AISC Steel Connection Design http://asp.civilbay.com/connect Moment Connection MC-1

Members & Components Summary

Member

Moment Connection

Code=AISC 360-10 LRFD

Column Section

W12X40

= 11.900

[in]

b_f

= 8.010

[in]

t_f

= 0.515

[in]

t_w

= 0.295

[in]

k_des

= 1.020

[in]

k_det

= 1.375

[in]

k₁

= 0.875

[in]

= 11.700

[in²]

S_x

= 51.50

[in³]

Z_x

= 57.00

[in³]

Steel Grade A992

F_y

= 50.0

[ksi]

F_u

= 65.0

[ksi]

Right Side Beam Section

W12X30

= 12.300

[in]

b_f

= 6.520

[in]

t_f

= 0.440

[in]

t_w

= 0.260

[in]

k_des

= 0.740

[in]

k_det

= 1.125

[in]

k₁

= 0.750

[in]

= 8.790

[in²]

S_x

= 38.60

[in³]

Z_x

= 43.10

[in³]

Steel Grade A992

F_y

= 50.0

[ksi]

F_u

= 65.0

[ksi]

Left Side Beam Section

W12X30

= 12.300

[in]

b_f

= 6.520

[in]

t_f

= 0.440

[in]

t_w

= 0.260

[in]

k_des

= 0.740

[in]

k_det

= 1.125

[in]

k₁

= 0.750

[in]

= 8.790

[in²]

S_x

= 38.60

[in³]

Z_x

= 43.10

[in³]

Steel Grade A992

F_y

= 50.0

[ksi]

F_u

= 65.0

[ksi]

Beam Flange Force Calc

Beam Flange Force - Right Side Beam

Beam section

d_b

= 12.300

[in]

t_fb

= 0.440

[in]

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

User input load

axial P_bR

= -25.00

[kips]

moment M_R

= 100.00

[kip-ft]

in tension

Beam flange force - top

P_f-TR

= P_bR / 2 + M_R / d_m

= 88.68

[kips]

Beam flange force - bottom

P_f-BR

= P_bR / 2 - M_R / d_m

= -113.68

[kips]

Beam Flange Force - Left Side Beam

Beam section

d_b

= 12.300

[in]

t_fb

= 0.440

[in]

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

User input load

axial P_bL

= -25.00

[kips]

moment M_L

= 45.00

[kip-ft]

in tension

Beam flange force - top

P_f-TL

= P_bL / 2 - M_L / d_m

= -58.03

[kips]

Beam flange force - bottom

P_f-BL

= P_bL / 2 + M_L / d_m

= 33.03

[kips]

Panel Zone Shear Force Calc

Column story shear

V_s

= from user input

= 0.00

[kips]

Panel zone shear force

V_p

= P_f-TR - P_f-TL - V_s

= 146.71

[kips]

Right Beam to Column

MC Connection

Code=AISC 360-10 LRFD

Result Summary

geometries & weld limitations = PASS

limit states max ratio

= 0.95

PASS

Geometry Restriction Checks

PASS

Min Bolt Edge Distance - Column Flange

Bolt diameter

d_b

= 0.750

[in]

Min edge distance allowed

L_e-min

= 1.000

[in]

AISC 14^th Table J3.4

Min edge distance in Column Flange

L_e

= 2.005

[in]

> L_e-min

Min Bolt Spacing - End Plate

Bolt diameter

d_b

= 0.750

[in]

Min bolt spacing allowed

L_s-min

= 2.667 d_b

= 2.000

[in]

AISC 14^th J3.3

Min Bolt spacing in End Plate

L_s

= 3.690

[in]

> L_s-min

Min Bolt Edge Distance - End Plate

Bolt diameter

d_b

= 0.750

[in]

Min edge distance allowed

L_e-min

= 1.000

[in]

AISC 14^th Table J3.4

Min edge distance in End Plate

L_e

= 1.375

[in]

> L_e-min

Max Bolt Edge Distance - End Plate

Connecting plate thickness

t_p

= 0.750

[in]

Max edge distance allowed

L_e-max

= min ( 12t , 6" )

= 6.000

[in]

AISC 14^th J3.5

Max edge distance in End Plate

L_e

= 2.245

[in]

< L_e-max

Beam Flange Fillet Weld Limitation

PASS

Min Fillet Weld Size

Thinner part joined thickness

= 0.440

[in]

Min fillet weld size allowed

w_min

= 0.188

[in]

AISC 14^th Table J2.4

Fillet weld size provided

= 0.313

[in]

> w_min

Min Fillet Weld Length

Fillet weld size provided

= 0.313

[in]

Min fillet weld length allowed

L_min

= 4 x w

= 1.250

[in]

AISC 14^th J2.2b

Min fillet weld length

= 0.5 b_fb - k_1b

= 2.510

[in]

> L_min

Beam Web Fillet Weld Limitation

PASS

Min Fillet Weld Size

Thinner part joined thickness

= 0.260

[in]

Min fillet weld size allowed

w_min

= 0.188

[in]

AISC 14^th Table J2.4

Fillet weld size provided

= 0.313

[in]

> w_min

Min Fillet Weld Length

Fillet weld size provided

= 0.313

[in]

Min fillet weld length allowed

L_min

= 4 x w

= 1.250

[in]

AISC 14^th J2.2b

Min fillet weld length

= 0.5 d_b - k_b

= 5.025

[in]

> L_min

Min Beam Web to End Plate Fillet Weld Size

Beam web to end-plate fillet weld in the tension-bolt region to develop the yield strength of the beam web

AISC DG4 Page 9 Item 7

Shear resistance factor-LRFD

φ_v

= 0.90

AISC 14^th G1

Fillet weld shear strength

φ R_n-w

= 1.392

[kip/in]

AISC 14^th Eq 8-2a

Fillet weld strength φ R_n-w x 1.5 x 2 to account for 90° load angle when it's in tension and double fillet

Min double fillet weld size to match beam web yield strength

D_min

= φ_vF_yb t_wb / ( φ R_n-w x 1.5 x 2 )

= 2.802

[1/16 "]

Fillet weld size provided

= 5.000

[1/16 "]

