Shear design decides how a reinforced concrete beam resists the diagonal tension that forms near the supports. Flexure sizes the longitudinal steel, but the shear reinforcement keeps the beam from splitting along inclined cracks, and the shear check usually governs the web thickness and the link spacing. Eurocode 2 uses the variable strut inclination method, where the designer chooses the angle of the concrete compression strut and sizes the links to match.
The worked example below follows the Eurocode 2 procedure end to end. The beam has an effective depth of 600 millimeters and a width of 300 millimeters. The ultimate design shear force at the face of the support is 800 kilonewtons, and the design shear at a distance d from the support face is 700 kilonewtons. The concrete cylinder strength fck is 30 newtons per square millimeter, and the steel yield strength fyk is 460 newtons per square millimeter. The same sequence applies to any rectangular section, while the equivalent member in structural steel design is checked through a different set of buckling and connection rules.
The Design Inputs and the Critical Section
The example starts with a rectangular section, but the method extends to T and L beams by using the effective flange width where it applies. Table 1 summarizes the inputs used in the calculation.
| Parameter | Symbol | Value |
|---|---|---|
| Beam width | bw | 300 mm |
| Effective depth | d | 600 mm |
| Design shear at the support face | VEd | 800 kN |
| Design shear at distance d | VEd | 700 kN |
| Concrete cylinder strength | fck | 30 N/mm² |
| Steel yield strength | fyk | 460 N/mm² |
Why the section is checked at distance d
The shear force at the face of the support is the largest value, but the critical section for link design sits at a distance d from the support face. Inside that region, part of the shear transfers directly into the support through the arch action of the compression strut, so the code allows the design shear to be taken at distance d. The section at the support face is still checked to confirm that the concrete strut itself does not crush.
Coordinate the section with the rest of the frame
Beam sizes and spans are settled while the structural grid is being laid out, and they interact with the architectural design and building envelope decisions that fix floor-to-floor heights and facade depths. A beam depth chosen for shear capacity can reduce the number of links, but it adds weight and eats into the storey height, so the shear check usually runs alongside the architectural coordination.
Checking the Maximum Shear Capacity
Before any link is sized, the section must prove it can carry the applied shear without crushing the concrete strut. Eurocode 2 expresses that capacity as VRd,max, the maximum design shear resistance of the member, calculated for the chosen strut angle. The 0.36 coefficient and the (1 minus fck over 250) term together account for the strength of the concrete strut under biaxial compression. The formula uses theta, the angle between the compression strut and the longitudinal axis of the beam: VRd,max equals 0.36 bw d (1 minus fck over 250) fck, all divided by (cot theta plus tan theta).
Capacity at a 22 degree strut angle
With theta equal to 22 degrees, the term 0.36 divided by (cot 22 plus tan 22) collapses to 0.124, which simplifies the formula to 0.124 bw d (1 minus fck over 250) fck. Substituting the values gives 0.124 times 300 times 600 times (1 minus 30 over 250) times 30, which equals 589.25 kilonewtons. That value falls below the applied shear of 700 kilonewtons, so the section cannot use a 22 degree strut.
Capacity at 45 degrees
At theta equal to 45 degrees, cot theta plus tan theta equals 2, so the coefficient becomes 0.18. The capacity rises to 0.18 times 300 times 600 times (1 minus 30 over 250) times 30, which equals 855.36 kilonewtons. This exceeds the 800 kilonewton force at the support face, so a strut angle between 22 and 45 degrees works and the maximum shear check passes.
The maximum shear check follows four steps:
- Calculate VRd,max with a 22 degree strut angle.
- Compare the result with the applied shear at distance d.
- If the capacity falls short, repeat the calculation with a 45 degree strut angle.
- Confirm that the 45 degree capacity covers the shear at the support face.
The angle search is the repetitive part of the procedure, and it is a good place to use a calculation aid. A doubly reinforced beam spreadsheet that covers flexure and shear lets the engineer test different strut angles and link sizes in seconds instead of repeating the algebra by hand for every span.
Finding the Strut Angle
With the capacity bounds established, the required strut angle follows from the applied shear at distance d. The formula assumes that the concrete carries the diagonal compression and the links carry the vertical tension, which is the basis of the truss model behind the method. The angle theta equals 0.5 times the inverse sine of VEd divided by 0.18 bw d (1 minus fck over 250) fck, which is the same as 0.5 times the inverse sine of VEd over VRd,max at 45 degrees. The result is capped at 45 degrees.
