US 11,821,806 B2 · Calculation method of ultimate moment resistance and moment-rotation curve for steel beam to concrete-filled steel tube column connections with bidirectional bolts

Abstract

The invention discloses a calculation method of ultimate moment resistance and moment-rotation relation for steel beam to concrete-filled steel tube column connections with bidirectional bolts, wherein the calculation method as follows: calculate ultimate moment resistance values of the connection for different failure modes, i.e. yielding of the endplate or T-stub in bending, failure of bolts in tension, failure of column in transverse compression, failure of panel zone in shear, and yielding of the steel beam in bending; the smallest one in the five ultimate moment resistance values is taken as the ultimate moment resistance of the connection; obtain the initial rotational stiffness of the connection by the test, simulation or theoretical calculation; then, the moment-rotation curve of the connection is obtained by substituting the initial rotational stiffness and the ultimate moment resistance into the proposed exponential model for the moment-rotation relation.

A calculation method of ultimate moment resistance for steel beam to concrete-filled steel tube column connections with bidirectional bolts, wherein the calculation method is applicable to an extended unstiffened endplate bidirectional bolted connection, an extended stiffened endplate bidirectional bolted connection, a flush endplate bidirectional bolted connection, and a bidirectional bolted T-stub connection;

the calculation method comprising steps of:
1) calculating the ultimate moment resistance of all of the connections for yielding of all of the endplates or T-stub in bending, wherein
firstly, yield line parameters for four common types of connections are calculated as follows:
for the extended unstiffened endplate bidirectional bolted connection, yield line parameter L1 is obtained by equation (1):
L
1
=
b
p
2
[
h
2
(
1
p
fi
+
1
s
)
+
h
1
(
1
p
f
⁢
e
)
-
1
2
]
+
2
g
[
h
2
(
p
fi
+
s
)
]
(
1
)
where bp is a width of the endplate;
h1 is a distance from centerline of first bolt row to lower surface of compression flange;
h2 is a distance from centerline of second bolt row to lower surface of the compression flange;
pfi is a distance from centerline of the second bolt row to lower surface of tension flange;
pfe is a distance from centerline of the first bolt row to upper surface of tension flange;
g is bolt gage;
s=0.5√{square root over (bpg)} is a distance from centerline of second bolt row to edge of the yield line pattern;
for the extended stiffened endplate bidirectional bolted connection, if de≤s, yield line parameter L2 is obtained by equation (2):
L
2
=
b
p
2
[
h
2
(
1
p
fi
+
1
s
)
+
h
1
(
1
p
f
⁢
e
+
1
2
⁢
s
)
]
+
2
g
[
h
2
(
p
fi
+
s
)
+
h
1
(
d
e
+
P
fe
)
]
(
2
)
where de is a distance from the centerline of the first bolt row to the edge of the endplate;
if de>s, the yield line parameter L2 is obtained by equation (3):
L
2
=
b
p
2
[
h
2
(
1
p
fi
+
1
s
)
+
h
1
(
1
p
f
⁢
e
+
1
2
⁢
s
)
]
+
2
g
[
h
2
(
p
fi
+
s
)
+
h
1
(
s
+
P
fe
)
]
(
3
)
for the flush endplate bidirectional bolted connection, if there is only one row of bolts in tensile zone, the yield line parameter L3 is obtained by equation (4):
L
3
=
b
p
⁢
h
1
2
⁢
(
1
p
fi
+
1
s
)
+
2
⁢
h
1
g
⁢
(
p
fi
+
s
)
(
4
)
if there are two rows of bolts in the tensile zone, the yield line parameter L3 is obtained by equation (5):
L
3
=
b
p
2
[
h
1
(
1
p
fi
)
+
h
2
(
1
s
)
]
+
2
g
[
h
1
(
p
fi
+
0
.
7
⁢
5
⁢
p
)
+
h
2
(
s
+
0.25
p
)
]
+
g
2
(
5
)
where p is a distance between the two rows of bolts;
for the bidirectional bolted T-stub connection, yield line parameter L4 is obtained by equation (6):
L
4
=
b
s
2
[
h
2
(
1
p
fi
)
+
h
1
(
1
p
fe
)
]
(
6
)
where bs is a width of the T-stub flange;
