1.) LAYOUT

2.) REQUIRED STRENGTHS:

Member 1: Axial Load, Ta = kips (Tension) Axial Load, Ca = kips (Compression)

Member 2: Axial Load, Ta = kips (Tension) Axial Load, Ca = kips (Compression)

Member 3: Axial Load, Ta = kips (Tension) Axial Load, Ca = kips (Compression)

Member 4: Axial Load, Ta = kips (Tension) Axial Load, Ca = kips (Compression)

3.) MATERIAL & GEOMETRIC PROPERTIES:

Design Calculation for Bracing Connection - Joint SWF-SF11

5.05.0

5.05.0

25.025.0

20.020.0

12

3

5

4

HSS8X4X1/8HSS8X4X1/8

HSS8X8X1/4

HSS8X8X1/4

HSS8X8X1/2

3/16"

3/16"

3/16"3/16"

4"4"

3/16" 8"Typ

Typ

PL 0.375 - A36

Typ

5"

10 3/16"

5"

11 11/16"

9"10"

1'-3 1/2'' 1'-1 1/2"

3/16"Typ

9"

8"

3/16" 8"

3/16" 4"

3/16" 4"

3/16" 8"

10"

10"

8.0

4.04.0

8.0

PL 0.375 - A36

Page 1 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11Member 1:

Size: ASTM A500 Gr. BFy = ksiFu = ksiB = inHT = inA = int = in

Member 2:Size: ASTM A500 Gr. BFy = ksiFu = ksiB = inHT = inA = int = in

Member 3:Size: ASTM A500 Gr. BFy = ksiFu = ksiB = inHT = inA = int = in

Member 4:Size: ASTM A500 Gr. BFy = ksiFu = ksiB = inHT = inA = int = in

Member 5:Size: ASTM A500 Gr. BFy = ksiFu = ksiB = inHT = inA = int = in

Gusset Plate: ASTM 36Fy = ksiFu = ksi

tgusset = in

4.) BRACE CONNECTION

MEMBER 1:

Brace to Gusset Plate Weld:

HSS8X4X1/84658

4.008.002.700.116

HSS8X4X1/84658

4.008.002.700.116

HSS8X8X1/44658

8.008.007.10

0.233

HSS8X8X1/44658

8.008.007.10

0.233

36583/8

HSS8X8X1/24658

8.008.0013.500.465

Page 2 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11

Electrode Class = E700XX

Fu = Nominal Tensile Strength of Weld= Ksi

Fv = Allowable Weld Shear Strength= 0.6 Fu / 2= Ksi

w = Size of Weld= in. (Use for calculation)

Pw = Shear Capacity of 1/8" weld per Linear Inch= 0.707 * Fv * w= (0.707 * 21 * 0.125)= Kips/in

L1 = Length of Weld= in.

Vw = Weld Shear Capacity

= Pw * 4 L2Vw = Kips > Kips (OK)

Tension Yielding of the Brace:

Rn/ = Capacity from 'Limit State of Tension Yielding of Brace'

= kips > kips (OK)

Tension Rupture of the Brace:

Rn/ = Capacity from 'Limit State of Tension Rupture of Brace'

where:L = in (Length of Weld in HSS)

B = in (Width of HSS Section)

H = in (Height of HSS Section)

x = (B2 + 2 * B * H) / (4 * (B + H))= in

U = 1 - (x / L)=

An = Ag1 - 2 * (tp + 0.0625) * t1= in

Ae = U * An= in0.866

=Fub * Ae

2.00

4.00

2.667

0.333

2.599

4.00

=Fyb * Ag1

1.6774.37

70.00

21.00

0.1250 in.

1.856

4.00

29.694 5.00

5.00

8.00

0.1875

Page 3 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11Rn/ = kips > kips (OK)

Whtimore Section

L = 2 lw tan 30 + B B = 4.00 in

L = in

Whitmore width in Vertical Member = inWhitmore width in Horizontal Member = in

Check tension yielding on the Whitmore section = 1.67

Rn = Fy Aw

Rn = 36 x [ ( 8.619 - 0 - 1.58 ) x 0.375 ]

Rn = kips

Rn/ = kips > kips (OK)

Check block shear rupture of the gusset

Rn = Nominal Block Shear Strength of Gusset ( = 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

= in2

Agv = Gross Area with Shear Resistance= 2 x lw x tgusset

= in2

Anv = Net Area with Shear Resistance

= in2

Rn/ = kips > kips (OK)

Plate Buckling of Connection Plate

Ap = Effective Plate Cross-sectional Area= L * t= in

Lcr = Plate Unbraced Length of Whitmore Section= in.