> D_min

Verify AISC DG4 Bolt No Prying Assumption

AISC DG4 Is Used

Bolt Moment Strength (No Prying)

bolt grade

= A325-N

F_t

= 90.0

[ksi]

AISC 14^th Table J3.2

bolt dia d_b

= 0.750

[in]

bolt area A_b

= 0.442

[in²]

Bolt norminal tensile strength

P_t

= F_t A_b

= 39.76

[kips]

AISC 14^th Eq J3-1

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

Bolt moment strength (no prying)

M_np

= 2 P_t ( h₀ + h₁ )

= 157.19

[kip-ft]

AISC DG4 Eq 3.7

Bolt resistance factor-LRFD

= 0.75

AISC 14^th Eq J3-1

φ M_np

= 117.89

[kip-ft]

End Plate Bending Strength

End plate width

b_plate

= 8.490

[in]

thickness t_p

= 0.750

[in]

Beam flange width

b_fb

= 6.520

[in]

Effective end plate width

b_p

= min ( b_plate , b_fb + 1" )

= 7.520

[in]

AISC DG4 Page 9 item 5

End plate yield strength

F_yp

= 50.0

[ksi]

See AISC DG4 Table 3.1 for all formulas to derive the following parameters

AISC DG4 Table 3.1

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

= 4.000

[in]

p_fi

= 1.625

[in]

p_fo

= 1.625

[in]

= 2.742

[in]

Y_p

= 88.61

[in]

Flexure resistance factor-LRFD

φ_b

= 0.90

AISC 14^th F1 (1)

End plate bending strength

φ_bM_pl

= φ_b F_yp t2p Y_p

= 186.90

[kip-ft]

AISC DG4 Table 3.1

Check thick end plate condition

φ_bM_pl >= 1.11 X φ M_np

AISC DG4 Eq 3.33

ratio

= 0.70 thick plate

Column Flange Bending Strength

See AISC DG4 Table 3.4 for all formulas to derive the following parameters

AISC DG4 Table 3.4

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

*** Stiffened Column Flange Case ***

Column section

b_fc

= 8.010

[in]

t_fc

= 0.515

[in]

F_yc

= 50.0

[ksi]

bolt gage g

= 4.000

[in]

= 2.830

[in]

= 3.690

[in]

Stiffener plate thickness

t_s

= 0.500

[in]

p_si

= 1.595

[in]

p_so

= 1.595

[in]

Y_c

= 145.6

[in]

Flexure resistance factor-LRFD

φ_b

= 0.90

AISC 14^th F1 (1)

Column flange bending strength

φ_bM_cf

= φ_b F_yc t2fc Y_c

= 144.82

[kip-ft]

AISC DG4 Table 3.4

Check thick column flange condition

φ_bM_cf >= 1.11 X φ M_np

AISC DG4 Eq 3.35

ratio

= 0.90 thick plate

The thick end plate and column flange conditions are met. AISG DG4 is used and
no bolt prying is considered

AISC DG4 Eq 3.33 & 3.35

Bolt Moment Strength (No Prying)

ratio = 113.68 / 119.28

= 0.95

PASS

bolt grade

= A325-N

F_t

= 90.0

[ksi]

AISC 14^th Table J3.2

bolt dia d_b

= 0.750

[in]

bolt area A_b

= 0.442

[in²]

Bolt norminal tensile strength

P_t

= F_t A_b

= 39.76

[kips]

AISC 14^th Eq J3-1

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 113.68

[kips]

Flange force resistance by bolt

F_n

= 2 P_t ( h₀ + h₁ ) / d_m

= 159.04

[kips]

AISC DG4 Eq 3.7

Bolt resistance factor-LRFD

= 0.75

AISC 14^th Eq J3-1

φ F_n

= 119.28

[kips]

AISC DG4 Eq 3.7

ratio

= 0.95

> P_{uf_t}

Bolt Shear Strength

ratio = 30.00 / 71.57

= 0.42

PASS

Bolt shear stress

bolt grade

= A325-N

F_nv

= 54.0

[ksi]

AISC 14^th Table J3.2

bolt dia d_b

= 0.750

[in]

bolt area A_b

= 0.442

[in²]

Number of bolt carried shear

n_s

= 4.0

shear plane m

= 1

Required shear strength

V_u

= 30.00

[kips]

Bolt shear strength

R_n

= F_nv A_b n_s m C_ec

= 95.43

[kips]

AISC 14^th Eq J3-1

Bolt resistance factor-LRFD

= 0.75

AISC 14^th Eq J3-1

φ R_n

= 71.57

[kips]

ratio

= 0.42

> V_u

Bolt Bearing/TearOut Strength on End Plate

ratio = 30.00 / 71.57

= 0.42

PASS

Single Bolt Shear Strength

Bolt shear stress

bolt grade

= A325-N

F_nv

= 54.0

[ksi]

AISC 14^th Table J3.2

bolt dia d_b

= 0.750

[in]

bolt area A_b

= 0.442

[in²]

Single bolt shear strength

R_n-bolt

= F_nv A_b

= 23.86

[kips]

AISC 14^th Eq J3-1

Bolt Bearing/TearOut Strength on Plate

Bolt hole diameter

bolt dia d_b

= ³⁄₄

[in]

bolt hole dia d_h

= ¹³⁄₁₆

[in]

AISC 14^th Table J3.3

Bolt spacing & edge distance

spacing L_s

= 3.690

[in]

edge distance L_e

= 1.375

[in]

Plate tensile strength

F_u

= 65.0

[ksi]

Plate thickness

= 0.750

[in]

Interior Bolt

Bolt hole edge clear distance

L_c

= L_s - d_h

= 2.878

[in]

Bolt tear out/bearing strength

R_n-t&b-in

= 1.5 L_c t F_u ≤ 3.0 d_b t F_u

AISC 14^th Eq J3-6b

= 210.42 ≤ 109.69

= 109.69

[kips]

Bolt strength at interior

R_n-in

= min ( R_n-t&b-in , R_n-bolt )

= 23.86

[kips]

Edge Bolt

Bolt hole edge clear distance

L_c

= L_e - d_h / 2

= 0.969

[in]

Bolt tear out/bearing strength

R_n-t&b-ed

= 1.5 L_c t F_u ≤ 3.0 d_b t F_u

AISC 14^th Eq J3-6b

= 70.84 ≤ 109.69

= 70.84

[kips]

Bolt strength at edge

R_n-ed

= min ( R_n-t&b-ed , R_n-bolt )

= 23.86

[kips]

Number of bolt

interior n_in

= 2

edge n_ed

= 2

Bolt bearing strength for all bolts

R_n

= n_in R_n-in + n_ed R_n-ed

= 95.43

[kips]

Required shear strength

V_u

= 30.00

[kips]

Bolt resistance factor-LRFD

= 0.75

AISC 14^th J3-10

φ R_n

= 71.57

[kips]

ratio

= 0.42

> V_u

Bolt Bearing/TearOut Strength on Column Flange

ratio = 30.00 / 71.57

= 0.42

PASS

Single Bolt Shear Strength

Bolt shear stress

bolt grade

= A325-N

F_nv

= 54.0

[ksi]

AISC 14^th Table J3.2

bolt dia d_b

= 0.750

[in]

bolt area A_b

= 0.442

[in²]

Single bolt shear strength

R_n-bolt

= F_nv A_b

= 23.86

[kips]

AISC 14^th Eq J3-1

Bolt Bearing/TearOut Strength on Plate

Bolt hole diameter

bolt dia d_b

= ³⁄₄

[in]

bolt hole dia d_h

= ¹³⁄₁₆

[in]

AISC 14^th Table J3.3

Bolt spacing

spacing L_s

= 3.690

[in]

Plate tensile strength

F_u

= 65.0

[ksi]

Plate thickness

= 0.515

[in]

Interior Bolt

Bolt hole edge clear distance

L_c

= L_s - d_h

= 2.878

[in]

Bolt tear out/bearing strength

R_n-t&b-in

= 1.5 L_c t F_u ≤ 3.0 d_b t m F_u

AISC 14^th Eq J3-6b

= 144.49 ≤ 75.32

= 75.32

[kips]

Bolt strength at interior

R_n-in

= min ( R_n-t&b-in , R_n-bolt )

= 23.86

[kips]

Number of bolt

interior n_in

= 4

Bolt bearing strength for all bolts

R_n

= n_in R_n-in

= 95.43

[kips]

Required shear strength

V_u

= 30.00

[kips]

Bolt resistance factor-LRFD

= 0.75

AISC 14^th J3-10

φ R_n

= 71.57

[kips]

ratio

= 0.42

> V_u

End Plate Flexural Yielding

ratio = 113.68 / 189.11

= 0.60

PASS

End Plate Bending Strength

End plate width

b_plate

= 8.490

[in]

thickness t_p

= 0.750

[in]

Beam flange width

b_fb

= 6.520

[in]

Effective end plate width

b_p

= min ( b_plate , b_fb + 1" )

= 7.520

[in]

AISC DG4 Page 9 item 5

End plate yield strength

F_yp

= 50.0

[ksi]

See AISC DG4 Table 3.1 for all formulas to derive the following parameters

AISC DG4 Table 3.1

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

= 4.000

[in]

p_fi

= 1.625

[in]

p_fo

= 1.625

[in]

= 2.742

[in]

Y_p

= 88.61

[in]

Flexure resistance factor-LRFD

φ_b

= 0.90

AISC 14^th F1 (1)

End plate bending strength

φ_bM_pl

= φ_b F_yp t2p Y_p

= 186.90

[kip-ft]

AISC DG4 Table 3.1

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 113.68

[kips]

Flange force provided by end plate bending

φ R_pl

= φ M_pl / d_m

= 189.11

[kips]

AISC DG4 Eq 3.10

ratio

= 0.60

> P_{uf_t}

End Plate Shear Yielding

ratio = 56.84 / 169.20

= 0.34

PASS

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 56.84

[kips]

End plate width

b_plate

= 8.490

[in]

thickness t_p

= 0.750

[in]

Beam flange width

b_fb

= 6.520

[in]

Effective end plate width

b_p

= min ( b_plate , b_fb + 1" )

= 7.520

[in]

AISC DG4 Page 9 item 5

Plate Shear Yielding Check

Plate size

width b_p

= 7.520

[in]

thickness t_p

= 0.750

[in]

Plate yield strength

F_y

= 50.0

[ksi]

Plate gross area in shear

A_gv

= b_p t_p

= 5.640

[in²]

Shear force required

0.5 P_{uf_t}

= 56.84

[kips]

Plate shear yielding strength

R_n

= 0.6 F_y A_gv

= 169.20

[kips]

AISC 14^th Eq J4-3

Resistance factor-LRFD

= 1.00

AISC 14^th Eq J4-3

φ R_n

= 169.20

[kips]

ratio

= 0.34

> 0.5 P_{uf_t}

End Plate Shear Rupture

ratio = 56.84 / 126.58

= 0.45

PASS

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 56.84

[kips]

End plate width

b_plate

= 8.490

[in]

thickness t_p

= 0.750

[in]

Beam flange width

b_fb

= 6.520

[in]

Effective end plate width

b_p

= min ( b_plate , b_fb + 1" )

= 7.520

[in]

AISC DG4 Page 9 item 5

Plate Shear Rupture Check

Bolt hole diameter

bolt dia d_b

= ³⁄₄

[in]

bolt hole dia d_h

= ⁷⁄₈

[in]

AISC 14^th B4.3b

Number of bolt

= 2

Plate size

width b_p

= 7.520

[in]

thickness t_p

= 0.750

[in]

Plate tensile strength

F_u

= 65.0

[ksi]

Plate net area in shear

A_nv

= ( b_p - n d_h ) t_p

= 4.328

[in²]

Shear force required

0.5 P_{uf_t}

= 56.84

[kips]

Plate shear rupture strength

R_n

= 0.6 F_u A_nv

= 168.77

[kips]

