Learn: RC compression resultant — rectangular block
A rectangular stress block replaces a nonlinear concrete compression distribution with a simpler uniform block. Its resultant force is stress times the area of that block, not the area of the whole section.
What the formula is saying
The block depth is λx, where x is neutral-axis depth. Its uniform stress is ηfcd. Multiplying the two with width b gives the compressive resultant used in force equilibrium.
Read the symbols in plain language
- η
- Stress-block factor
Stress-block factor. The stress coefficient modifies the supplied design compressive strength.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- fcd
- Design concrete strength
Design concrete strength. The stress coefficient modifies the supplied design compressive strength.
N/mm²One N/mm² equals one MPa.
- b
- Section width
Section width. Uniform stress over the rectangular compression area gives its resultant force.
mmMillimetres measure length; 1000 mm = 1 m.
- λ
- Block depth factor
Block depth factor. The block depth is a specified fraction of the neutral-axis depth, not necessarily equal to it.
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. The block depth is a specified fraction of the neutral-axis depth, not necessarily equal to it.
mmMillimetres measure length; 1000 mm = 1 m.
- C
- Result to find
RC compression resultant — rectangular block. Report the force in kilonewtons after completing the millimetre-based calculation.
kN
Sort out the units first
fcd is N/mm² and b and x are mm. η and λ are dimensionless. The raw force is N, converted to kN by division by 1000.
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 C and explain the result in the stated output unit.
- η · Stress-block factor
- 1
- fcd · Design concrete strength
- 20 N/mm²
- b · Section width
- 300 mm
- λ · Block depth factor
- 0.8
- x · Neutral-axis depth
- 200 mm
Find the equivalent block depth
The block depth is a specified fraction of the neutral-axis depth, not necessarily equal to it.
(0.8) × (200) = 160 mmFind the equivalent block stress
The stress coefficient modifies the supplied design compressive strength.
(1) × (20) = 20 N/mm²Multiply stress by block area
Uniform stress over the rectangular compression area gives its resultant force.
(20) × (300) × (160) = 960000 NConvert the compression force
Report the force in kilonewtons after completing the millimetre-based calculation.
(960000) ÷ 1000 = 960 kN
Does this worked answer make sense?
At fixed block parameters, doubling b or x doubles force. A force result alone does not locate the reinforcement or prove that concrete and steel forces balance.
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.
- η · Stress-block factor
- 1
- fcd · Design concrete strength
- 25 N/mm²
- b · Section width
- 250 mm
- λ · Block depth factor
- 0.8
- x · Neutral-axis depth
- 150 mm
Find the equivalent block depth
The block depth is a specified fraction of the neutral-axis depth, not necessarily equal to it.
(0.8) × (150) = 120 mmFind the equivalent block stress
The stress coefficient modifies the supplied design compressive strength.
(1) × (25) = 25 N/mm²Multiply stress by block area
Uniform stress over the rectangular compression area gives its resultant force.
(25) × (250) × (120) = 750000 NConvert the compression force
Report the force in kilonewtons after completing the millimetre-based calculation.
(750000) ÷ 1000 = 750 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.
- η · Stress-block factor
- 1
- fcd · Design concrete strength
- 20 N/mm²
- b · Section width
- 350 mm
- λ · Block depth factor
- 0.8
- x · Neutral-axis depth
- 180 mm
Find: Learn: RC compression resultant — rectangular block
A hint, not the answer
The block depth is λx, where x is neutral-axis depth. Its uniform stress is ηfcd. Multiplying the two with width b gives the compressive resultant used in force equilibrium.
fcd is N/mm² and b and x are mm. η and λ are dimensionless. The raw force is N, converted to kN by division by 1000.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find the equivalent block depth
The block depth is a specified fraction of the neutral-axis depth, not necessarily equal to it.
(0.8) × (180) = 144 mmFind the equivalent block stress
The stress coefficient modifies the supplied design compressive strength.
(1) × (20) = 20 N/mm²Multiply stress by block area
Uniform stress over the rectangular compression area gives its resultant force.
(20) × (350) × (144) = 1008000 NConvert the compression force
Report the force in kilonewtons after completing the millimetre-based calculation.
(1008000) ÷ 1000 = 1008 kN
Avoid the common trap
Do not take x as the full member depth or use λ twice. Do not confuse η, which changes stress, with λ, which changes block depth.
When this method applies — and when it does not
The rectangular block must lie within a constant-width compression region and use parameters compatible with the concrete strength. Flanged sections, a block crossing a width change and doubly reinforced equilibrium require additional treatment.
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 compression resultant — 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.