🪨Fundamental Assumptions for RC Flexural Design in EC2

The RC design of members are depending on obersved and tested behaviours, though it can be complex, based on Cl.6.1 in BSEN1992-1-1, we should always remain these assumption taken:

1. Plane section remain plane Cl.6.1(2), BSEN1992-1-1

P section neutral axis compression tension

2. Stress in compression are derived by stress-strain curveCl.6.1(2), BSEN1992-1-1

εcc σc fck current strain Move Here 0 tensionpart Fcc N.A.

3. Strain of rebar in tension or compression are same as surrounding concrete.Cl.6.1(2), BSEN1992-1-1

4. Tension strength of concrete is ignored.Cl.6.1(2), BSEN1992-1-1

5. Stress in reinforcement are derived by stress-strain curve.Cl.6.1(2), BSEN1992-1-1

εst σs fyk y s current strain Move Here 0 compressionpart Fst

6. Force equilibrium: Resutlant forces developed by the section must be in equilibrium.Section 6.4, BSEN1990

Froce Equilibrium
T = C
Tension in section = Compression in section

📜 Ductility and Code Requirements

While the assumptions above describe the mechanical behaviour of reinforced concrete sections, EC2 also imposes additional limits to ensure ductile and safe structural behaviour.

1. Tensile steel yields before concrete crushes, neutral axis xu/d is limited to 0.45, ensure sufficient ductility and rotation capacity Cl.5.5 (4), BSEN1992-1-1

Ac As d x z Fcc Fst
Section Equilibrium
x/d ≤ 0.45
z/d ≥ 0.82 and K ≤ 0.167 are corresponding derived

2. To ensure minimum compression stripe, z/d ≤ 0.95 Good Common Practice

Min. CompressionStripe Ac As d x z Fcc Fst
Section Equilibrium
z/d ≤ 0.95
xu/d ≥ 0.125 and K ≥ 0.054 are corresponding derived

3. Maximum and Mimimum reinforcement ratio, 0.04Ac and 0.26 Cl. 9.2.1.1, BSEN1992-1-1

↔️ Upper and lower bounrdery of K, xu/d and z/d

Based on item 1. and 2. in ductility and code required, and the relationship between K, xu/d and z/d, we can conclude with below upper and lower limits.

Limit of xu/d
0.125 [2] ≤ xu/d ≤ 0.45 [1]
Limit of z/d
0.82 [1] ≤ z/d ≤ 0.95 [2]
Limit of K
0.054 [1] ≤ K ≤ 0.167 [2]

Details derivative of these boundaries, please check out this article,Derivation of relationship of x/d, z/d and K.

📝Summary & Key Takeaways

  1. RC flexural design assumes strain compatibility and equilibrium, with bilinear material behaviour and no concrete tension.
  2. EC2 adds limits on neutral axis, lever arm, and reinforcement action to ensure ductile steel-yielding failure.
#rc design #glossary #construction tips #shear #worked example #structural
CivilSimple Team

CivilSimple Team

The CivilSimple Team writes practical engineering guides for the profession and the curious. All articles are reviewed for technical accuracy before publication.