AISC 14^th Eq J4-4

Resistance factor-LRFD

= 0.75

AISC 14^th Eq J4-4

φ R_n

= 126.58

[kips]

ratio

= 0.45

> 0.5 P_{uf_t}

Beam Flange Weld Strength

ratio = 113.68 / 120.47

= 0.94

PASS

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 113.68

[kips]

Fillet weld length - double fillet

= [b_fb + ( b_fb - 2k_1b )] /2 as dbl fillet

= 5.770

[in]

Fillet Weld Strength Check

Fillet weld leg size

= ⁵⁄₁₆

[in]

load angle θ

= 90.0

[°]

Electrode strength

F_EXX

= 70.0

[ksi]

strength coeff C₁

= 1.00

AISC 14^th Table 8-3

Number of weld line

= 2 for double fillet

Load angle coefficient

C₂

= ( 1 + 0.5 sin^1.5 θ )

= 1.50

AISC 14^th Page 8-9

Fillet weld shear strength

R_n-w

= 0.6 (C₁ x 70 ksi) 0.707 w n C₂

= 27.838

[kip/in]

AISC 14^th Eq 8-1

Base metal - beam flange

thickness t

= 0.440

[in]

tensile F_u

= 65.0

[ksi]

Base metal - beam flange is in tension, tensile rupture as per AISC 14^th Eq J4-2 is checked

AISC 14^th J2.4

Base metal tensile rupture

R_n-b

= F_u t

= 28.600

[kip/in]

AISC 14^th Eq J4-2

Double fillet linear shear strength

R_n

= min ( R_n-w , R_n-b )

= 27.838

[kip/in]

AISC 14^th Eq 9-2

Resistance factor-LRFD

= 0.75

AISC 14^th Eq 8-1

φ R_n

= 20.879

[kip/in]

Shear resistance required

P_{uf_t}

= 113.68

[kips]

Fillet weld length - double fillet

= 5.770

[in]

Shear resistance provided

φ F_n

= φ R_n x L

= 120.47

[kips]

ratio

= 0.94

> P_{uf_t}

Beam Web Weld Strength

ratio = 30.00 / 38.22

= 0.79

PASS

Beam Web Effective Weld Length Calc

Beam section

d_b

= 12.300

[in]

t_fb

= 0.440

[in]

k_b

= 1.125

[in]

Bolt diameter

d_bolt

= 0.750

[in]

bolt inner pitch p_fi

= 1.625

[in]

Effective weld length case 1

L₁

= 0.5 d_b - k_b

= 5.025

[in]

AISC DG4 Page 38

Effective weld length case 2

L₂

= d_b - 2t_fb - p_fi - 2 d_bolt

= 8.295

[in]

AISC DG4 Page 38

Fillet weld length - double fillet

= min( L₁ , L₂ )

= 5.025

[in]

Fillet Weld Strength Check

Fillet weld leg size

= ⁵⁄₁₆

[in]

load angle θ

= 0.0

[°]

Electrode strength

F_EXX

= 70.0

[ksi]

strength coeff C₁

= 1.00

AISC 14^th Table 8-3

Number of weld line

= 2 for double fillet

Load angle coefficient

C₂

= ( 1 + 0.5 sin^1.5 θ )

= 1.00

AISC 14^th Page 8-9

Fillet weld shear strength

R_n-w

= 0.6 (C₁ x 70 ksi) 0.707 w n C₂

= 18.559

[kip/in]

AISC 14^th Eq 8-1

Base metal - beam web

thickness t

= 0.260

[in]

tensile F_u

= 65.0

[ksi]

Base metal - beam web is in shear, shear rupture as per AISC 14^th Eq J4-4 is checked

AISC 14^th J2.4

Base metal shear rupture

R_n-b

= 0.6 F_u t

= 10.140

[kip/in]

AISC 14^th Eq J4-4

Double fillet linear shear strength

R_n

= min ( R_n-w , R_n-b )

= 10.140

[kip/in]

AISC 14^th Eq 9-2

Resistance factor-LRFD

= 0.75

AISC 14^th Eq 8-1

φ R_n

= 7.605

[kip/in]

Shear resistance required

V_u

= 30.00

[kips]

Fillet weld length - double fillet

= 5.025

[in]

Shear resistance provided

φ F_n

= φ R_n x L

= 38.22

[kips]

ratio

= 0.79

> V_u

Column Flexural Yielding

ratio = 113.68 / 146.53

= 0.78

PASS

Column Flange Bending Strength

See AISC DG4 Table 3.4 for all formulas to derive the following parameters

AISC DG4 Table 3.4

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

*** Stiffened Column Flange Case ***

Column section

b_fc

= 8.010

[in]

t_fc

= 0.515

[in]

F_yc

= 50.0

[ksi]

bolt gage g

= 4.000

[in]

= 2.830

[in]

= 3.690

[in]

Stiffener plate thickness

t_s

= 0.500

[in]

p_si

= 1.595

[in]

p_so

= 1.595

[in]

Y_c

= 145.6

[in]

Flexure resistance factor-LRFD

φ_b

= 0.90

AISC 14^th F1 (1)

Column flange bending strength

φ_bM_cf

= φ_b F_yc t2fc Y_c

= 144.82

[kip-ft]

AISC DG4 Table 3.4

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 113.68

[kips]

Flange force provided by column flange bending

φ R_cf

= φ M_cf / d_m

= 146.53

[kips]

AISC DG4 Eq 3.21

ratio

= 0.78

> P_{uf_t}

Column Web Yielding

ratio = 113.68 / 290.95

= 0.39

PASS

Column web thickness

t_wc

= 0.295

[in]

yield F_y

= 50.0

[ksi]

Doubler plate thickness

t_dp

= 0.375

[in]

yield F_ydp

= 50.0

[ksi]

Equivalent web thickness when considering doubler plate

t_w-eq

= t_wc + t_dp x F_ydp / F_y

= 0.670

[in]

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force in demand

P_uf

= max ( P_{uf_t} , P_{uf_c} )

= 113.68

[kips]

AISC DG13 Eq 4.2-1

Column section

d_c

= 11.900

[in]

t_fc

= 0.515

[in]

t_wc

= 0.295

[in]

k_c

= 1.020

[in]

Column yield strength

F_yc

= 50.0

[ksi]

