosses the full depth of the section the beam loses its load path almost without warning. That is why every beam design ends with a one-way shear check: the designer works out the factored shear demand along the span and then confirms that the section, together with its transverse reinforcement, can deliver more strength than the demand at every point.

This page implements the standard ACI 318-19 approach for non-prestressed members with vertical stirrups. Shear strength is split into two additive parts. The concrete contribution V_c represents the shear transferred by the uncracked compression zone, by aggregate interlock across the crack faces, by residual tension in the crack and by dowel action of the longitudinal bars. The steel contribution V_s represents the stirrup legs that cross the diagonal crack and yield in tension, effectively stitching the crack shut. Their sum is the nominal strength V_n, and multiplying by the strength reduction factor φ gives the design strength φV_n that must equal or exceed the factored demand V_u.

What this beam shear calculator reports

• Concrete shear contribution V_c, in kN.
• Shear reinforcement contribution V_s, in kN.
• Nominal shear strength V_n = V_c + V_s, in kN.
• Design shear strength φV_n, in kN, with φ = 0.75 for shear.
• Utilisation against an optional factored demand V_u, expressed as a percentage of φV_n.
• Three code checks: the governing maximum stirrup spacing, the minimum area of shear reinforcement, and the upper limit on V_s that guards against web crushing.

Units. Everything is SI. Lengths and areas are entered in millimetres and square millimetres, strengths in megapascals, and every shear force is reported in kilonewtons. Because 1 MPa equals 1 N/mm², the raw products come out in newtons and the page divides by 1000 before display.

Inputs explained (SI units: mm, MPa, kN)

• Web width b_w (mm): the width of the web that resists shear. For a rectangular beam this is the full width; for a T-beam it is the stem width, not the flange width.
• Effective depth d (mm): distance from the extreme compression fibre to the centroid of the longitudinal tension reinforcement.
• Concrete compressive strength f′_c (MPa): the specified cylinder strength. ACI 318-19 limits the square root of f′_c used in shear equations to 8.3 MPa, which corresponds to about 69 MPa concrete; this page applies that cap and tells you when it bites.
• Lightweight factor λ: 1.00 for normalweight concrete, 0.85 for sand-lightweight and 0.75 for all-lightweight concrete, per ACI 318-19 Table 19.2.4.2.
• Shear reinforcement area A_v (mm²): total cross-sectional area of the stirrup legs crossing a potential diagonal crack within one spacing. A two-leg 10 mm stirrup gives A_v = 2 × 78.5 = 157 mm²; a two-leg 12 mm stirrup gives 226 mm².
• Stirrup spacing s (mm): centre-to-centre spacing measured along the span.
• Transverse steel yield strength f_yt (MPa): ACI 318-19 caps f_yt at 420 MPa for most shear reinforcement, and 550 MPa for deformed welded wire reinforcement.
• Strength reduction factor φ: 0.75 for shear and torsion in ACI 318-19 Table 21.2.1.
• Factored shear demand V_u (kN, optional): the shear at the section being checked, taken from your load combinations. Leave it blank if you only want capacity.

Formula: assembling φV_n from V_c and V_s

The concrete contribution for a non-prestressed member with at least the minimum area of shear reinforcement uses the simplified expression of ACI 318-19 Table 22.5.5.1, with f′_c in MPa and b_w and d in mm so the result is in newtons:

The stirrup contribution for vertical stirrups follows ACI 318-19 Section 22.5.8.5.3. It is the yield force of all legs crossing one spacing, multiplied by the number of spacings a 45-degree crack crosses, which is d divided by s:

The two contributions add, and the design check compares the reduced nominal strength with the factored demand at the section:

Two further inequalities keep the result physically meaningful. The first caps the stirrup contribution so that the concrete web cannot crush in diagonal compression before the stirrups yield (ACI 318-19 Section 22.5.1.2):

The second sets the minimum area of shear reinforcement wherever stirrups are required (ACI 318-19 Table 9.6.3.4), which prevents a brittle failure the instant the first diagonal crack forms:

ACI 318-19 detailing limits this page checks

Capacity arithmetic alone does not make a beam safe. Three detailing rules decide whether the arithmetic is even admissible, and the calculator evaluates all three every time you press the button.

• Maximum stirrup spacing. While V_s stays at or below 0.33√f′_c·b_w·d, spacing must not exceed the lesser of d/2 and 600 mm. Above that threshold the limit halves to the lesser of d/4 and 300 mm. The rule guarantees that any 45-degree crack is crossed by at least one stirrup, which is the assumption behind the V_s formula.
• Minimum shear reinforcement. Where V_u exceeds 0.5·φV_c, at least A_v,min must be provided. Beams with less than the minimum lose the reserve that lets the concrete term be counted on at all.
• Upper limit on V_s. If the required V_s exceeds 0.66√f′_c·b_w·d, no amount of extra transverse steel helps. The section must be made wider or deeper, or the concrete strength raised.

Worked example: a 300 x 500 mm beam with two-leg 10 mm stirrups

The calculator opens with this exact scenario, so you can press Compute Shear Strength and watch the numbers below appear.

