Design Calculation for Bracing Connection - Joint SWF-SF13
1.)
LAYOUT
W36X232
1'-1/4"
See calcs
attached
8 1/4"
6"
3/16"
6"
Typ
5 3/16"
PL 0.375 - A36
Gusset Offset = 1/2''
2
8 3/8"
1'-1"
1'-3 3/4"
3/16"
6.00
HSS8X6X1/4
1
3/16"
4"
3/16"
4"
Typ
4.0
9 1/2"
HSS8X4X1/8
5"
2.)
REQUIRED STRENGTHS:
Member 1:
Axial Load, Ta
Axial Load, Ca
3.)
=
=
5.0
5.0
kips (Tension)
kips (Compression)
Member 2: (See below for details)
Axial Load, Ta
=
4.0
Axial Load, Ca
=
4.0
6.0
Shear Load, Va
=
kips (Tension)
kips (Compression)
kips
MATERIAL & GEOMETRIC PROPERTIES:
Member 1:
Size:
Fy
Fu
B
HT
A
HSS8X4X1/8
=
46
=
58
4.00
=
8.00
=
2.70
=
ASTM A500 Gr. B
ksi
ksi
in
in
in
Page 1 of 13
Design Calculation for Bracing Connection - Joint SWF-SF13
t
=
0.116
Member 2:
Size:
Fy
Fu
B
HT
A
t
HSS8X6X1/4
=
46
=
58
6.00
=
8.00
=
6.17
=
0.233
=
ksi
ksi
in
in
in
in
Member 3:
Size:
Fy
Fu
B
HT
A
t
HSS8X8X1/4
=
46
=
58
8.00
=
8.00
=
7.10
=
0.233
=
ksi
ksi
in
in
in
in
Gusset Plate:
Fy
=
Fu
=
tgusset
=
4.)
in
ASTM A500 Gr. B
ASTM A500 Gr. B
ASTM 36
ksi
ksi
in
36
58
3/8
BRACE CONNECTION
MEMBER 1:
Brace to Gusset Plate Weld:
Electrode Class
=
E700XX
Fu
=
=
Nominal Tensile Strength of Weld
70.00
Ksi
Fv
=
=
=
Allowable Weld Shear Strength
0.6 Fu / 2
21.00
Ksi
w
=
=
Size of Weld
0.1875
in.
(Use
0.1250 in. for calculation)
Pw
=
=
=
=
Shear Capacity of 1/8" weld per Linear Inch
0.707 * Fv * w
(0.707 * 21 * 0.125)
1.856 Kips/in
L1
Vw
=
=
=
Length of Weld
4.00
in.
Weld Shear Capacity
Vw
=
=
Pw * 4 L2
29.694 Kips
>
5.00
Kips
(OK)
Tension Yielding of the Brace:
Page 2 of 13
Design Calculation for Bracing Connection - Joint SWF-SF13
Rn/Ω
=
=
=
Capacity from 'Limit State of Tension Yielding of Brace'
Fyb * Ag1
1.67
74.37 kips
>
5.00 kips (OK)
Tension Rupture of the Brace:
Rn/Ω
Rn/Ω
=
Capacity from 'Limit State of Tension Rupture of Brace'
Fub * Ae
=
2.00
where:
4.00 in
=
(Length of Weld in HSS)
L
B
=
8.00
in
(Width of HSS Section)
H
=
4.00
in
(Height of HSS Section)
x
=
=
2
(B + 2 * B * H) / (4 * (B + H))
2.667 in
U
=
=
1 - (x / L)
0.333
An
=
=
Ag1 - 2 * (tp + 0.0625) * t1
2.599
in²
Ae
=
=
U * An
0.866
25.12
=
in²
kips
5.00
>
kips
(OK)
Whtimore Section
L=
L=
2 lw tan 30 + B
8.619
B=
4.00 in
in
Whitmore width in Vertical Edge =
Whitmore width in Horizontal Edge =
0.000
0.600
Check tension yielding on the Whitmore section
in
in
Ω = 1.67
Rn = Fy Aw
Rn = 36 x [ ( 8.619 - 0 - 0.6 ) x 0.375 ]
Rn =
108.25
Rn/Ω
=
kips
64.82
kips
>
5.00
kips
(OK)
Check block shear rupture of the gusset
Rn
=
Nominal Block Shear Strength of Gusset
(Ω =2)
=
2 x Min[ (0.6 x Fu x Anv + Ubs x Fu x Ant);
Page 3 of 13
Design Calculation for Bracing Connection - Joint SWF-SF13
(0.6 x Fy x Agv + Ubs x Fu x Ant) ]
Where:
Ubs = 1.0
Ant = Net Area with Tension Resistance
= Bbrace x tgusset
in
1.50
=
2
Agv = Gross Area with Shear Resistance
= 2 x lw x tgusset
=
in
3.00
2
Anv = Net Area with Shear Resistance
=
Rn/Ω
=
2
3.00
in
75.90
kips
>
5.00
kips
(OK)
Plate Buckling of Connection Plate
Ap
=
=
=
Effective Plate Cross-sectional Area
L*t
3.232 in²
Lcr
=
=
Plate Unbraced Length of Whitmore Section
4.63 in.