Top column condition

it's not a top column case

C_t

= 1.0

AISC DG4 Eq 3.24

Beam flange fillet weld size

= 0.313

[in]

beam flange t_fb

= 0.440

[in]

Length of bearing

= t_fb + 2 w

= 1.065

[in]

AISC DG4 Eq 3.24

End plate thickness

t_p

= 0.750

[in]

Column web yielding strength

R_n

= C_t ( 6 k_c + N + 2 t_p ) F_yc t_w-eq

= 290.95

[kips]

AISC DG4 Eq 3.24

Resistance factor-LRFD

= 1.00

AISC 14^th J10.2

φ R_n

= 290.95

[kips]

ratio

= 0.39

> P_uf

Column Web Buckling

ratio = 88.68 / 206.83

= 0.43

PASS

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force required in compression

P_{uf_c}

= P_u / 2 - M_u / d_m

= 88.68

[kips]

Column section

d_c

= 11.900

[in]

t_fc

= 0.515

[in]

t_wc

= 0.295

[in]

k_c

= 1.020

[in]

= d_c - 2 k_c

= 9.860

[in]

Column yield strength

F_yc

= 50.0

[ksi]

E_c

= 29000

[ksi]

Top column condition

it's not a top column case

C_t

= 1.0

AISC 14^th J10.5

Column web buckling strength

R_n1

C_t 24 t3wc √E_c F_yc/h

= 75.25

[kips]

AISC 14^th Eq J10-8

Doubler plate thickness

t_dp

= 0.375

[in]

yield F_ydp

= 50.0

[ksi]

Doubler plate buckling strength

R_n2

C_t 24 t3dp √E_c F_ydp/h

= 154.57

[kips]

AISC 14^th Eq J10-8

Total buckling strength

R_n

= R_n1 + R_n2

= 229.81

[kips]

Resistance factor-LRFD

= 0.90

AISC 14^th J10.5

φ R_n

= 206.83

[kips]

ratio

= 0.43

> P_{uf_c}

Column Web Crippling

ratio = 88.68 / 273.27

= 0.32

PASS

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force required in compression

P_{uf_c}

= P_u / 2 - M_u / d_m

= 88.68

[kips]

Column section

d_c

= 11.900

[in]

t_fc

= 0.515

[in]

t_wc

= 0.295

[in]

k_c

= 1.020

[in]

Column yield strength

F_yc

= 50.0

[ksi]

E_c

= 29000

[ksi]

Beam flange fillet weld size

= 0.313

[in]

beam flange t_fb

= 0.440

[in]

End plate thickness

t_p

= 0.750

[in]

Length of bearing

l_b

= t_fb + 2 w + 2 t_p

= 2.565

[in]

Distance from top of column to top of beam flange

d_end-flg

= 4.000

[in]

Top column condition

it's not a top column case, use Eq J10-4

AISC 14^th J10.3 (a)

Column web crippling strength

R_n1

= 0.8 t2wc [1+3

l_b/d_c

(

t_wc/t_fc

)^1.5]x

= 141.82

[kips]

AISC 14^th Eq J10-4

(

E_c F_yc t_fc/t_wc

)^0.5

Doubler plate thickness

t_dp

= 0.375

[in]

yield F_ydp

= 50.0

[ksi]

Doubler plate crippling strength

R_n2

= 0.8 t2dp [1+3

l_b/d_c

(

t_dp/t_fc

)^1.5]x

= 222.54

[kips]

AISC 14^th Eq J10-4

(

E_c F_ydp t_fc/t_dp

)^0.5

Total crippling strength

R_n

= R_n1 + R_n2

= 364.36

[kips]

Resistance factor-LRFD

= 0.75

AISC 14^th J10.3

φ R_n

= 273.27

[kips]

ratio

= 0.32

> P_{uf_c}

Column Panel Zone Shear

146.71 / 94.78

N/A

Panel zone shear force

V_p

= P_f-TR - P_f-TL - V_s

= 146.71

[kips]

Column section

d_c

= 11.900

[in]

t_wc

= 0.295

[in]

A_c

= 11.700

[in²]

F_yc

= 50.0

[ksi]

Column axial compression - user input

P_r

= 0.00

[kips]

P_c

= P_y = F_yc A_c

= 585.00

[kips]

AISC 14^th J10.6

P_r ≤ 0.4 P_c , use Eq J10-9

AISC 14^th Eq J10-9

Web panel zone capacity

R_n

= 0.6 F_yc d_c t_wc

= 105.32

[kips]

AISC 14^th Eq J10-9

Resistance factor-LRFD

= 0.90

AISC 14^th J10.6

φ R_n

= 94.78

[kips]

Unbalanced force to be resisted by doubler plate

V_dp

= R_p - φ R_n

= 51.93

[kips]

Doubler Geometry Restriction

PASS

Min Doubler Thickness to Allow for Proper Beveling of Plate

AISC DG13 Eq 4.4-4

Column section

t_fc

= 0.515

[in]

k_c

= 1.020

[in]

Allowed fillet encroachment

r_e

= 0.250

[in]

AISC 14^th Fig 10-3

Min doubler plate thickness

t_pmin

= k_c - t_fc - r_e

= 0.255

[in]

AISC DG13 Eq 4.4-4

Doubler plate thickness

t_dp

= 0.375

[in]

> t_pmin

Min Doubler Thickness to Avoid Shear Buckling of Plate

AISC DG13 Eq 4.4-5

Column section

d_c

= 11.900

[in]

k_c

= 1.020

[in]

= d_c - 2 k_c

= 9.860

[in]

Doubler plate steel

F_y

= 50.0

[ksi]

= 29000

[ksi]

Min doubler plate thickness

t_pmin

= h / 2.24 √E / F_y

= 0.183

[in]

AISC 14^th G2.1 (a)

Doubler plate thickness

t_dp

= 0.375

[in]

> t_pmin

Doubler Plate Shear Yield

ratio = 51.93 / 133.88

= 0.39

PASS

Doubler plate thickness

t_dp

= 0.375

[in]

yield strength F_y

= 50.0

[ksi]

