Learn: RC lever arm — rectangular block
The lever arm is the distance between the tensile-steel force and the concrete compression resultant. For a rectangular uniform stress block, the compression force acts at the middle of that block.
What the formula is saying
The compression resultant is λx/2 from the compression face. Subtract that distance from effective depth d, measured to the tensile-steel centroid, to obtain z.
Read the symbols in plain language
- d
- Effective depth
Distance from the extreme compression face to the centroid of tensile reinforcement; do not substitute the overall section depth.
mmMillimetres measure length; 1000 mm = 1 m.
- λ
- Block depth factor
Block depth factor. A uniform rectangular stress block has its resultant halfway through its depth.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- x
- Neutral-axis depth
Neutral-axis depth. A uniform rectangular stress block has its resultant halfway through its depth.
mmMillimetres measure length; 1000 mm = 1 m.
- z
- Result to find
RC lever arm — rectangular block. Subtract the compression-resultant depth from the tensile-steel effective depth.
mm
Sort out the units first
d, x and z are in mm; λ has no unit. Effective depth is not overall section depth: it is measured from the compression face to the centroid of the relevant tensile reinforcement.
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 z and explain the result in the stated output unit.
- d · Effective depth
- 550 mm
- λ · Block depth factor
- 0.8
- x · Neutral-axis depth
- 200 mm
Locate the compression resultant
A uniform rectangular stress block has its resultant halfway through its depth.
(0.8) × (200) ÷ 2 = 80 mmFind the distance to the tensile force
Subtract the compression-resultant depth from the tensile-steel effective depth.
(550)-(80) = 470 mm
Does this worked answer make sense?
The lever arm is less than d but must remain positive. Increasing x moves the compression resultant downward and reduces z when d and λ stay fixed.
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.
- d · Effective depth
- 500 mm
- λ · Block depth factor
- 0.8
- x · Neutral-axis depth
- 150 mm
Locate the compression resultant
A uniform rectangular stress block has its resultant halfway through its depth.
(0.8) × (150) ÷ 2 = 60 mmFind the distance to the tensile force
Subtract the compression-resultant depth from the tensile-steel effective depth.
(500)-(60) = 440 mm
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.
- d · Effective depth
- 600 mm
- λ · Block depth factor
- 0.8
- x · Neutral-axis depth
- 250 mm
Find: Learn: RC lever arm — rectangular block
A hint, not the answer
The compression resultant is λx/2 from the compression face. Subtract that distance from effective depth d, measured to the tensile-steel centroid, to obtain z.
d, x and z are in mm; λ has no unit. Effective depth is not overall section depth: it is measured from the compression face to the centroid of the relevant tensile reinforcement.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Locate the compression resultant
A uniform rectangular stress block has its resultant halfway through its depth.
(0.8) × (250) ÷ 2 = 100 mmFind the distance to the tensile force
Subtract the compression-resultant depth from the tensile-steel effective depth.
(600)-(100) = 500 mm
Avoid the common trap
Do not subtract the whole block depth λx. Do not use overall depth instead of d, or confuse neutral-axis depth x with the depth of the equivalent block.
When this method applies — and when it does not
This geometry assumes a rectangular constant-width compression block and a tension-steel layer below the neutral axis. The lesson requires 0 < x < d and 0 < λ ≤ 1. Code limits on neutral-axis depth and ductility still need checking.
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.
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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: RC lever arm — rectangular block. 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.