5.00

8.619

0.0001.580

95.02

56.90 5.00

1.50

3.00

25.12 5.00

3.232

4.65

3.00

75.90

Page 4 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11K = Effective Length Factor

=

r = Radius of Gyration= t / 3.464= in.

K Lcr/r = > 25

From Specification E3

Fe = ()*E/(KL/r)= ksi > 0.44*Fy = 15.84 ksi

Fcr = [0.658^(Fy/Fe)]*Fy ksi

Rn/ = Allowable Strength in Compression=

= kips > kips (OK)

MEMBER 2:

Brace to Gusset Plate Weld:

Electrode Class = E700XX

Fu = Nominal Tensile Strength of Weld= Ksi

Fv = Allowable Weld Shear Strength= 0.6 Fu / 2= Ksi

w = Size of Weld= in. (Use for calculation)

Pw = Shear Capacity of 1/8" weld per Linear Inch= 0.707 * Fv * w= (0.707 * 21 * 0.125)= Kips/in

L1 = Length of Weld= in.

Vw = Weld Shear Capacity

= Pw * 4 L2Vw = Kips > Kips (OK)

Tension Yielding of the Brace:

70.00

21.00

0.1875 0.1250 in.

1.856

4.00

29.694

1.200

0.108

51.544

5.00

Ap * Fcr1.67

60.58

5.00

107.73

31.30

Page 5 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11Rn/ = Capacity from 'Limit State of Tension Yielding of Brace'

= kips > kips (OK)

Tension Rupture of the Brace:

Rn/ = Capacity from 'Limit State of Tension Rupture of Brace'

where:L = in (Length of Weld in HSS)

B = in (Width of HSS Section)

H = in (Height of HSS Section)

x = (B2 + 2 * B * H) / (4 * (B + H))= in

U = 1 - (x / L)=

An = Ag2 - 2 * (tp + 0.0625) * t2= in

Ae = U * An= in

Rn/ = kips > kips (OK)

Whtimore Section

L = 2 lw tan 30 + B B = in

L = in

Whitmore width in Vertical Member = inWhitmore width in Horizontal Member = in

Check tension yielding on the Whitmore section = 1.67

Rn = Fy Aw

Rn = 36 x [ ( 8.619 - 0 - 1.67 ) x 0.375 ]

Rn = kips

Rn/ = kips > kips (OK)

Check block shear rupture of the gusset

5.00

8.619

0.0001.670

4.00

0.333

2.599

0.866

25.12

4.00

8.00

4.00

2.667

5.00

=Fub * Ae

2.00

=Fyb * Ag2

1.67

74.37

56.17

93.81

5.00

Page 6 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11Rn = Nominal Block Shear Strength of Gusset ( = 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

= in2

Agv = Gross Area with Shear Resistance= 2 x lw x tgusset

= in2

Anv = Net Area with Shear Resistance

= in2

Rn/ = kips > kips (OK)

Plate Buckling of Gusset Plate

Ap = Effective Plate Cross-sectional Area= L * t= in

Lcr = Plate Unbraced Length of Whitmore Section= in.

K = Effective Length Factor=

r = Radius of Gyration= t / 3.464= in.

K Lcr/r = > 25

From Specification E3

Fe = ()*E/(KL/r)= ksi > 0.44*Fy = 15.84 ksi

Fcr = [0.658^(Fy/Fe)]*Fy ksi

Rn/ = Allowable Strength in Compression=

= kips > kips (OK)

MEMBER 3:

Ap * Fcr1.67

62.98 5.00

0.108

43.785

149.30

32.54

75.90 5.00

3.95

1.200

1.50

3.00

3.00

3.232

Page 7 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11

Brace to Gusset Plate Weld:

Electrode Class = E700XX

Fu = Nominal Tensile Strength of Weld= Ksi

Fv = Allowable Weld Shear Strength= 0.6 Fu / 2= Ksi

w = Size of Weld= in. (Use for calculation)

Pw = Shear Capacity of 1/8" weld per Linear Inch= 0.707 * Fv * w= (0.707 * 21 * 0.125)= Kips/in

L1 = Length of Weld= in.