Number of doubler

N_dbl

= 1 for one side

Column depth

d_c

= 11.900

[in]

Area of web

A_w

= t_dp x d_c

= 4.463

[in²]

AISC DG13 Eq 4.4-1

Shear coefficient

C_v

= 1.0

AISC 14^th Eq G2-2

Doubler plate shear in demand

R_dp

= unbalanced force from column

= 51.93

[kips]

panel zone shear calc

Doubler plate shear strength

R_n

= N_dbl 0.6 F_y A_w C_v

= 133.88

[kips]

AISC 14^th Eq G2-1

Resistance factor-LRFD

= 1.00

AISC 14^th G2.1 (a)

φ R_n

= 133.88

[kips]

ratio

= 0.39

> R_dp

Doubler to Column Flange Fillet Weld Limitation

PASS

Min Fillet Weld Size

Thinner part joined thickness

= 0.375

[in]

Min fillet weld size allowed

w_min

= 0.188

[in]

AISC 14^th Table J2.4

Fillet weld size provided

= 0.250

[in]

> w_min

Min Fillet Weld Length

Fillet weld size provided

= 0.250

[in]

Min fillet weld length allowed

L_min

= 4 x w

= 1.000

[in]

AISC 14^th J2.2b

Min fillet weld length

= d_b + ( 3 k_c + t_p )x 2 Ends

= 19.920

[in]

> L_min

Doubler to Column Web Fillet Weld Limitation

PASS

Min Fillet Weld Size

Thinner part joined thickness

= 0.295

[in]

Min fillet weld size allowed

w_min

= 0.188

[in]

AISC 14^th Table J2.4

Fillet weld size provided

= 0.250

[in]

> w_min

Min Fillet Weld Length

Fillet weld size provided

= 0.250

[in]

Min fillet weld length allowed

L_min

= 4 x w

= 1.000

[in]

AISC 14^th J2.2b

Min fillet weld length

= d_c - 2 x k_c

= 9.860

[in]

> L_min

Doubler Weld Strength at Column Flange

ratio = 51.93 / 110.91

= 0.47

PASS

Doubler Plate to Column Flange Weld Length Calc

Beam section

d_b

= 12.300

[in]

column section k_c

= 1.020

[in]

End plate thickness

t_p

= 0.750

[in]

Doubler plate to column flange weld length - single fillet

= d_b +(3 k_c + t_p ) x 2 ends

= 19.920

[in]

AISC DG13 Fig 4-3

Fillet Weld Strength Check

Fillet weld leg size

= ¹⁄₄

[in]

load angle θ

= 0.0

[°]

Electrode strength

F_EXX

= 70.0

[ksi]

strength coeff C₁

= 1.00

AISC 14^th Table 8-3

Number of weld line

= 1 for single fillet

Load angle coefficient

C₂

= ( 1 + 0.5 sin^1.5 θ )

= 1.00

AISC 14^th Page 8-9

Fillet weld shear strength

R_n-w

= 0.6 (C₁ x 70 ksi) 0.707 w n C₂

= 7.424

[kip/in]

AISC 14^th Eq 8-1

Base metal - doubler plate

thickness t

= 0.375

[in]

tensile F_u

= 65.0

[ksi]

Base metal - doubler plate is in shear, shear rupture as per AISC 14^th Eq J4-4 is checked

AISC 14^th J2.4

Base metal shear rupture

R_n-b

= 0.6 F_u t

= 14.625

[kip/in]

AISC 14^th Eq J4-4

Single fillet linear shear strength

R_n

= min ( R_n-w , R_n-b )

= 7.424

[kip/in]

AISC 14^th Eq 9-2

Resistance factor-LRFD

= 0.75

AISC 14^th Eq 8-1

φ R_n

= 5.568

[kip/in]

Shear resistance required

R_dp

= 51.93

[kips]

Fillet weld length - single fillet

= 19.920

[in]

Shear resistance provided

φ F_n

= φ R_n x L

= 110.91

[kips]

ratio

= 0.47

> R_dp

Doubler Weld Strength at Column Web

ratio = 51.93 / 54.90

= 0.95

PASS

Doubler Plate to Column Web Weld Length Calc

Column section

d_c

= 11.900

[in]

k_c

= 1.020

[in]

Doubler plate to column web weld length - single fillet

= d_c - 2 x k_c

= 9.860

[in]

Fillet Weld Strength Check

Fillet weld leg size

= ¹⁄₄

[in]

load angle θ

= 0.0

[°]

Electrode strength

F_EXX

= 70.0

[ksi]

strength coeff C₁

= 1.00

AISC 14^th Table 8-3

Number of weld line

= 1 for single fillet

Load angle coefficient

C₂

= ( 1 + 0.5 sin^1.5 θ )

= 1.00

AISC 14^th Page 8-9

Fillet weld shear strength

R_n-w

= 0.6 (C₁ x 70 ksi) 0.707 w n C₂

= 7.424

[kip/in]

AISC 14^th Eq 8-1

Base metal - doubler plate

thickness t

= 0.375

[in]

tensile F_u

= 65.0

[ksi]

Base metal - doubler plate is in shear, shear rupture as per AISC 14^th Eq J4-4 is checked

AISC 14^th J2.4

Base metal shear rupture

R_n-b

= 0.6 F_u t

= 14.625

[kip/in]

AISC 14^th Eq J4-4

Single fillet linear shear strength

R_n

= min ( R_n-w , R_n-b )

= 7.424

[kip/in]

AISC 14^th Eq 9-2

Resistance factor-LRFD

= 0.75

AISC 14^th Eq 8-1

φ R_n

= 5.568

[kip/in]

Shear resistance required

R_dp

= 51.93

[kips]

Fillet weld length - single fillet

= 9.860

[in]

Shear resistance provided

φ F_n

= φ R_n x L

= 54.90

[kips]

ratio

= 0.95

> R_dp

Left Beam to Column

MC Connection

Code=AISC 360-10 LRFD

Result Summary

geometries & weld limitations = PASS

limit states max ratio

= 0.95

PASS

Geometry Restriction Checks

PASS

Min Bolt Edge Distance - Column Flange

Bolt diameter

d_b

= 0.750

[in]

