Civil's Guide

Concrete Bending Capacity

Concrete Bending Capacity

Bending of concrete beams

Concrete is strong in compression and weak in tension. When a beam supported at 2 ends, cracking will occur along the bottom of the concrete. Reinforcement is added to minimise cracking and the top flange/section of concrete will be in compression.

Material properties

  • EC2 uses the characteristic cylinder strength fck unlike BS 8110 which uses the characteristic cube strength fcu
  • Concrete classes are expressed as C20/25, C30/37, C35/45 in EC2 where the first number is the cylinder strength and the second number is the cube strength
  • The design compressive strength of concrete is given by
  • \(f_{cd} = \alpha f_{ck} \gamma_m = 0.85 f_{ck} /1.5 = 0.567 f_{ck}\)
  • (where \(\alpha\) = 0.85 from UK National Annex for flexure and axial loading)
  • The density of concrete is given as 25 kN/m3″> kN/m3 in EN 1991-1-1

Steel Reinforcement Material Properties

  • The design strength of reinforcement in tension and compression fyd is given by:
  • \(f_{yd}/ \gamma_m = f_{yk}/1.15\)
  • fyk is the characteristic yield strength (5%) and gm is the material factor of safety for reinforcement
  • The characteristic strength of reinforcement  \(f_{yk}\) = 500 MPa
  • The elastic modulus of reinforcement is 200 GPa

ULS Section Analysis - Assumptions

  • 1. Plane sections remain plane.
  • 2. Stresses in the flexural compressive zone may be derived from a design curve relating stress and strain.
  • 3. The strain in the extreme compressive fibre εcu is defined at failure (εcu = 0.0035 for flexure in EC2).
  • 4. The tensile strength of the concrete is neglected.
  • 5. The stress in the reinforcement is calculated using an idealised bi-linear stress-strain diagram.
  • Design Stress = \(\frac{ \alpha f_{ck} }{\gamma_c} = \frac{0.85f_{ck}}{1.5} = 0.567f_{ck}\)
  • \(f_{cd}=0.85f_{ck}/1.5 = 0.567f_{ck}\)