Horse Construction Fiber Reinforced Polymer(FRP) Design Software

1. Basic Information

1.1. Design Criteria

ACI 318M-14 Building Code Requirements for Structural Concrete

ACI-440-2R-17 Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures

1.2. Design Requirement

Required axial load: 10000 kN∙m

1.3.Basic Information

1.3.1 Information of existing member

Height: 610mm

Width: 610mm

Radius of edges of a prismatic cross section confined with CFRP: 25mm

Area of the steel reinforcement: 9650.96 mm2

Concrete compressive strength：45MPa

Yield strength of tensile reinforcement：414 MPa

Elastic modulus of tensile reinforcement: 200000 MPa

1.3.2 Strengthening system

 Material: HM-60-I

Ultimate tensile strength of the FRP material as reported by the manufacturer: 4084 MPa

Ultimate rupture strain of FRP reinforcement: 0.0158

Elastic modulus of CFRP: 259251 MPa

Environmental reduction factor: 0.85

Design ultimate tensile strength of FRP: f_fu=C_E f_fu^*=3471.4 MPa

Design rupture strain of FRP reinforcement: ε_fu=C_E ε_fu^*=0.0134

Number of layers: 3 

2. Design Calculations

2.1 Compute the design FRP material properties

Design ultimate tensile strength of FRP：f_fu= C_E f_fu^* = 3471.4 MPa

Design rupture strain of FRP reinforcement：ε_fu= C_E ε_fu^*= 0.0134

2.2 Capacity of existing column ϕP_n,existing

Gross area of concrete column: A_g = 372100 mm²

Strength reduction factor: ϕ=0.65

Strength of existing column: ϕP_{n(A),existing =}0.8ϕ[0.85 f_c’(A_g - A_st)+ f_yA_st]= 0.8× 0.65 ×(0.85× 45 ×( 372100- 9650.96)+ 414 ×9650.96)=9286770.95N

2.3 Capacity of strengthen column ϕP_n

Effective strain in the CFRP: ε_fe=κ_eε_fu=0.55ε_fu=0.55×0.01= 0.0074

Maximum confining pressure due to CFRP jacket: f_ℓ =2nE_ft_fε_fe/D=2×3 × 259251 ×0.333 × 0.0074/862.67 =4.44 MPa

Ratio of A_st to A_g of compression column: ρg = A_st/A_g =9650.96/ 372100= 0.0259

A_e/A_c={1-[(b/h)(h-2rc)²+(h/b)(b-2rc)²]/3/A_g -ρg}/(1-ρg)={1-[(610/ 610)( 610-2×25)²+(610/ 610)( 610-2×25)²]/3/372100- 0.0259}/(1-0.03)= 0.42

Efficiency factor: k_a=(A_e/A_c)(b/h)²=0.42 ×( 610/ 610)²= 0.42

Efficiency factor: k_b =(A_e/A_c)(h/b)^0.5=0.42 ×( 610/ 610)²= 0.42

Additional reduction factor: ψ_f = 0.95

Compressive strength of confined concrete: f_cc′= f_c′+ψ_f3.3k_af_ℓ=45+ 0.95 ×3.3×0.42 ×4.44= 50.88 MPa

Strength reduction factor: ϕ=0.65

Strength of existing column: ϕP_{n =}0.8ϕ[0.85 f_cc’(A_g - A_st)+ f_yA_st]= 0.8×0.65 ×[0.85×50.88 ×( 372100- 9650.96)+ 414 ×9650.96]= 10229409.18 N

3. Conclusion

Notes：

This software application and the results derived from its utilization are intended only for use by professional users with expert knowledge in the area of the intended application. Users must independently verify the results before any use and take into account the site and application conditions, product data sheet and product literature, technical state of the art as well as local applicable standards and regulations.