Min edge distance allowed

L_e-min

= 1.000

[in]

AISC 14^th Table J3.4

Min edge distance in Column Flange

L_e

= 2.005

[in]

> L_e-min

Min Bolt Spacing - End Plate

Bolt diameter

d_b

= 0.750

[in]

Min bolt spacing allowed

L_s-min

= 2.667 d_b

= 2.000

[in]

AISC 14^th J3.3

Min Bolt spacing in End Plate

L_s

= 3.690

[in]

> L_s-min

Min Bolt Edge Distance - End Plate

Bolt diameter

d_b

= 0.750

[in]

Min edge distance allowed

L_e-min

= 1.000

[in]

AISC 14^th Table J3.4

Min edge distance in End Plate

L_e

= 1.375

[in]

> L_e-min

Max Bolt Edge Distance - End Plate

Connecting plate thickness

t_p

= 0.750

[in]

Max edge distance allowed

L_e-max

= min ( 12t , 6" )

= 6.000

[in]

AISC 14^th J3.5

Max edge distance in End Plate

L_e

= 2.245

[in]

< L_e-max

Beam Flange Fillet Weld Limitation

PASS

Min Fillet Weld Size

Thinner part joined thickness

= 0.440

[in]

Min fillet weld size allowed

w_min

= 0.188

[in]

AISC 14^th Table J2.4

Fillet weld size provided

= 0.313

[in]

> w_min

Min Fillet Weld Length

Fillet weld size provided

= 0.313

[in]

Min fillet weld length allowed

L_min

= 4 x w

= 1.250

[in]

AISC 14^th J2.2b

Min fillet weld length

= 0.5 b_fb - k_1b

= 2.510

[in]

> L_min

Beam Web Fillet Weld Limitation

PASS

Min Fillet Weld Size

Thinner part joined thickness

= 0.260

[in]

Min fillet weld size allowed

w_min

= 0.188

[in]

AISC 14^th Table J2.4

Fillet weld size provided

= 0.313

[in]

> w_min

Min Fillet Weld Length

Fillet weld size provided

= 0.313

[in]

Min fillet weld length allowed

L_min

= 4 x w

= 1.250

[in]

AISC 14^th J2.2b

Min fillet weld length

= 0.5 d_b - k_b

= 5.025

[in]

> L_min

Min Beam Web to End Plate Fillet Weld Size

Beam web to end-plate fillet weld in the tension-bolt region to develop the yield strength of the beam web

AISC DG4 Page 9 Item 7

Shear resistance factor-LRFD

φ_v

= 0.90

AISC 14^th G1

Fillet weld shear strength

φ R_n-w

= 1.392

[kip/in]

AISC 14^th Eq 8-2a

Fillet weld strength φ R_n-w x 1.5 x 2 to account for 90° load angle when it's in tension and double fillet

Min double fillet weld size to match beam web yield strength

D_min

= φ_vF_yb t_wb / ( φ R_n-w x 1.5 x 2 )

= 2.802

[1/16 "]

Fillet weld size provided

= 5.000

[1/16 "]

> D_min

Verify AISC DG4 Bolt No Prying Assumption

AISC DG4 Is Used

Bolt Moment Strength (No Prying)

bolt grade

= A325-N

F_t

= 90.0

[ksi]

AISC 14^th Table J3.2

bolt dia d_b

= 0.750

[in]

bolt area A_b

= 0.442

[in²]

Bolt norminal tensile strength

P_t

= F_t A_b

= 39.76

[kips]

AISC 14^th Eq J3-1

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

Bolt moment strength (no prying)

M_np

= 2 P_t ( h₀ + h₁ )

= 157.19

[kip-ft]

AISC DG4 Eq 3.7

Bolt resistance factor-LRFD

= 0.75

AISC 14^th Eq J3-1

φ M_np

= 117.89

[kip-ft]

End Plate Bending Strength

End plate width

b_plate

= 8.490

[in]

thickness t_p

= 0.750

[in]

Beam flange width

b_fb

= 6.520

[in]

Effective end plate width

b_p

= min ( b_plate , b_fb + 1" )

= 7.520

[in]

AISC DG4 Page 9 item 5

End plate yield strength

F_yp

= 50.0

[ksi]

See AISC DG4 Table 3.1 for all formulas to derive the following parameters

AISC DG4 Table 3.1

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

= 4.000

[in]

p_fi

= 1.625

[in]

p_fo

= 1.625

[in]

= 2.742

[in]

Y_p

= 88.61

[in]

Flexure resistance factor-LRFD

φ_b

= 0.90

AISC 14^th F1 (1)

End plate bending strength

φ_bM_pl

= φ_b F_yp t2p Y_p

= 186.90

[kip-ft]

AISC DG4 Table 3.1

Check thick end plate condition

φ_bM_pl >= 1.11 X φ M_np

AISC DG4 Eq 3.33

ratio

= 0.70 thick plate

Column Flange Bending Strength

See AISC DG4 Table 3.4 for all formulas to derive the following parameters

AISC DG4 Table 3.4

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

*** Stiffened Column Flange Case ***

Column section

b_fc

= 8.010

[in]

t_fc

= 0.515

[in]

F_yc

= 50.0

[ksi]

bolt gage g

= 4.000

[in]

= 2.830

[in]

= 3.690

[in]

Stiffener plate thickness

t_s

= 0.500

[in]

p_si

= 1.595

[in]

p_so

= 1.595

[in]

Y_c

= 145.6

[in]

Flexure resistance factor-LRFD

φ_b

= 0.90

AISC 14^th F1 (1)

Column flange bending strength

φ_bM_cf

= φ_b F_yc t2fc Y_c

= 144.82

[kip-ft]

AISC DG4 Table 3.4

Check thick column flange condition

φ_bM_cf >= 1.11 X φ M_np

AISC DG4 Eq 3.35

ratio

= 0.90 thick plate

The thick end plate and column flange conditions are met. AISG DG4 is used and
no bolt prying is considered

AISC DG4 Eq 3.33 & 3.35

Bolt Moment Strength (No Prying)

ratio = 58.03 / 119.28

= 0.49

PASS

bolt grade

= A325-N

F_t

= 90.0

[ksi]