then, substituting the above yield line parameter L into equation (7), the ultimate moment resistance Mep of all of the connections for yielding of the endplate or T-stub in bending is obtained:
Mep=fytep2L (7)
where fy is yield strength of the endplate, tep is the thickness of the endplate or T-shaped flange, and L is the yield line parameter of the connection, i.e. L1, L2, L3 or L1;
2) calculating the ultimate moment resistance of the connection for failure of bidirectional bolts in tension, wherein
for endplate bidirectional bolted connections, the ultimate moment resistance of the connection for failure of bidirectional bolts in tension Mbo1 is obtained by equation (8):
Mbo1=nt·min(0.9fubAs,0.48πdmtepfup)·(hb−tbf) (8)
for the bidirectional bolted T-stub connection, the ultimate moment resistance of the connection for failure of bidirectional bolts in tension Mbo2 is obtained by equation (9):
Mbo2=nt·min(0.9fubAs,0.48πdmtepfup)·(hb+tbf) (9)
where nt is the number of bolts in tension zone;
fub is the ultimate tensile strength of the bolt, AS is the effective tensile area of the bolt, dm is a nominal diameter of the bolt head, hb is the height of the steel beam, tbf is the thickness of beam flange, and fup is the ultimate tensile strength of the endplate or T-stub flange;
3) calculating the ultimate moment resistance of the connection for failure of the panel zone in shear, wherein
for endplate bidirectional bolted connections, the ultimate moment resistance of the connection for failure of the panel zone in shear Mpz1 is obtained by equation (10):
M
pz
⁢
1
=
(
1.8
f
y
,
cw
⁢
A
v
⁢
c
3
+
0
.
8
⁢
5
⁢
vA
c
⁢
f
c
⁢
d
⁢
sin
⁢
α
)
·
(
h
b
-
t
b
⁢
f
)
(
10
)
for the bidirectional bolted T-stub connection, the ultimate moment resistance of the connection for failure of a panel zone in shear Mpz2 is obtained by equation (11):
M
pz
⁢
2
=
(
1
⁢
8
⁢
f
y
,
cw
⁢
A
v
⁢
c
3
+
0.85
vA
c
⁢
f
c
⁢
d
⁢
sin
⁢
α
)
·
(
h
b
+
t
bf
)
(
11
)
where fy,cw is yield strength of a steel tube web of the concrete-filled steel tube column;
Avc is the cross-sectional area of the steel tube web in shear;
v is a reduction factor to allow for the effect of longitudinal compression of steel tube in the concrete-filled steel tube column on resistance in shear;
Ac is the cross-sectional area of the encased concrete;
fcd is a design value of the cylindrical compressive strength of an encased concrete of the concrete-filled steel tube column;
α is an angle in a panel zone;
the reduction factor to allow for the effect of longitudinal compression of the concrete-filled steel tube column on resistance in shear, i.e. v, is calculated according to equation (12):
v
=
0
.
5
⁢
5
⁢
(
1
+
2
⁢
N
N
u
)
(
12
)
where N is a design compressive normal force in the concrete-filled steel tube column, and Nu is an ultimate compressive bearing capacity of the concrete-filled steel tube column;
the angle α in the panel zone is calculated according to equation (13):
α=arctan[(wc−2tcf)/z] (13)
where wc is a width of the concrete-filled steel tube column;
tcf is the thickness of the steel tube flange of the concrete-filled steel tube column;
z is a length of the lever arm for the connection, and z is (hb−tbf) for endplate bidirectional bolted connections, while z is (hb+tbf) for the bidirectional bolted T-stub connection;
4) calculating the ultimate moment resistance of the connection for failure of column in transverse compression, wherein
for endplate bidirectional bolted connections, the ultimate moment resistance of the connection for failure of column in transverse compression Mc1 is obtained by equation (14):
Mc1=[2ωρkcwbeff,cwtcwfy,cw+0.85kcbeff,c(dc−2tcw)fcd]·(hb−tbf) (14)
for the bidirectional bolted T-stub connection, the ultimate moment resistance of the connection for failure of column in transverse compression Mc2 is obtained by equation (15):
Mc2=[2ωρkcwbeff,cwtcwfy,cw+0.85kcbeff,c(dc−2tcw)fcd]·(hb+tbf) (15)
