This chapter presents the mechanical behaviour: of the constituent materials of concrete members, namely concrete and reinforcing steel, as well as of their interaction; and of concrete members typical of buildings, under cyclic loading of the type induced by strong earthquake shaking. This behaviour determines how concrete and reinforcing steel are used in concrete elements (notably, the shape and dimensions of concrete members and the shape, amount and layout of their reinforcement), for satisfactory seismic performance of the members and the structural system as a whole.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
A member is conventionally considered to have reached its ultimate deformation, if its (lateral) force resistance cannot increase above 80% of the maximum ever force resistance (defined as the force capacity of the member) by increasing the member’s deformation, see Section 3.2.2.7.
- 2.
Whatever effect, internal or external, increases the strength of steel, typically reduces its ductility and elongation at failure.
- 3.
- 4.
- 5.
As we will see shortly, the concept of bond strength as a property of the concrete for given relative rib area and position of the bar with respect to casting, albeit convenient, is not representative of reality.
- 6.
- 7.
This is the σ-ɛ law used in CEN (2004b) and CEB (1991) for the calculation of the resistance of cross-sections.
- 8.
Symmetric deflection cycles, i.e. from a deflection δ r to –δ r; as commonly applied on test specimens, produce almost but not quite symmetric curvature cycles at the member end where yielding takes place.
- 9.
If a large fraction of the reinforcement is distributed between the top and the bottom of the section, e.g., along the two sides that are parallel to the plane of bending, as in large columns or walls, most, if not all, of this reinforcement is normally in tension, because the compression zone is limited to (much) less than half of the effective section depth. So, the tension reinforcement is always more than the compression reinforcement and can easily drive it to yielding and beyond.
- 10.
If the value of the axial force varies around the column balance load, there is no clear-cut effect of this variation on the column flexural behaviour.
- 11.
Strictly speaking the increase is to a value of ϕ y[(L s–z)(1–z/L s )(1+0.5z/L s )/3+z(1–0.5z/L s )], but the difference from ϕ y(L s+z)/3 is practically insignificant.
- 12.
If moments and curvatures change sign between sections A and B, θ AB is not the angle between the tangent to the member axis at these two sections, but the sum of the absolute values of relative rotations between section A and the point of inflection and between the point of inflection and section B.
- 13.
Except for the value of the terminal strain, these assumptions are the same as those made for the calculation of the uniaxial moment resistance in Section 3.2.2.5. The computed components of the biaxial moment resistance were found to be fairly insensitive to the precise value of this limit strain.
- 14.
If the Lam and Teng Eq. (3.27b) is used for ɛ cu * instead of Eqs. (3.29) and (3.30), the ultimate curvature of the FRP-wrapped member is underpredicted by a factor of about 2.3. So, notwithstanding any adverse effect of the cycling, the FRP that confines the extreme compression fibres seems to be put under lower demands by cyclic bending than by the condition of monotonic concentric compression for which Eq. (3.27b) has been developed, a condition inducing a uniformly large strain to the FRP all around the section.
- 15.
As noted in Section 3.1.2.4, in Lam and Teng (2003a,b) this percentage value is proposed only for CFRP or GFRP, and 85% is given for AFRP, but on the basis of few test results.
- 16.
The symbol δ is used here instead of the symbol θ normally used for the angle of inclination, to avoid confusion with chord rotations.
- 17.
The symbol n is used here instead of the symbol v used in both Eurocode 2 and CEB/FIP Model Code 90, to avoid confusion with the normalised axial force v = N/A c f c.
- 18.
Being symmetrically reinforced, each end section will resist the bending moments there through approximately equal and opposite forces in the two “chords”, that produce no net contribution to N.
- 19.
In members the chord rotation ductility factor, μ θ, is the same as the displacement ductility factor.
- 20.
Normally we take n = 1 for flexure with axial load without shear.
- 21.
In squat members whose moment resistance is reduced owing to shear, the yield moment is essentially equal to the moment resistance.
- 22.
Normally column vertical bars are the same above and below the joint: A sc,top = A sc,bot, except at the joints of the top floor where A sc,top = 0.
- 23.
The upward bend of the bottom bars at the far face of the joint does not deliver forces to the joint core when these bars are in compression.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Fardis, M.N. (2009). Concrete Members Under Cyclic Loading. In: Seismic Design, Assessment and Retrofitting of Concrete Buildings. Geotechnical, Geological, and Earthquake Engineering, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9842-0_3
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9842-0_3
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9841-3
Online ISBN: 978-1-4020-9842-0
eBook Packages: EngineeringEngineering (R0)