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RC member design for biaxial bending and axial force

In this page we discuss the results for RC design for a cantilever beam subjected to biaxial bending and axial force.

Axial force\(N_{Ed}\)\(\)2000kN
Bending moment X\(M_{Ed,X}\)\(\)234kNm
Bending moment Z\(M_{Ed,Z}\)\(\)100kNm

You can find the model in WeStatiX ready for your calculation.

RC design biaxial bending axial force

In the table below you can read the cross section parameters

Overall width of a cross-section\(b\)\(\)300mm
Top concrete cover\(d_1\)\(\)50mm
Bottom concrete cover\(d_2\)\(\)50mm
ratio for interaction diagram choice\(d’/h\)\(\),13

And the material parameters

Characteristic compressive cylinder
strength of concrete at 28 days
Characteristic yield strength
of reinforcement
Coefficient taking account
of long term effects
Partial factor for concrete\(\gamma_c\)\(\)1,50
Partial factor for reinforcing
or prestressing steel
Design value of concrete
compressive strength
\(f_{cd}\)\(\alpha_{cc} f_{ck}/\gamma_c\)28.333,33kPa
Design value for yield
strength of reinforcement

If you take a look to the RC member design results you will find the total area of reinforcement to be \(A_{s,tot}=29,02 cm^2\).

RC design biaxial bending axial force

You can check it by using the interaction diagrams as suggested in [1]. According to it, you need to find the following parameters

\(\beta\)\(1-N_d/b \cdot h \cdot f_{ck}\)0,61
Effective uniaxial moment\(M’_z\)\(M_x+\beta M_y d/b’ \)322,64kNm
Parameterized axial force\(\nu\)\(N_d/b \cdot h \cdot f_{cd}\)0,59
Parameterized bending moment\(\mu\)\(M’_z/b\cdot h^2 \cdot f_{cd}\)0,24

So you have to consider the interaction diagrams for the design for biaxial bending and axial force for a section with d’/h=0,10 and d’/h=0,15, showed below

It’s easy then to find the reinforcement total area

Coefficient from interaction diagram\(A_s \cdot f_{yd} / b \cdot h \cdot f_{cd}\)\(\)0,41
Total reinforcement area\(A_{s,tot}\)\(\)29,16cm^2

You can finally calculate the error as follows

\( \epsilon = 1-\frac{29,02}{29,16} = 0,48\% \)

WeStatiX matches the solution.

[1] A.W.. BEEBY and R.S: NARAYANAN – Designers’ guide to Eurocode 2: design of concrete structures. – Designers’ guide to EN1992-1-1 and EN1992-1-2 Eurocode 2: design of concrete structures. General rules and rules for buildings and structural fire design.