How to Calculate Lever Arm of Internal Forces (z)

A short tutorial to show you how to calculate lever arm of internal forces (z) in accordance with Eurocode 2 (EN1992) and UK National Annex.

Numerical example showing how to use z: youtu.be/91Iepc7dwCw


M – Bending moment
Fs – Tensile force
Fc – Compressive force

b – Overall width of cross-section
d – Effective depth of cross-section
x – Depth of compression zone
z – Lever arm of internal forces
As – Cross sectional area of reinforcement
Es – Design value of modulus of elasticity of reinforcing steel

f_yk – Characteristic yield strength of reinforcement
f_yd – Design yield strength of reinforcement
f_av – Average stress in concrete
f_cd – Design value of concrete cylinder strength of concrete at 28 days

Gamma_s – Partial material factor for reinforcing steel
Beta – Centroid ratio – depth to the centroid of the compressive force over depth of compression zone
Eta – Effective strength factor
Lambda – Effective height factor
Sigma_cu3 – Ultimate compressive strain in the concrete

#LeverArm #InternalForces #NumericalExample

Design to Eurocodes:
EN 1990 (EC0) - Basis of structural design
Design to Eurocode 1 - EN 1991 (EC1) - Actions on structures
Design to Eurocode 2 - (EN 1992 EC2) - Design of concrete structures including concrete bridges
Design to Eurocode 3 - (EN 1993 EC3) - Design of steel structures including steel bridges
Design to Eurocode 4 - (EN 1994 EC4) - Design of composite steel & concrete structures including composite bridges
Design to Eurocode 7 - (EN 1997 EC7) - Geotechnical design

Terms of use in addition to "Standard YouTube Licence": eurocoded.com/mod/page/view.php?id=16