US 12,099,785 B2 · Optimization method and system for hybrid FRP and steel bars

Abstract

The present disclosure relates to an optimization method and system for hybrid FRP and steel bars. The optimization method includes: determining a cross-sectional bending bearing capacity, a maximum cross-sectional bending bearing capacity, and a minimum cross-sectional bending bearing capacity according to basic material parameters and a design value of a bending moment; determining whether the cross-sectional bending bearing capacity, the maximum cross-sectional bending bearing capacity, and the minimum cross-sectional bending bearing capacity meet a first preset condition; if yes, determining a maximum steel bar area according to the basic material parameters; determining a maximum ductility of a steel bar beam; determining whether the maximum ductility and the target ductility meet a second preset condition; if yes, determining a minimum steel bar area and a maximum FRP bar area according to the maximum steel bar area; and determining an actual steel bar area and an actual FRP bar area.

An optimization method for preparing a concrete structure, comprising:

obtaining a design value of a bending moment, a target ductility, and basic material parameters;
determining a cross-sectional bending bearing capacity, a maximum cross-sectional bending bearing capacity, and a minimum cross-sectional bending bearing capacity according to the basic material parameters and the design value of the bending moment;
determining whether the cross-sectional bending bearing capacity, the maximum cross-sectional bending bearing capacity, and the minimum cross-sectional bending bearing capacity meet a first preset condition, wherein the first preset condition is as follows:
η
min
<
η
de
<
η
max
wherein ηde represents the cross-sectional bending bearing capacity;
ηmin represents the minimum cross-sectional bending bearing capacity;
and ηmax represents the maximum cross-sectional bending bearing capacity
if yes, determining a maximum steel bar area according to the basic material parameters, wherein the maximum steel bar area is calculated by the following formula:
A
s
,
max
=
α
1
⁢
bf
c
⁢
h
1
-
α
1
⁢
bf
c
(
α
1
⁢
bf
c
⁢
h
1
2
-
2
⁢
M
de
)
f
y
wherein As,max represents the maximum steel bar area;
α1 represents a first equivalent stress rectangle coefficient;
b represents a width in preset cross-sectional dimension values;
fc represents a compressive strength of concrete;
h1 represents a height of a steel bar from a top;
Mde represents the design value of the bending moment;
and the fy represents a steel bar yield strength;
determining a maximum ductility of a steel bar beam;
determining whether the maximum ductility and the target ductility meet a second preset condition;
wherein the second preset condition is as follows:
μ
max
>
μ
de
wherein μmax represents the maximum ductility, and μde represents the target ductility
if yes, determining a minimum steel bar area and a maximum FRP bar area according to the maximum steel bar area;
obtaining a third preset condition;
determining an actual steel bar area and an actual FRP bar area according to the third preset condition, the minimum steel bar area, and the maximum FRP bar area;
and
preparing the concrete structure according to the actual steel bar area and the actual FRP bar area,
wherein the determining a cross-sectional bending bearing capacity, a maximum cross-sectional bending bearing capacity, and a minimum cross-sectional bending bearing capacity according to the basic material parameters and the design value of the bending moment specifically comprises:
calculating the cross-sectional bending bearing capacity ηde and the maximum and minimum cross-sectional bending bearing capacities ηmax and ηmin according to the basic material parameters and the design value of the bending moment Mde,
wherein the cross-sectional bending bearing capacity ηde is calculated by the following formula:
η
de
=
M
de
f
c
⁢
bd
2
,
wherein d represents a height in the preset cross-sectional dimension values,
wherein maximum and minimum bending bearing capacities for a specified cross section are calculated by the following formulas:
η
min
=
M
u
,
min
f
c
⁢
bd
2
=
0.85
β
1
⁢
ε
cu
ε
cu
+
ε
fu
⁢
(
1
-
β
1
⁢
ε
cu
2
⁢
(
ε
cu
+
ε
fu
)
)
,
η
max
=
M
u
,
max
f
c
⁢
bd
2
=
0.85
β
1
⁢
ε
cu
ε
cu
+
ε
y
⁢
(
1
-
β
1
⁢
ε
cu
2
⁢
(
ε
cu
+
ε
y
)
)
,
wherein β1 represents a second stress rectangle coefficient;
εcu represents an ultimate strain of concrete;
εfu represents an ultimate strain of FRP;
and εy represents a steel bar yield strain;
the determining a minimum steel bar area and a maximum FRP bar area according to the maximum steel bar area specifically comprises:
obtaining a preset step size;
gradually reducing a steel bar area and increasing an FRP bar area from the maximum steel bar area according to the preset step size, and determining a current ductility after reducing the steel bar area each time;
calculating an error between the current ductility and the target ductility;
determining whether the error is less than an allowable error;
and
if no, stopping reducing the steel bar area and increasing the FRP bar area to obtain the minimum steel bar area and the maximum FRP bar area;
and
the determining an actual steel bar area and an actual FRP bar area according to the third preset condition, the minimum steel bar area, and the maximum FRP bar area specifically comprises:
determining a steel bar selection range as As,min≤As≤As,max and an FRP bar selection range as 0≤Af≤Af,max when the carrying capacity and the target ductility are met;
and
according to actual engineering requirements, selecting a steel bar area As,min≤As≤As,max and an FRP bar area 0≤Af≤Af,max, and guaranteeing Mu≥Mde and μ0≥μde,
wherein As represents the actual steel bar area;
Af represents the actual FRP bar area;
As,min represents the minimum steel bar area;
Af,max represents the maximum FRP bar area;
Mu represents a bending moment in an ultimate state;
and μ0 represents an actual ductility.

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Optimization method and system for hybrid FRP and steel bars

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Optimization method and system for hybrid FRP and steel bars

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Abstract

Claims7