Optimum Design of Carbon Fiber-Reinforced Polymer for Increasing Shear Capacity of Beams: Optimization of CFRP for RC Beams

Introduction

In addition to design of new reinforced concrete structures, design of existing structures for retrofit is needed. Since the first design of structures is done according to unforeseen effects and situations, retrofit of RC structures may be needed. Retrofit of structures are done for renovation or safety situation as follows:

Renovation:

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  Adding a span to structure.

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  Adding a floor to structure.

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  Changing span lengths for increasing free space.

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  Adding a non-structural component for storage or architectural renovation.

Safety:

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  To consider unforeseen effect of forces in design.

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  Effects resulting from unforeseen winds and earthquakes.

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  Durability reasons resulting with the strength loss of existing materials.

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  Blast and accidents damaging or affected the structure with vibration.

All the mentioned reasons have an internal force increase effect. Generally, retrofit of structures are done to increase the strength capacity of structure. For that reason, it involves adding new members (dampers, shear walls, additional columns and beams, structural control systems like tuned mass dampers), increasing the dimensions of existing members by adding rebars (jacketing) and adding new materials (steel profiles, wrapping of member via a composite material). As a composite, carbon fiber reinforced polymer (CFRP) is highly used and it is a non-destructive application, and the use of structure can be provided during retrofit. Since optimization of RC members is an important issue, the optimum retrofit design is also important. In this chapter, optimum design of CFRP for increasing shear force capacity of RC beams is presented.

Methodology

In the presented methodology, the objective of the optimization is to minimize the required CFRP area per meter; A, by finding optimum values of the design variables such as width; w_f, spacing; s_f and angle; β of CFRP. The aim of the application is to gain an additional shear force capacity for an RC cross section with breadth; b_w and effective depth; d. For that reason, the design constraints are related to the shear capacity, and these constraints are defined according to ACI-318: Building code requirements for structural concrete and ACI-440: Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structure. The T-shaped cross section and the design variables are shown as Fig. 1a for β=90 and Fig. 1b for general cases. d_f is the depth of the RC member covered with CFRP and it is formulated as Eq. (1), and h_f denotes the height of the RC slab.

Figure 1.

The design variables

(Kayabekir, Sayin, Bekdaş, & Nigdeli, 2018)

The objective function is formulated as Eq. (2). The optimum design of beam is done for unit m length of beam.

The objective function must be minimized by providing the following constraints: