Method for design of seismic-damping partition wall with variable friction energy dissipation
The method for design of a seismic-damping partition wall with variable-friction-force energy dissipation provided by the present application includes the following steps: building a bare frame model without considering lateral resisting stiffness of a partition wall, and calculating an inter-story shear force and an inter-story displacement of a structure under action of an earthquake; calculating an elastic strain energy of the structure, and determining an expected additional damping ratio provided by a seismic-damping partition wall for the structure; determining a friction damping force-sliding displacement curve of a single group of seismic-damping partition wall panels, and establishing a relational expression between a total friction hysteretic energy and a friction damping force and a target sliding displacement of the single group of seismic-damping partition wall panels, and the seismic resilience of the partition wall and the structure can be synergistically improved.
1. A method for design of a seismic-damping partition wall with variable-friction energy dissipation, wherein the seismic-damping partition wall comprises a peripheral frame and a single group of seismic-damping partition wall panels arranged in the peripheral frame, upper encased reinforcing boxes and lower encased reinforcing boxes are arranged at corners of a top end and a bottom end of the single group of seismic-damping partition wall panels, respectively, elastic members are arranged between the upper encased reinforcing boxes and the peripheral frame, partial backing plates are arranged at a bottom of the single group of seismic-damping partition wall panels and below the lower encased reinforcing boxes, the single group of seismic-damping partition wall panels comprises a plurality of partition wall panels, and anti-shear connecting members are arranged between adjacent partition wall panels; and the method comprises following steps:
step 1: building a bare frame structure model without considering lateral resisting stiffness of a partition wall, and calculating an inter-story shear force and an inter-story displacement of a structure under action of an earthquake;
step 2: according to the inter-story shear force and the inter-story displacement obtained in step 1, calculating an elastic strain energy W e of the structure, and determining an expected additional damping ratio ξ a0 provided by a seismic-damping partition wall in the structure for the structure;
step 3: according to a friction damping force-sliding displacement curve of the single group of seismic-damping partition wall panels, establishing a relational expression between a total friction hysteretic energy W d of the seismic-damping partition wall in the structure and a first friction damping force F Hu1 , a second friction damping force F Hu2 and a target sliding displacement Δ H of the single group of seismic-damping partition wall panels, and calculating the total friction hysteretic energy W d :
W
d
=
∑
W
d
,
i
=
∑
(
2
F
H
0
,
i
+
F
Hu
1
,
i
+
F
Hu
2
,
i
)
Δ
H
,
i
F
H
0
,
i
=
n
F
H
0
F
Hu
1
,
i
=
n
F
H
u
1
F
Hu
2
,
i
=
n
F
H
u
2
where W d,i is a total friction hysteretic energy of all the single groups of seismic-damping partition wall panels of an ith story of the structure; n is a number of seismic-damping partition walls or seismic-damping partition wall groups of the ith story: Δ H,i is a target sliding displacement of a single group of seismic-damping partition wall panels of the 4 th story: F H0,i is a total sliding occurrence force of all the single groups of seismic-damping partition wall panels of the ith story; F H0 is a sliding occurrence force of a single group of seismic-damping partition wall panels of the ith story, calculated according to a sliding friction coefficient and a gravity of the single group of seismic-damping partition wall panels; F Hu1,i is a sum of first friction damping forces of all the single groups of seismic-damping partition wall panels of the ith story; F Hu1 is a first friction damping force of a corresponding single group of seismic-damping partition wall panels; F Hu2,i is a sum of second friction damping forces of all the single groups of seismic-damping partition wall panels of the ith story; and F Hu2 is a second friction damping force of a corresponding single group of seismic-damping partition wall panels;
wherein abscissas of the friction damping force-sliding displacement curve of the single group of seismic-damping partition wall panels represent a sliding displacement Δ w of the single group of seismic-damping partition wall panels, ordinates represent a friction damping force F H of the single group of seismic-damping partition wall panels, and the friction damping force-sliding displacement curve of the single group of seismic-damping partition wall panels is determined by means of a plurality of feature points in end-to-end connection closure on the friction damping force-sliding displacement curve of the single group of seismic-damping partition wall panels;
wherein a number of the feature points is 7, and the 7 feature points are defined as point 0 and point a to point f; the point 0 is coordinate point 0; the point a is a feature point when the single group of seismic-damping partition wall panels slides just after overcoming a maximum static friction, and corresponding coordinates are (0, F H0 ), where F H0 is a sliding occurrence force of the single group of seismic-damping partition wall panels; point b is a feature point where the single group of seismic-damping partition wall panels slides from the point a to a positive target sliding displacement Δ H , and corresponding coordinates are (Δ H , F Hu1 ), where F Hu1 is a friction damping force of the single group of seismic-damping partition wall panels in this state; point c is a feature point where the single group of seismic-damping partition wall panels just changes when sliding back from a positive target sliding displacement Δ H point to the point 0, and at this moment, it is considered that a sliding displacement of the partition wall remains unchanged, i.e., Δ w =Δ H , but a direction and a magnitude of the friction damping force change, and corresponding coordinates are (Δ H , −F Hu2 ), where −F Hu2 is a friction damping force of the single group of seismic-damping partition wall panels in this state; point d is a feature point where the single group of seismic-damping partition wall panels slides back from the point c to the point 0, and corresponding coordinates are (0, −F H0 ), where −F H0 is a friction damping force of the single group of seismic-damping partition wall panels in this state; point e is a feature point where the single group of seismic-damping partition wall panels slides from the point d to a negative target sliding displacement −Δ H , and corresponding coordinates are (group −Δ H , −F Hu1 ), where −F Hu1 is a friction damping force of the single of seismic-damping partition wall panels in this state; the point f is a feature point where the single group of seismic-damping partition wall panels just changes when sliding back from a negative target sliding displacement −Δ H point to the point 0, and corresponding coordinates are (−Δ H , F Hu2 ), where F Hu2 is a friction damping force of the single group of seismic-damping partition wall panels in this state
step 4: solving a calculated additional damping ratio ξ a provided by the seismic-damping partition wall for the structure, and subjecting the calculated additional damping ratio ξ a and the expected additional damping ratio ξ a0 to simultaneous comparison; if an expected design target is satisfied, i.e., ξ a ≥ξ a0 , determining the first friction damping force F Hu1 and the second friction damping force F Hu2 of the single group of seismic-damping partition wall panels; otherwise, continuing to adjust until the expected design target is satisfied, wherein a formula for the calculated additional damping ratio ξ a is:
ξ
a
=
W
d
4
π
W
e
≥
ξ
a
0
step 5: according to vertical compression requirements and elastic deformation requirements of the elastic members in the single group of seismic-damping partition wall panels, designing construction of the elastic members, wherein an actual vertical stiffness design value K B,d and an elastic deformation requirement Δ y of the elastic members need to simultaneously satisfy following formulas:
K
B
,
d
=
γ
K
B
=
γ
F
B
φ
L
B
λ
Δ
y
≥
φ
L
B
λ
where γ is a design tolerance; K B is a theoretical required vertical stiffness value of the elastic members; F B is a vertical compression of the elastic members against the seismic-damping partition wall; φ is an inter-story displacement ratio of the peripheral frame where the single group of seismic-damping partition wall panels is located; L B is a vertical distance from a down-press point of the elastic members to a central line of a column section; and λ is a coefficient of variation between a rigid body frame deformation mechanism and an actual frame deformation mechanism;
step 6: according to the first friction damping force F Hu1 of the single group of seismic-damping partition wall panels, calculating an anti-shear bearing force V s at a connection between the anti-shear connecting members, and designing a form and construction of connection between the anti-shear connecting members;
step 7: performing damage control check on concrete wall panels near the lower encased reinforcing boxes of the single group of seismic-damping partition wall panels; and
step 8: completing the design of the seismic-damping partition wall with variable-friction energy dissipation.
2. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 1 , wherein a calculation formula for the elastic strain energy of the structure in step 2 is:
W
e
=
∑
W
e
,
i
=
1
2
∑
Q
i
Δ
i
where W e,i is an elastic strain energy of the ith story of the structure; Q i is an W inter-story shear force of the ith story of the structure; and Δ i is an inter-story displacement of the ith story of the structure.
3. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 1 , wherein the expected additional damping ratio ξ a0 provided by the seismic-damping partition wall for the structure in step 2 is determined according to the inter-story displacement ratio of the structure.
4. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 1 , wherein the first friction damping force F Hu1 and the second friction damping force F Hu2 are calculated by means of the following formula:
F
H
u
1
=
κ
1
-
κ
μ
2
S
(
F
B
+
G
w
)
F
H
u
2
=
κ
′
1
-
κ
′
μ
2
S
(
F
B
+
G
w
)
κ
=
μ
1
S
η
1
+
μ
1
S
η
2
+
μ
1
C
η
3
κ
′
=
μ
1
S
η
1
′
+
μ
1
S
η
2
′
+
μ
1
C
η
3
′
where F B is a vertical compression of the elastic members against the single group of seismic-damping partition wall panels; G w is a total gravity of the single group of seismic-damping partition wall panels; μ 1S and μ 1C are a coefficient of friction between the lower encased reinforcing boxes in the single group of seismic-damping partition wall panels and the partial backing plates, and a coefficient of friction between concrete-friction seismic-damping layers, respectively; μ 2S is a coefficient of friction between a top sliding driving point of the single group of seismic-damping partition wall panels and a horizontal force transmission member; η 1 and η 2 are coefficients of distribution of normal compressions at two corners of a bottom surface of the partition wall when the single group of seismic-damping partition wall panels slides from the point 0 to a positive or negative target sliding displacement; η 3 is a coefficient of distribution of a normal compression in a middle of the bottom surface of the partition wall when the single group of seismic-damping partition wall panels slides from the point 0 to the positive or negative target sliding displacement; n′ 1 and n′ 2 are coefficients of distribution of normal compressions at the two corners of the bottom surface of the partition wall when the single group of seismic-damping partition wall panels slides back from the positive or negative target sliding displacement to the point 0; η′ 3 is a coefficient of distribution of a normal compression in the middle of the bottom surface of the partition wall when the single group of seismic-damping partition wall panels slides back from the positive or negative target sliding displacement to the point 0; κ is a coefficient of calculation of the first friction damping force; and κ′ is a coefficient of calculation of the second friction damping force.
5. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 1 , wherein in step 4, according to actual engineering requirements, the inter-story shear force and the elastic strain energy of the structure are corrected by considering a friction damping force, then a relationship between a corrected calculated additional damping ratio ξ′ a and the expected additional damping ratio ξ a0 are checked, and the corrected calculated additional damping ratio ξ′ a is adjusted to satisfy a design target.
6. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 1 , wherein the elastic members in step 5 are constructed and designed according to requirements of the first friction damping force F Hu1 and the second friction damping force F Hu2 of the single group of seismic-damping partition wall panels and the elastic deformation requirements of the elastic members.
7. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 1 , wherein the anti-shear bearing force V s of the anti-shear connecting members in step 6 is proposed based on a control target in which the partition wall panels in the single group of seismic-damping partition wall panels do not rock and a relative sliding deformation does not occur between the partition wall panels, and the anti-shear bearing force V s needs to satisfy
V
s
≥
ψ
V
V
=
F
H
u
1
(
h
w
-
μ
2
S
b
w
)
-
F
B
x
-
G
w
1
b
w
/
2
μ
1
C
β
h
1
-
(
G
w
-
G
w
1
)
where ψ is a coefficient of adjustment of a shear force at a connection between single anti-shear connecting members; V is a maximum critical shear force expected to be borne by the connection between the anti-shear connecting members; h w is a distance from a bottom surface of the single group of seismic-damping partition wall panels to a top sliding driving point; μ 2S is a coefficient of friction between the top sliding driving point of the single group of seismic-damping partition wall panels and a horizontal force transmission member; b w is a width of a single partition wall panel in the single group of seismic-damping partition wall panels; F B is a vertical compression of the elastic members against the single group of seismic-damping partition wall panels; x is a distance from an acting point of a concentrated load of the elastic members to a right edge of a first partition wall panel; G w1 is a gravity of the first partition wall panel in the single group of seismic-damping partition wall panels; G w is a total gravity of the single group of seismic-damping partition wall panels; μ 1C is a coefficient of friction between concrete-friction seismic-damping layers; β is a safety reserve factor; and h 1 is a distance from an acting point of a horizontal resistance force borne by the first partition wall panel to a bottom surface of the first partition wall panel.
8. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 1 , wherein a method for damage control check of the seismic-damping partition wall in step 7 is proposed on a premise that concrete in encased reinforcing boxes at corners of the seismic-damping partition wall is not broken prior to concrete outside the encased reinforcing boxes, and the method for check is:
σ
c
≤
[
α
f
c
]
σ
c
=
μ
2
S
F
H
u
1
+
F
B
+
G
w
ω
A
c
where σ c is a compressive stress of concrete near the lower encased reinforcing boxes of the single group of seismic-damping partition wall panels; α is a safety factor when the damage control check is performed on the concrete wall panels; ƒ c is an axial compressive strength of a concrete material in the single group of seismic-damping partition wall panels: μ 2S is a coefficient of friction between a top sliding driving point of the single group of seismic-damping partition wall panels and a horizontal force transmission member; F Hu1 is a first friction damping force of the single group of seismic-damping partition wall panels: ω is an area reduction factor when the damage control check is performed on the concrete wall panels; A c is a projection area of the lower encased reinforcing boxes of the seismic-damping partition wall; F B is vertical compression of the elastic members against the single group of seismic-damping partition wall panels; and G w is a total gravity of the single group of seismic-damping partition wall panels.
9. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 2 , wherein a method for damage control check of the seismic-damping partition wall in step 7 is proposed on a premise that concrete in encased reinforcing boxes at corners of the seismic-damping partition wall is not broken prior to concrete outside the encased reinforcing boxes, and the method for check is:
σ
c
≤
[
α
f
c
]
σ
c
=
μ
2
S
F
H
u
1
+
F
B
+
G
w
ω
A
c
where σ c is a compressive stress of concrete near the lower encased reinforcing boxes of the single group of seismic-damping partition wall panels; α is a safety factor when the damage control check is performed on the concrete wall panels; ƒ c is an axial compressive strength of a concrete material in the single group of seismic-damping partition wall panels; μ 2S is a coefficient of friction between a top sliding driving point of the single group of seismic-damping partition wall panels and a horizontal force transmission member; F Hu1 is a first friction damping force of the single group of seismic-damping partition wall panels; ω is an area reduction factor when the damage control check is performed on the concrete wall panels; A c is a projection area of the lower encased reinforcing boxes of the seismic-damping partition wall; F B is vertical compression of the elastic members against the single group of seismic-damping partition wall panels; and G w is a total gravity of the single group of seismic-damping partition wall panels.
10. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 3 , wherein a method for damage control check of the seismic-damping partition wall in step 7 is proposed on a premise that concrete in encased reinforcing boxes at corners of the seismic-damping partition wall is not broken prior to concrete outside the encased reinforcing boxes, and the method for check is:
σ
c
≤
[
α
f
c
]
σ
c
=
μ
2
S
F
H
u
1
+
F
B
+
G
w
ω
A
c
where σ c is a compressive stress of concrete near the lower encased reinforcing boxes of the single group of seismic-damping partition wall panels; α is a safety factor when the damage control check is performed on the concrete wall panels; ƒ c is an axial compressive strength of a concrete material in the single group of seismic-damping partition wall panels; μ 2S is a coefficient of friction between a top sliding driving point of the single group of seismic-damping partition wall panels and a horizontal force transmission member; F Hu1 is a first friction damping force of the single group of seismic-damping partition wall panels; ω is an area reduction factor when the damage control check is performed on the concrete wall panels; A c is a projection area of the lower encased reinforcing boxes of the seismic-damping partition wall; F B is vertical compression of the elastic members against the single group of seismic-damping partition wall panels; and G w is a total gravity of the single group of seismic-damping partition wall panels.
11. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 4 , wherein a method for damage control check of the seismic-damping partition wall in step 7 is proposed on a premise that concrete in encased reinforcing boxes at corners of the seismic-damping partition wall is not broken prior to concrete outside the encased reinforcing boxes, and the method for check is:
σ
c
≤
[
α
f
c
]
σ
c
=
μ
2
S
F
H
u
1
+
F
B
+
G
w
ω
A
c
where σ c is a compressive stress of concrete near the lower encased reinforcing boxes of the single group of seismic-damping partition wall panels: α is a safety factor when the damage control check is performed on the concrete wall panels; ƒ c is an axial compressive strength of a concrete material in the single group of seismic-damping partition wall panels; μ 2S is a coefficient of friction between a top sliding driving point of the single group of seismic-damping partition wall panels and a horizontal force transmission member; F Hu1 is a first friction damping force of the single group of seismic-damping partition wall panels; ω is an area reduction factor when the damage control check is performed on the concrete wall panels; A c is a projection area of the lower encased reinforcing boxes of the seismic-damping partition wall; F B is vertical compression of the elastic members against the single group of seismic-damping partition wall panels; and G w is a total gravity of the single group of seismic-damping partition wall panels.
12. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 5 , wherein a method for damage control check of the seismic-damping partition wall in step 7 is proposed on a premise that concrete in encased reinforcing boxes at corners of the seismic-damping partition wall is not broken prior to concrete outside the encased reinforcing boxes, and the method for check is:
σ
c
≤
[
α
f
c
]
σ
c
=
μ
2
S
F
H
u
1
+
F
B
+
G
w
ω
A
c
where σ c is a compressive stress of concrete near the lower encased reinforcing boxes of the single group of seismic-damping partition wall panels; α is a safety factor when the damage control check is performed on the concrete wall panels; ƒ c is an axial compressive strength of a concrete material in the single group of seismic-damping partition wall panels; μ 2S is a coefficient of friction between a top sliding driving point of the single group of seismic-damping partition wall panels and a horizontal force transmission member; F Hu1 is a first friction damping force of the single group of seismic-damping partition wall panels; ω is an area reduction factor when the damage control check is performed on the concrete wall panels; A c is a projection area of the lower encased reinforcing boxes of the seismic-damping partition wall; F B is vertical compression of the elastic members against the single group of seismic-damping partition wall panels; and G w is a total gravity of the single group of seismic-damping partition wall panels.
13. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 6 , wherein a method for damage control check of the seismic-damping partition wall in step 7 is proposed on a premise that concrete in encased reinforcing boxes at corners of the seismic-damping partition wall is not broken prior to concrete outside the encased reinforcing boxes, and the method for check is:
σ
c
≤
[
α
f
c
]
σ
c
=
μ
2
S
F
H
u
1
+
F
B
+
G
w
ω
A
c
where σ c is a compressive stress of concrete near the lower encased reinforcing boxes of the single group of seismic-damping partition wall panels; α is a safety factor when the damage control check is performed on the concrete wall panels; ƒ c is an axial compressive strength of a concrete material in the single group of seismic-damping partition wall panels; μ 2S is a coefficient of friction between a top sliding driving point of the single group of seismic-damping partition wall panels and a horizontal force transmission member; F Hu1 is a first friction damping force of the single group of seismic-damping partition wall panels: ω is an area reduction factor when the damage control check is performed on the concrete wall panels; A c is a projection area of the lower encased reinforcing boxes of the seismic-damping partition wall; F B is vertical compression of the elastic members against the single group of seismic-damping partition wall panels; and G w is a total gravity of the single group of seismic-damping partition wall panels.
14. The method for design of a seismic-damping partition wall with variable-friction energy dissipation according to claim 7 , wherein a method for damage control check of the seismic-damping partition wall in step 7 is proposed on a premise that concrete in encased reinforcing boxes at corners of the seismic-damping partition wall is not broken prior to concrete outside the encased reinforcing boxes, and the method for check is:
σ
c
≤
[
α
f
c
]
σ
c
=
μ
2
S
F
H
u
1
+
F
B
+
G
w
ω
A
c
where σ c is a compressive stress of concrete near the lower encased reinforcing boxes of the single group of seismic-damping partition wall panels; α is a safety factor when the damage control check is performed on the concrete wall panels; ƒ c is an axial compressive strength of a concrete material in the single group of seismic-damping partition wall panels; μ 2S is a coefficient of friction between a top sliding driving point of the single group of seismic-damping partition wall panels and a horizontal force transmission member; F Hu1 is a first friction damping force of the single group of seismic-damping partition wall panels; ω is an area reduction factor when the damage control check is performed on the concrete wall panels; A c is a projection area of the lower encased reinforcing boxes of the seismic-damping partition wall; F B is vertical compression of the elastic members against the single group of seismic-damping partition wall panels; and G w is a total gravity of the single group of seismic-damping partition wall panels.