Shear Design of Fiber Reinforced Concrete Structural Elements
Madeh Izat Hamakareem
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Fiber Reinforced concrete is used for concrete structural members for around thirty years and developed for both prestressed and conventional or ordinary reinforced concrete elements. Fiber reinforced polymer bars are used as reinforcement in these concrete.
There are different types of fiber reinforced concrete with various properties for instance Glass FRP, Carbon FRP, and Aramid FRP reinforced concrete. The reinforcement bars of these polymers are manufactured with textures and surface deformation to enhance the bond between concrete and FRP bars.
In this article, shear design of fiber reinforced concrete structural members is explained as per ACI 440.1 R-06: Guide for the design and construction of structural concrete reinforced with FRP bars code is followed.
Design Consideration for Fiber Reinforced Concrete
There are various problems which are required to be accounted for shear design of FRP reinforced concrete members:
The tensile strength of bent FRP bar is considerably smaller than that of straight portion
There is no yield point in FRP and it has high tensile strength
Modulus of elasticity of FRP is relatively low
FRP has low transverse shear resistance
Shear Design of FRP Reinforced Concrete Members
FRP shear reinforcement design is based on strength design method and the strength reduction factor of 0.75, which is recommended by ACI 318-11 for decreasing nominal shear capacity of steel reinforced concrete element, is employed for FRP reinforcement as well.
For the section under consideration, the ultimate shear force (Vu) has to be equal or smaller than the design shear strength.
Types of Shear Failure of FRP Reinforced Concrete
Shear tension failure: controlled by rupture of FRP reinforcement.
Shear compression failure: controlled by crushing of concrete.
Shear Capacity with FRP Main Tension Bars and FRP Shear Reinforcement:
There are number of factors that affect nominal shear capacity of FRP reinforced concrete element, which is loaded in flexure such as the mechanical properties of FRP main tension reinforcing bars, FRP shear reinforcement that is normally produced in advance and provided in the form of stirrups.
Moreover, compression area in fiber reinforced concrete member is smaller and deflection is larger at flexural failure compared with the same member reinforced with steel bars.
Furthermore, due to shallow compression depth and low FRP elastic modulus, crack width in concrete member reinforced with FRP bars is larger and, consequently shear resistance provided by compressed concrete and aggregate interlock is smaller, compare with crack width and shear strength contribution of both compressed concrete and aggregate interlock in steel reinforced concrete member.
That is why the strain in FRP stirrups is determined and restricted to avoid large shear crack development in Fiber-reinforced Polymer reinforced concrete members. Additionally, the strength of FRP stirrups is decreased when it is bent owing to production process used to manufacture FRP stirrups and linear elastic properties of Fiber reinforced polymer.
As per ACI Code, the nominal shear capacity of fiber reinforced concrete element is consist of shear resistance provided by concrete plus FRP shear reinforcement.
Where:Vn: Nominal shear capacity of FRP reinforced concrete element
Vc: Nominal shear capacity of concrete in which FRP bars is embedded as longitudinal reinforcement
Vf: FRP stirrup nominal shear capacity
The nominal shear capacity of concrete reinforced with FRP bars is computed as follow:
Where:fc': Concrete strength
bw: Width of the web of the beam
c: Neutral axis depth in the cracked transformed section
Neutral axis depth can be calculated for singly reinforced rectangular section as per the following formulas:
Where:k: Depth ratio
: FRP reinforcement ratio
nf: Modular ratio
Both FRP reinforcement ratio and modular ratio can be computed according to the following equations respectively:
The shear resistance provided by FRP stirrups which are perpendicular to axis of the element is calculated according to the following equation:
Where:Vf: shear resistance of FRP stirrups
Avf: Area of FRP stirrups
ffv: is the strength of FRP stirrup
d: Effective depth of the section
S: Spacing between two stirrups
Stress level in FRP stirrups is limited in order to restrict shear crack width and prevent failure at bend part of the FRP stirrup:
Where:Ef: FRP modulus of elasticity
ffb: FRP strength at its bend which can be found out using the following expression:
Where:rb: is the inside radius of the bend
db: is the diameter of the FRP bars
ffu: is the design strength in the straight portion of FRP bar
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