Learn: Shear reinforcement resistance
Vertical stirrups resist shear as part of a truss-like mechanism with inclined concrete compression struts. This equation estimates the stirrup contribution using the amount of steel per unit length and a specified strut angle.
What the formula is saying
Asw/s is stirrup area per longitudinal spacing. Multiplying by z, fywd and cot θ gives the shear carried by the idealized vertical reinforcement; cot θ means 1/tan θ.
Read the symbols in plain language
- Asw
- Shear steel area per spacing set
Area of the specified participating steel, not automatically the gross member area. Respect whether the equation asks for bars, bolt threads or stirrup legs.
mm²Square millimetres measure area; 1 mm² = 10⁻⁶ m².
- s
- Spacing
Spacing. Dividing link area by spacing expresses how much vertical steel is present along the member.
mmMillimetres measure length; 1000 mm = 1 m.
- z
- Lever arm
Perpendicular distance between the tensile and compressive resultants that form the resisting internal couple.
mmMillimetres measure length; 1000 mm = 1 m.
- fywd
- Design shear steel strength
Steel design stress after the relevant material factor; multiplying this by steel area gives the corresponding force.
N/mm²One N/mm² equals one MPa.
- θ
- Strut angle
Angle between the concrete compression strut and the longitudinal member axis; the calculator converts degrees for trigonometry.
degAngles are entered in degrees; multiply by π/180 for trigonometric calculations in radians.
- VRd,s
- Result to find
Shear reinforcement resistance. Convert the force from newtons without changing the underlying resistance model.
kN
Sort out the units first
Asw is mm², s and z are mm, and fywd is N/mm². The intermediate result is N and is divided by 1000 for kN. θ is entered in degrees and converted to radians for the tangent calculation.
Assumptions before calculating
Use the first-generation EC2 teaching model and the supplied design coefficients. Material strengths, geometry, load situation and coefficients must be mutually compatible; selecting them from the adopted code and National Annex is outside this calculation.
This is a first-generation Eurocode teaching relationship or an explicitly simplified coefficient calculation. The numbers supplied here are exercise data, not a recommendation for any country. Check the adopted edition, relevant clause, National Annex, applicability conditions and all other limit states before any real design.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find VRd,s and explain the result in the stated output unit.
- Asw · Shear steel area per spacing set
- 200 mm²
- s · Spacing
- 200 mm
- z · Lever arm
- 500 mm
- fywd · Design shear steel strength
- 435 N/mm²
- θ · Strut angle
- 45 deg
Find steel area per unit length
Dividing link area by spacing expresses how much vertical steel is present along the member.
(200) ÷ (200) = 1 mm²/mmCalculate the strut-angle cotangent
Convert degrees to radians before taking the tangent, then take its reciprocal.
1 ÷ tan((45) × π ÷ 180) = 1Compute the stirrup shear contribution
The truss model combines reinforcement density, lever arm, design stress and inclination.
(1) × (500) × (435) × (1) = 217500 NReport the shear contribution in kN
Convert the force from newtons without changing the underlying resistance model.
(217500) ÷ 1000 = 217.5 kN
Does this worked answer make sense?
At θ = 45°, cot θ = 1. Halving link spacing doubles the computed stirrup contribution, but the concrete-strut resistance may then govern.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- Asw · Shear steel area per spacing set
- 157 mm²
- s · Spacing
- 150 mm
- z · Lever arm
- 450 mm
- fywd · Design shear steel strength
- 435 N/mm²
- θ · Strut angle
- 30 deg
Find steel area per unit length
Dividing link area by spacing expresses how much vertical steel is present along the member.
(157) ÷ (150) ≈ 1.046666667 mm²/mmCalculate the strut-angle cotangent
Convert degrees to radians before taking the tangent, then take its reciprocal.
1 ÷ tan((30) × π ÷ 180) ≈ 1.732050808Compute the stirrup shear contribution
The truss model combines reinforcement density, lever arm, design stress and inclination.
(1.046666667) × (450) × (435) × (1.732050808) ≈ 354871.2297 NReport the shear contribution in kN
Convert the force from newtons without changing the underlying resistance model.
(354871.2297) ÷ 1000 ≈ 354.8712297 kN
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- Asw · Shear steel area per spacing set
- 200 mm²
- s · Spacing
- 250 mm
- z · Lever arm
- 500 mm
- fywd · Design shear steel strength
- 435 N/mm²
- θ · Strut angle
- 35 deg
Find: Learn: Shear reinforcement resistance
A hint, not the answer
Asw/s is stirrup area per longitudinal spacing. Multiplying by z, fywd and cot θ gives the shear carried by the idealized vertical reinforcement; cot θ means 1/tan θ.
Asw is mm², s and z are mm, and fywd is N/mm². The intermediate result is N and is divided by 1000 for kN. θ is entered in degrees and converted to radians for the tangent calculation.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find steel area per unit length
Dividing link area by spacing expresses how much vertical steel is present along the member.
(200) ÷ (250) = 0.8 mm²/mmCalculate the strut-angle cotangent
Convert degrees to radians before taking the tangent, then take its reciprocal.
1 ÷ tan((35) × π ÷ 180) ≈ 1.428148007Compute the stirrup shear contribution
The truss model combines reinforcement density, lever arm, design stress and inclination.
(0.8) × (500) × (435) × (1.428148007) ≈ 248497.7532 NReport the shear contribution in kN
Convert the force from newtons without changing the underlying resistance model.
(248497.7532) ÷ 1000 ≈ 248.4977532 kN
Avoid the common trap
Asw includes the effective legs crossing the shear mechanism, not the area of just one bar unless that is appropriate. Do not confuse tan θ with cot θ or multiply a result already in kN by another conversion factor.
When this method applies — and when it does not
The expression is for vertical shear reinforcement. The calculator requires 0 < θ < 90° mathematically but does not approve that angle as code-compliant. Strut crushing, permitted cotangent bounds, minimum links, spacing and anchorage remain separate checks.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
One idea understood. Keep going.
This optional checkmark is saved only in this browser. It is your own progress note, not a certificate.
Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Shear reinforcement resistance. First-generation EN 1992 teaching: material properties and the relevant bending, shear, serviceability, detailing or prestress relationship. Read the applicability conditions as well as the expression.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.