Background Knowledge - Strengthening Design of Reinforced Concrete with FRP - page 9

2 Background Knowledge
2.1 OVERVIEW
Before starting the discussion on FRP strengthening, it is important to refresh the
basics of concrete design of sections and members upon which the FRP strengthen-
ing design equations are built. Consequently, this chapter revisits the following four
background topics:
1. Flexural design of RC sections
2. Shear design of RC beams
3. Internal reinforcement to confine RC columns
4. Service load calculations in beams
The inclusion of these four topics was based on the fact that they represent the pri-
mary structural strengthening subjects addressed in this topic.
2.2 FLEXURAL DESIGN OF RC SECTIONS
The fundamental principles of flexural design are strain compatibility, force, and
moment equilibrium, as well as material constitutive (stress-strain) relationships.
2.2.1 S train C ompatibility
Shallow-beam theory accurately assumes that plane sections before bending remain
plane after bending, directly translating into linear strain distribution across the
beam section until ultimate failure of that section. Typical reinforced concrete sec-
tions fail in flexure by concrete crushing when concrete compressive strain reaches
around 0.003 after the yielding of primary tensile reinforcement. The value of 0.003
is selected by the American Concrete Institute code to mark the attainment of con-
crete crushing (ACI 318-11). This basic failure mode is a ductile one, since the
member shows high deformability prior to reaching ultimate capacity. Conversely,
beams may fail in flexure by concrete crushing prior to the yielding of primary
steel, which is an undesirable brittle failure that is not allowed by ACI 318-11 code
for beams, while the latter failure mode is allowed for other structural members by
reducing the ϕ factor significantly (i.e., increasing the margin of strength), as shown
in Figure 2.1 for sections with grade 60 reinforcement.
ACI 318-11 section 10.3.5 states that for members with factored axial compressive
load less than 0.1 f c A g (beams), the strain at the extreme level of reinforcement (ε t ) at
nominal strength shall not be less than 0.004, yielding a ductile failure of the beam,
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