K
=
=
Effective Length Factor
1.200
r
=
=
=
Radius of Gyration
t / 3.464
0.108 in.
K Lcr/r
=
51.323
>
25
From Specification E3
Fe =
=
Fcr =
Rn/Ω
=
=
=
(π²)*E/(KL/r)²
108.66
ksi
>
0.44*Fy = 15.84 ksi
[0.658^(Fy/Fe)]*Fy
31.34
ksi
Allowable Strength in Compression
Ap * Fcr
1.67
60.65
kips
>
5.00
kips
(OK)
MEMBER 2:
Brace to Gusset Plate Weld:
Page 4 of 13
Design Calculation for Bracing Connection - Joint SWF-SF13
Electrode Class
=
E700XX
Fu
=
=
Nominal Tensile Strength of Weld
Ksi
70.00
Ө
=
tan-1(
w
=
=
6.00
4.03
rad
0.97883
deg
56.0827
=
=
Size of Weld
in.
0.1875
)
(Use
0.1250 in. for calculation)
Fv
=
=
=
Allowable Weld Shear Strength
0.6 Fu / 2
Ksi
21.00
Pw
=
=
=
=
Shear Capacity of 1/8" weld per Linear Inch
0.707 * Fv * w
(0.707 * 21 * 0.125)
1.856 Kips/in
P
=
=
√ ( 6² + 4.03² )
7.23028 kips
L
=
=
Length of Weld
in.
6.00
P/2
=
3.61514
kips
(See attached Calcs)
Tension Yielding of the Brace:
Rn/Ω
=
=
Capacity from 'Limit State of Tension Yielding of Brace'
Fyb * Ag2
1.67
=
169.95
kips
>
4.03
kips
(OK)
Tension Rupture of the Brace:
Rn/Ω
=
Capacity from 'Limit State of Tension Rupture of Brace'
Fub * Ae
=
2.00
where:
L
=
(Length of Weld in HSS)
6.00 in
B
=
6.00
in
(Width of HSS Section)
H
=
8.00
in
(Height of HSS Section)
x
=
=
2
(B + 2 * B * H) / (4 * (B + H))
2.357 in
Page 5 of 13
Design Calculation for Bracing Connection - Joint SWF-SF13
Rn/Ω
U
=
=
1 - (x / L)
0.607
An
=
=
Ag3 - 2 * (tp + 0.0625) * t3
5.966
in²
Ae
=
=
U * An
3.622
=
105.05
in²
kips
>
4.03
kips
(OK)
Whtimore Section
L=
L=
2 lw tan 30 + B
14.928
B=
8.00
in
0.000
2.600
in
in
in
Whitmore width in Vertical Edge =
Whitmore width in Horizontal Edge =
Check tension yielding on the Whitmore section
Ω = 1.67
Rn = Fy Aw
Rn = 36 x [ ( 14.928 - 0 - 2.6 ) x 0.375 ]
Rn =
166.43
Rn/Ω
=
kips
99.66
kips
>
4.03
kips
(OK)
Check block shear rupture of the gusset
Rn
=
Nominal Block Shear Strength of Gusset
(Ω =2)
=
2 x Min[ (0.6 x Fu x Anv + Ubs x Fu x Ant);
(0.6 x Fy x Agv + Ubs x Fu x Ant) ]
Where:
Ubs = 1.0
Ant = Net Area with Tension Resistance
= Bbrace x tgusset
=
3.00
in
2
Agv = Gross Area with Shear Resistance
= 2 x lw x tgusset
=
4.50
in
2
Anv = Net Area with Shear Resistance
=
Rn/Ω
=
4.50
135.60
in
2
kips
>
4.03
kips
(OK)
Page 6 of 13
Design Calculation for Bracing Connection - Joint SWF-SF13
Plate Buckling of Gusset Plate
Ap
=
=
=
Effective Plate Cross-sectional Area
L*t
5.598 in²
Lcr
=
=
Plate Unbraced Length of Whitmore Section
1.00 in.
K
=
=
Effective Length Factor
1.200
r
=
=
=
Radius of Gyration
t / 3.464
0.108 in.
K Lcr/r
=
<
11.085
Thus Fcr = Fy =
Rn/Ω
=
=
=
36
25
ksi
Allowable Strength in Compression
Ap * Fcr
1.67
120.68
kips
>
4.03
kips
(OK)
Gusset Plate to Colum:
Face of support
Px
Py
P (Tension or compression)
Solving for component forces:
Px
=
=
Py
=
5 (1.366)
√ [ (1) ² + (1.366) ² ]
4.0
kips
5 (1)
√ [ (1) ² + (1.366) ² ]
Page 7 of 13
Design Calculation for Bracing Connection - Joint SWF-SF13
=
3.0
kips
It can be shown that Px is balanced by the force from the horizontal HSS
member. Thus, the web is relieved from this force.
Designed gusset connection for pure shear (Py + V) only.
(See attached.)
Page 8 of 13