Working through the numbers
Substituting 700 kilonewtons for VEd and 855.36 kilonewtons for VRd,max at 45 degrees gives theta equal to 0.5 times the inverse sine of 700 divided by 855.36. The inverse sine of 0.818 is 55.0 degrees, and half of that is 27.5 degrees. The cotangent of 27.5 degrees is 1.92, which feeds into the link formula in the next step.
Where the angle fits inside the code limits
Eurocode 2 restricts the strut angle to the range between 21.8 and 45 degrees, and the 27.5 degree result sits comfortably inside that band. A steeper angle would reduce the link demand slightly but raise the force in the concrete strut, so most designers take the angle straight from the formula and round it to the nearest half degree. The strut angle interacts with the wider checks in reinforced concrete design, where flexural analysis, shear, and torsion are all handled for the same member.
Sizing the Shear Links
The required area of shear reinforcement per unit length, Asw over s, is VEd divided by 0.78 d fyk cot theta. The 0.78 factor in the denominator combines the lever arm of the internal forces with the cotangent of the strut angle and the partial safety factor for the steel. With VEd equal to 700 kilonewtons, d equal to 600 millimeters, fyk equal to 460 newtons per square millimeter, and cot theta equal to 1.92, the calculation gives 700,000 divided by (0.78 times 600 times 460 times 1.92), which equals 1.69 square millimeters per millimeter. The links must supply at least that much steel on every millimeter of the beam.
Converting the ratio into a bar spacing
A two-legged link provides twice the area of a single bar. For T12 bars, each bar has an area of 113 square millimeters, so two legs give 226 square millimeters. The spacing comes from 226 divided by 1.69, which equals 134 millimeters, so T12 links at 125 millimeters center to center satisfy the demand. T10 bars give two legs of 157 square millimeters and a required spacing of about 90 millimeters, which is tighter and uses more steel per meter.
| Link size | Area of two legs (mm²) | Required spacing (mm) | Adopted spacing |
|---|---|---|---|
| T8 | 101 | 60 | 50 mm |
| T10 | 157 | 93 | 90 mm |
| T12 | 226 | 134 | 125 mm |
Checking the spacing against the code limits
The adopted spacing must also satisfy the maximum spacing rules in Eurocode 2. For vertical links, the longitudinal spacing must not exceed 0.75 times the effective depth, which is 450 millimeters here, and the transverse spacing of the legs must not exceed 600 millimeters. The T12 links at 125 millimeters sit well inside both limits, so the detailing is acceptable. The link layout also interacts with the vertical members at the ends of the span, because shear walls and columns transfer the reactions down to the foundation and the end links are often thickened where the beam frames into those supports.
Four values are checked before a link layout is adopted:
- The required Asw over s from the applied shear and the strut angle.
- The bar size and number of legs that satisfy the ratio.
- The maximum longitudinal spacing of 0.75 times d.
- The maximum transverse spacing of 600 millimeters between legs.
Minimum Reinforcement and Practical Detailing
A beam with no shear demand still needs a minimum quantity of links to hold the cage together and control cracking. Eurocode 2 requires rho w,min equal to 0.08 times the square root of fck divided by fyk. With fck at 30 and fyk at 460, that gives 0.08 times 5.48 divided by 460, which equals 0.00095. The minimum Asw over s is rho w,min times bw, or 0.00095 times 300, which equals 0.29 square millimeters per millimeter. The designed value of 1.69 is close to six times that, so the minimum does not govern.
Detailing the links on the drawing
The links should be drawn as closed stirrups with a 135 degree bend at the ends, anchored inside the compression zone, with the number of legs and the spacing marked for each zone of the span. Where the shear force varies along the length, the spacing steps down near the supports and opens up toward midspan, which keeps the steel quantity close to the demand. The way the member is drawn and scheduled is part of the evolution of beam design, where detailing practice has moved from prescriptive tables toward performance-based rules.
Extending the check to the support region
The face-of-support shear of 800 kilonewtons was verified against VRd,max, and the links were sized for the 700 kilonewton value at distance d. Many designers extend the first links right up to the face of the support and start the full spacing pattern from there, which covers the tension that develops near the bearing without adding much steel.
The worked example produces a clear answer: the 300 by 600 millimeter beam needs T12 links at 125 millimeters center to center, with the strut angle set at 27.5 degrees. Running the same sequence of maximum shear check, angle calculation, and link sizing on every span is the fastest way to keep reinforced concrete beam design consistent across a project, and it catches weak webs before they reach the site.