where ω is the reduction factor to allow for the effects of panel zone in shear on a transverse compression resistance of the steel tube web of the concrete-filled steel tube column;
ρ is the reduction factor to allow for the steel tube web buckling in the concrete-filled steel tube column;
kcw and kc are two factors to allow for the effect of longitudinal compressive stress on the transverse compression resistance of the steel tube and the encased concrete, respectively;
beff,cw and beff,c are effective lengths of steel tube web and encased concrete in compression respectively;
dc is section depth of the concrete-filled steel tube column;
tcw is the thickness of the steel tube web;
the reduction factor to allow for the effects of panel zone in shear on the transverse compression resistance of the steel tube web of the concrete-filled steel tube column, i.e. ω, is obtained by equation (16):
ω
=
{
1
1
+
1.3
(
b
eff
,
cw
⁢
t
c
⁢
w
/
A
v
⁢
c
)
2
(
for
⁢
exterior
⁢
connections
)
1
(
for
⁢
interior
⁢
connections
)
(
16
)
the reduction factor to allow for the steel tube web buckling in the concrete-filled steel tube column ρ, is obtained by equations (17):
ρ
=
{
(
λ
-
0
.
2
)
/
λ
2
(
λ
>
0
.
7
⁢
2
)
1
(
λ
≤
0
.
7
⁢
2
)
(
17
)
λ
=
0.
9
⁢
3
⁢
2
⁢
b
eff
,
cw
(
w
c
-
2
⁢
t
cf
-
2
⁢
t
)
⁢
f
y
,
cw
E
⁢
t
cw
2
(
18
)
where λ is slenderness ratio of the steel tube web in the concrete-filled steel tube column;
for rolled section of the steel tube, t is the inner radius of corners in the steel tube with rolled section;
for welded section of the steel tube, t is the height of the steel tube weld leg;
E is elastic modulus of the steel tube;
the factors to allow for effect of longitudinal compressive stress on the transverse compression resistance of the steel tube and encased concrete or kcw and kc, are obtained by equations (19) and (20):
k
cw
=
{
1
(
σ
col
≤
0
.
7
⁢
f
y
,
cw
)
1.7
-
σ
col
f
y
,
cw
(
σ
col
>
0
.
7
⁢
f
y
,
cw
)
(
19
)
k
c
=
1.3
+
3.3
σ
c
f
cd
,
and
⁢
k
c
=
2
⁢
if
⁢
it
⁢
is
⁢
greater
⁢
than
⁢
2
(
20
)
where σcol is the longitudinal compressive stress in the steel tube of the concrete-filled steel tube column, σc is longitudinal compressive stress in encased concrete;
the effective lengths of steel tube web and encased concrete in compression beff,cw and beff,c, are obtained by equation (21):
beff,cw=beff,c=tbf+2√{square root over (2)}he+5(tcf+t)+sp (21)
where he is an effective height of a weld seam between a steel beam flange and the endplate;
sp is length obtained by dispersion through the endplate, and its minimum is the thickness of the endplate, and its maximum is double thickness of the endplate;
5) calculating the ultimate moment resistance of the connection for yielding of the steel beam in bending, wherein
the ultimate moment resistance of the connection for yielding of the steel beam in bending Mb is obtained by equation (22):
Mb=fybWp (22)
where fyb is yield strength of the steel beam;
Wp is a plastic section modulus of the steel beam;
6) calculating the final ultimate moment resistance and failure mode of the connection, wherein
the smallest value of ultimate moment resistances for the above five failure modes is the final ultimate moment resistance of the connection, and the corresponding failure mode is an actual failure mode;
for endplate bidirectional bolted connections, the ultimate moment resistance Mu1 can be obtained:
Mu1=min(Mep,Mbo1,Mpz1,Mc1,Mb) (23)
for the bidirectional bolted T-stub connections, the ultimate moment resistance Mu2 can be obtained:
Mu2=min(Mep,Mbo2,Mpz2,Mc2,Mb) (24).

660 more elements

Calculation method of ultimate moment resistance and moment-rotation curve for steel beam to concrete-filled steel tube column connections with bidirectional bolts

Life of this patent

Calculation method of ultimate moment resistance and moment-rotation curve for steel beam to concrete-filled steel tube column connections with bidirectional bolts

Life of this patent

Abstract

Claims2