Vw = Weld Shear Capacity

= Pw * 4 L2Vw = Kips > Kips (OK)

Tension Yielding of the Brace:

Rn/ = Capacity from 'Limit State of Tension Yielding of Brace'

= kips > kips (OK)

Tension Rupture of the Brace:

Rn/ = Capacity from 'Limit State of Tension Rupture of Brace'

where:L = in (Length of Weld in HSS)

B = in (Width of HSS Section)

H = in (Height of HSS Section)

x = (B2 + 2 * B * H) / (4 * (B + H))= in

U = 1 - (x / L)=

70.00

21.00

0.1875 0.1250 in.

1.856

8.00

59.388 25.00

=Fyb * Ag3

1.67

195.57 25.00

=Fub * Ae

2.00

8.00

8.00

8.00

3.000

0.625

Page 8 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11An = Ag3 - 2 * (tp + 0.0625) * t3

= in

Ae = U * An= in

Rn/ = kips > kips (OK)

Whtimore Section

L = 2 lw tan 30 + B B = in

L = in

Whitmore width in Vertical Member = inWhitmore width in Horizontal Member = in

Check tension yielding on the Whitmore section = 1.67

Rn = Fy Aw

Rn = 36 x [ ( 17.238 - 0 - 0 ) x 0.375 ]

Rn = kips

Rn/ = kips > kips (OK)

Check block shear rupture of the gusset

Rn = Nominal Block Shear Strength of Gusset ( = 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

= in2

Agv = Gross Area with Shear Resistance= 2 x lw x tgusset

= in2

Anv = Net Area with Shear Resistance

= in2

Rn/ = kips > kips (OK)

Plate Buckling of Gusset Plate

Ap = Effective Plate Cross-sectional Area

6.896

4.310

124.99 25.00

8.00

17.238

0.0000.000

232.71

139.35 25.00

3.00

6.00

6.00

151.80 25.00

Page 9 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11= L * t= in

Lcr = Plate Unbraced Length of Whitmore Section= in.

K = Effective Length Factor=

r = Radius of Gyration= t / 3.464= in.

K Lcr/r = < 25

Thus Fcr = Fy = 36 ksi

Rn/ = Allowable Strength in Compression=

= kips > kips (OK)

Gusset Plate to Colum:

Solving for component forces:

[ (1) + (1.44) ]

= kips

[ (1) + (1.44) ]

= kips2.9

= 5 (1.44)

4.1

C1H

C1V =5 (1)

6.464

1.00

1.200

0.108

11.085

Ap * Fcr1.67

139.35 25.00

e2e1

C1 T2T3

C1v

C1H

A AT2v

T2H

L1 L2

T3

Page 10 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11

[ (1) + (1.2) ]

= kips

[ (1) + (1.2) ]

= kips

T3 = kips

e1 = ine2 = in

L1 = inL2 = in

L = L1 + L2L = in

The normal stress is,

ft = P/L + 3M/L

The in-plane stress is,

fv = V/L

Consider section A-A

P = T3 + T2V - C1V= kips

M = C1V x e1= kip-in

then,ft = kip/in

and,

V = C1H + T2H= kips

fv = kip/in

The resultant is,

f = [ (0.933) + (0.274) ]= kip/in

Check weld size

Fv = Allowable Weld Shear Strength

15.513.5

29.0

7.9

0.274

0.972

3.2

25.0

0.933

25.3

16.5

5.774.79

3.8

T2V =5 (1)

T2H =5 (1.2)

Page 11 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11= 0.6 Fexx / 2 [ Fexx = 70ksi]= Ksi

= deg= rad

w = Size of Weld= in. (Use for calculation)

Pw = Shear Capacity of 1/8" weld per Linear Inch= 0.707 * Fv * w * (1.0 + 0.50 sin