• b_w = 300 mm, d = 500 mm
• f′_c = 30 MPa, λ = 1.00 (normalweight)
• A_v = 157 mm² (two legs of 10 mm bar), s = 150 mm
• f_yt = 420 MPa, φ = 0.75
• V_u = 200 kN at the critical section

Step 1 — concrete term. √30 = 5.477, so V_c = 0.17 × 1.00 × 5.477 × 300 × 500 = 139 669 N ≈ 139.7 kN.

Step 2 — stirrup term. V_s = (157 × 420 × 500) / 150 = 32 970 000 / 150 = 219 800 N ≈ 219.8 kN.

Step 3 — nominal and design strength. V_n = 139.7 + 219.8 = 359.5 kN, and φV_n = 0.75 × 359.5 = 269.6 kN.

Step 4 — demand check. V_u = 200 kN against φV_n = 269.6 kN gives a utilisation of 200 / 269.6 = 74.2 %, so the section passes with reserve.

Step 5 — detailing checks. The spacing threshold 0.33√f′_c·b_w·d = 271.1 kN is above V_s = 219.8 kN, so the governing maximum spacing is the lesser of d/2 = 250 mm and 600 mm, that is 250 mm; the provided 150 mm is comfortably inside it. The minimum steel requirement is max(0.062 × 5.477, 0.35) × 300 × 150 / 420 = 0.35 × 300 × 150 / 420 = 37.5 mm², well below the 157 mm² supplied. The V_s ceiling is 0.66 × 5.477 × 300 × 500 = 542.2 kN, so there is still room to tighten the stirrups if the load grows. All three checks pass.

How to use the concrete beam shear capacity calculator

1. Enter the web width b_w and effective depth d in millimetres. Use the stem width for T-beams and measure d to the centroid of the tension steel, not to the bottom of the beam.
2. Enter the specified concrete strength f′_c in MPa and pick the lightweight factor λ that matches the mix.
3. Enter the stirrup area A_v for all legs crossing one spacing, and the spacing s in millimetres. Enter zero for A_v if you want the plain-concrete capacity only.
4. Set the transverse yield strength f_yt and keep φ = 0.75 unless your governing code says otherwise.
5. Optionally enter the factored shear V_u at the section you are checking, usually taken a distance d from the face of the support for a member loaded on its top face.
6. Press Compute Shear Strength. The result panel lists V_c, V_s, V_n and φV_n, then the three detailing checks, and the chart stacks the concrete and stirrup contributions against the design strength line.
7. Press Reset to the worked example to return every field to the values used above.

Quick comparison: how each input moves the answer

Limitations and assumptions behind this shear estimate

• Simplified V_c expression. ACI 318-19 also offers detailed equations that include the longitudinal reinforcement ratio, the axial force and a size-effect modifier λ_s for deep members without minimum stirrups. Those can give a noticeably lower V_c for large, lightly reinforced sections.
• Vertical stirrups only. Inclined stirrups and bent-up bars use a different V_s expression that includes the sine and cosine of the bar angle.
• Slender beams only. Deep beams, corbels, brackets, ledges and other disturbed regions are governed by strut-and-tie modelling, not by this sectional method.
• No axial load, prestress or torsion. Axial compression raises the concrete term, axial tension lowers it, and torsion interacts with shear through a combined stress check that is not performed here.
• Anchorage assumed. The V_s formula presumes stirrups are closed or properly hooked around longitudinal bars so they can develop their yield strength across the crack.
• Demand is your responsibility. The calculator does not perform structural analysis. Factored shear must come from your own load combinations, and the critical section, support conditions and any concentrated loads near supports must be judged by the engineer.
• Not a substitute for the code. Use this page for preliminary sizing, checking, teaching and sanity checks. Final designs must be verified against the full text of the governing standard and sealed by a qualified engineer.

Practise shear design in the Stirrup Lab game below

Underneath the calculator sits Stirrup Lab, an interactive beam elevation that uses exactly the equations above. A factored shear envelope sweeps down from each support to zero at midspan, the concrete term φV_c appears as a flat base band, and every stirrup zone you tighten stacks φV_s on top of it. Wherever demand pokes above capacity a diagonal crack propagates through the web, so the feedback is immediate and physical. The goal is coverage everywhere with the least steel, which is exactly the trade-off a real shear design makes: tight stirrups near the supports, wider spacing towards midspan, and bare concrete only where V_u drops below half of φV_c.

Frequently asked questions about beam shear capacity

Sources verified against: the concrete term V_c = 0.17λ√f′_c·b_w·d (Table 22.5.5.1), the stirrup term V_s = A_vf_ytd/s (Section 22.5.8.5.3), the V_s ceiling 0.66√f′_c·b_w·d (Section 22.5.1.2), the √f′_c ≤ 8.3 MPa limit (Section 22.5.3.1), minimum shear reinforcement (Table 9.6.3.4), maximum stirrup spacing (Table 9.7.6.2.2), the lightweight factor λ (Table 19.2.4.2) and φ = 0.75 for shear (Table 21.2.1) all follow ACI 318-19, Building Code Requirements for Structural Concrete, published by the American Concrete Institute. For the European alternative treatment of shear by the variable-strut-inclination method, see EN 1992-1-1 (Eurocode 2), Section 6.2. This tool is a preliminary estimator and is not a substitute for the full code text or for engineering judgement.