Shear design of a reinforced or prestressed concrete section to EN 1992-1-1 6.2: V_Rd,c, strut angle, links and spacings. Duplicate and check your beam.
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About this Shear Design of a General Concrete Cross-Section Calculator
This calculator designs a reinforced or prestressed concrete section for shear to EN 1992-1-1 Clauses 6.2.1 to 6.2.3. It works the resistance without shear reinforcement, chooses the flattest strut angle of the variable-inclination truss for which the struts do not crush, and sizes vertical or inclined shear reinforcement with its minimum ratio and maximum spacings from Clause 9.2.2.
- Beam and transfer girder designer size links for a deep member, letting the page pick the strut angle that minimises reinforcement without crushing the web.
- Bridge or precast engineer include axial compression or prestress through σ_cp and α_cw, and test inclined reinforcement.
- Reviewer check whether a section needs designed shear reinforcement at all, and whether the chosen strut angle is inside the national limits.
The nationally determined parameters are inputs, so the same page serves the recommended values or a national annex. It is an engineering-grade calculation on CalcTree that shows each expression as it is applied.
More info on Shear Design of a Concrete Cross-Section
Resistance without shear reinforcement
Expression (6.2a) gives V_Rd,c from the size factor k, the ratio of tension steel anchored beyond the section and the axial stress, with Expression (6.2b) and v_min from Expression (6.3N) as the lower bound. The size factor, reinforcement ratio and axial stress are capped as Clause 6.2.2(1) requires, and a pass here means no designed shear reinforcement is needed.
Choosing the strut angle
Expression (6.14) gives the crushing limit V_Rd,max for reinforcement at angle α. Setting V_Ed equal to V_Rd,max gives a quadratic in cot θ; the page takes the larger root and holds it between the lower and upper limits of cot θ. If no angle in the range works, cot θ falls to the lower limit and the crushing check fails, which tells you the web is too thin.
Shear reinforcement and spacing
Expression (6.13) gives the reinforcement per unit length, A_sw/s, for the chosen angle, and the minimum ratio of Expression (9.5N) is applied through ρ_w = A_sw / (s b_w sin α). The maximum longitudinal spacing follows Expression (9.6N) and the maximum transverse spacing of the legs Expression (9.8N). The reinforcement angle is checked against the range permitted by Clause 9.2.2(1).
Nationally determined parameters
C_Rd,c, k_1 and the upper and lower limits on cot θ are inputs alongside the partial factors and α_cc, so you can apply your national annex. The lever arm is entered as a ratio of the effective depth, with 0.9d being the approximation of Clause 6.2.3(1).
Common Calculation Errors to Avoid
- Counting steel that is not anchored ρ_l should include only tension steel anchored at least l_bd + d beyond the section considered.
- Adding V_Rd,c to the link resistance once V_Ed exceeds V_Rd,c, the variable-inclination truss carries the whole shear through the reinforcement; the concrete contribution is not added.
- Fixing θ without checking the struts a flat strut angle saves links but raises the strut stress; always confirm V_Ed is within V_Rd,max at the angle used.
- Applying α_cw to a member without compression α_cw is 1 for a member with no axial compression, and only rises with compressive stress per Expressions (6.11aN) to (6.11cN).
- Ignoring the minimum ratio the minimum of Expression (9.5N) can govern for lightly loaded sections, so the design area is the larger of the required and the minimum.
Engineering templates
Common calculators
Design guides
FAQs
What is the variable strut inclination method?
EN 1992-1-1 models a member with shear reinforcement as a truss whose concrete struts can be inclined at any angle θ within national limits. A flatter strut mobilises more links per unit length so less reinforcement is needed, but the strut stress rises, so the design is a balance between link area and web crushing.
How does the page pick cot θ?
It solves for the cot θ at which V_Ed just equals V_Rd,max from Expression (6.14), then caps it at the upper limit and floors it at the lower limit. That gives the flattest angle the web can take, which needs the least reinforcement.
Can I design inclined links or reinforcement?
Yes. Enter the angle of the shear reinforcement to the member axis. Expressions (6.13) and (6.14) are the general forms for reinforcement at angle α, and the page checks that α is within the range Clause 9.2.2(1) allows.
How are axial load and prestress handled?
Enter the mean compressive stress σ_cp and mark the member as prestressed or axially compressed. σ_cp raises V_Rd,c through k_1, capped at 0.2 f_cd, and sets α_cw for the crushing limit.
What is not covered?
The maximum effective reinforcement of Expression (6.12), the additional tensile force ΔF_td, loads close to supports, members with ducts and bent-up bars as shear reinforcement are outside the scope of this page.
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