1.5)= (0.707 * 21 * 0.125) * (1.075)= Kips/in

2 Pw = Kips/in > Kips/in (OK)

Check plate stress

fa = ksi < 22 ksi (OK)

fv = ksi < 14 ksi (OK)

Check HSS wall

Force component perpendicular to HSS wall

Ft = ft x L = kips

HSS wall capacity

Rn/ = [ Fy t2 / (1- tp/B)] [ (2N/B + 4(1 -tp/B)0.5 ) Qf] ( = 1.5)

where:Fy =t =

tp =B =N =

Qf =

Rn/ = kips > kips (OK)

MEMBER 4:

Brace to Gusset Plate Weld:

0.4653/8

27.05

29.01

77.6063

8.00

27.05

46

= tan ( )0.2740.93316.37340.286

( = 1.5)tgusset 0.38

0.731 0.6Fy/ =

2.487 Fy/ =

fv =fv =

0.27

3.990 0.97

fa =ft =

0.93( = 1.67)

tgusset 0.375

21.00

0.1875 0.1250 in.

1.995

Page 12 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11Electrode Class = E700XX

Fu = Nominal Tensile Strength of Weld= Ksi

Fv = Allowable Weld Shear Strength= 0.6 Fu / 2= Ksi

w = Size of Weld= in. (Use for calculation)

Pw = Shear Capacity of 1/8" weld per Linear Inch= 0.707 * Fv * w= (0.707 * 21 * 0.125)= Kips/in

L1 = Length of Weld= in.

Vw = Weld Shear Capacity

= Pw * 4 L2Vw = Kips > Kips (OK)

Tension Yielding of the Brace:

Rn/ = Capacity from 'Limit State of Tension Yielding of Brace'

= kips > kips (OK)

Tension Rupture of the Brace:

Rn/ = Capacity from 'Limit State of Tension Rupture of Brace'

where:L = in (Length of Weld in HSS)

B = in (Width of HSS Section)

H = in (Height of HSS Section)

x = (B2 + 2 * B * H) / (4 * (B + H))= in

U = 1 - (x / L)=

An = Ag4 - 2 * (tp + 0.0625) * t4= in

70.00

21.00

0.1875 0.125 in.

1.856

8.00

59.388 20.00

=Fyb * Ag4

1.67

195.57 20.00

=Fub * Ae

2.00

8.00

8.00

8.00

3.000

0.625

6.896

Page 13 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11Ae = U * An

= in

Rn/ = kips > kips (OK)

Whtimore Section

L = Width of Whitmore SectionMinimum[ (2 x 8.00 tan 30 + 8) , 10 ]

L = in

Check tension yielding on the Whitmore section = 1.67

Rn = Fy Aw

Rn = 36 x [10 x 0.375 ]

Rn = kips

Rn/ = kips > kips (OK)

Check block shear rupture of the gusset

Rn = Nominal Block Shear Strength of Gusset ( = 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

= in2

Agv = Gross Area with Shear Resistance= 2 x lw x tgusset

= in2

Anv = Net Area with Shear Resistance

= in2

Rn/ = kips > kips (OK)

Plate Buckling of Gusset Plate

Ap = Effective Plate Cross-sectional Area= L * t= in

Lcr = Plate Unbraced Length of Whitmore Section= in.

4.310

124.99 20.00

10.000

135.00

80.84 20.00

3.00

6.00

6.00

151.80 20.00

3.750

1.00

Page 14 of 15

Design Calculation for Bracing Connection - Joint SWF-SF11K = Effective Length Factor

=

r = Radius of Gyration= t / 3.464= in.

K Lcr/r = < 25

Thus Fcr = Fy = 36 ksi

Rn/ = Allowable Strength in Compression=

= kips > kips (OK)

HSS wall capacity

Rn/ = [ Fy t2 / (1- tp/B)] [ (2N/B + 4(1 -tp/B)0.5 ) Qf] ( = 1.5)

where:Fy =t =

tp =B =N =

Qf =

Rn/ = kips > kips (OK)

46

1.200

0.108

11.085

Ap * Fcr1.67

80.84 20.00

0.4653/8

8.0010.0

1

44.5605 20.00

Page 15 of 15