AISC 14^th Table J3.2

bolt dia d_b

= 0.750

[in]

bolt area A_b

= 0.442

[in²]

Bolt norminal tensile strength

P_t

= F_t A_b

= 39.76

[kips]

AISC 14^th Eq J3-1

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 58.03

[kips]

Flange force resistance by bolt

F_n

= 2 P_t ( h₀ + h₁ ) / d_m

= 159.04

[kips]

AISC DG4 Eq 3.7

Bolt resistance factor-LRFD

= 0.75

AISC 14^th Eq J3-1

φ F_n

= 119.28

[kips]

AISC DG4 Eq 3.7

ratio

= 0.49

> P_{uf_t}

Bolt Shear Strength

ratio = 30.00 / 71.57

= 0.42

PASS

Bolt shear stress

bolt grade

= A325-N

F_nv

= 54.0

[ksi]

AISC 14^th Table J3.2

bolt dia d_b

= 0.750

[in]

bolt area A_b

= 0.442

[in²]

Number of bolt carried shear

n_s

= 4.0

shear plane m

= 1

Required shear strength

V_u

= 30.00

[kips]

Bolt shear strength

R_n

= F_nv A_b n_s m C_ec

= 95.43

[kips]

AISC 14^th Eq J3-1

Bolt resistance factor-LRFD

= 0.75

AISC 14^th Eq J3-1

φ R_n

= 71.57

[kips]

ratio

= 0.42

> V_u

Bolt Bearing/TearOut Strength on End Plate

ratio = 30.00 / 71.57

= 0.42

PASS

Single Bolt Shear Strength

Bolt shear stress

bolt grade

= A325-N

F_nv

= 54.0

[ksi]

AISC 14^th Table J3.2

bolt dia d_b

= 0.750

[in]

bolt area A_b

= 0.442

[in²]

Single bolt shear strength

R_n-bolt

= F_nv A_b

= 23.86

[kips]

AISC 14^th Eq J3-1

Bolt Bearing/TearOut Strength on Plate

Bolt hole diameter

bolt dia d_b

= ³⁄₄

[in]

bolt hole dia d_h

= ¹³⁄₁₆

[in]

AISC 14^th Table J3.3

Bolt spacing & edge distance

spacing L_s

= 3.690

[in]

edge distance L_e

= 1.375

[in]

Plate tensile strength

F_u

= 65.0

[ksi]

Plate thickness

= 0.750

[in]

Interior Bolt

Bolt hole edge clear distance

L_c

= L_s - d_h

= 2.878

[in]

Bolt tear out/bearing strength

R_n-t&b-in

= 1.5 L_c t F_u ≤ 3.0 d_b t F_u

AISC 14^th Eq J3-6b

= 210.42 ≤ 109.69

= 109.69

[kips]

Bolt strength at interior

R_n-in

= min ( R_n-t&b-in , R_n-bolt )

= 23.86

[kips]

Edge Bolt

Bolt hole edge clear distance

L_c

= L_e - d_h / 2

= 0.969

[in]

Bolt tear out/bearing strength

R_n-t&b-ed

= 1.5 L_c t F_u ≤ 3.0 d_b t F_u

AISC 14^th Eq J3-6b

= 70.84 ≤ 109.69

= 70.84

[kips]

Bolt strength at edge

R_n-ed

= min ( R_n-t&b-ed , R_n-bolt )

= 23.86

[kips]

Number of bolt

interior n_in

= 2

edge n_ed

= 2

Bolt bearing strength for all bolts

R_n

= n_in R_n-in + n_ed R_n-ed

= 95.43

[kips]

Required shear strength

V_u

= 30.00

[kips]

Bolt resistance factor-LRFD

= 0.75

AISC 14^th J3-10

φ R_n

= 71.57

[kips]

ratio

= 0.42

> V_u

Bolt Bearing/TearOut Strength on Column Flange

ratio = 30.00 / 71.57

= 0.42

PASS

Single Bolt Shear Strength

Bolt shear stress

bolt grade

= A325-N

F_nv

= 54.0

[ksi]

AISC 14^th Table J3.2

bolt dia d_b

= 0.750

[in]

bolt area A_b

= 0.442

[in²]

Single bolt shear strength

R_n-bolt

= F_nv A_b

= 23.86

[kips]

AISC 14^th Eq J3-1

Bolt Bearing/TearOut Strength on Plate

Bolt hole diameter

bolt dia d_b

= ³⁄₄

[in]

bolt hole dia d_h

= ¹³⁄₁₆

[in]

AISC 14^th Table J3.3

Bolt spacing

spacing L_s

= 3.690

[in]

Plate tensile strength

F_u

= 65.0

[ksi]

Plate thickness

= 0.515

[in]

Interior Bolt

Bolt hole edge clear distance

L_c

= L_s - d_h

= 2.878

[in]

Bolt tear out/bearing strength

R_n-t&b-in

= 1.5 L_c t F_u ≤ 3.0 d_b t m F_u

AISC 14^th Eq J3-6b

= 144.49 ≤ 75.32

= 75.32

[kips]

Bolt strength at interior

R_n-in

= min ( R_n-t&b-in , R_n-bolt )

= 23.86

[kips]

Number of bolt

interior n_in

= 4

Bolt bearing strength for all bolts

R_n

= n_in R_n-in

= 95.43

[kips]

Required shear strength

V_u

= 30.00

[kips]

Bolt resistance factor-LRFD

= 0.75

AISC 14^th J3-10

φ R_n

= 71.57

[kips]

ratio

= 0.42

> V_u

End Plate Flexural Yielding

ratio = 58.03 / 189.11

= 0.31

PASS

End Plate Bending Strength

End plate width

b_plate

= 8.490

[in]

thickness t_p

= 0.750

[in]

Beam flange width

b_fb

= 6.520

[in]

Effective end plate width

b_p

= min ( b_plate , b_fb + 1" )

= 7.520

[in]

AISC DG4 Page 9 item 5

End plate yield strength

F_yp

= 50.0

[ksi]

See AISC DG4 Table 3.1 for all formulas to derive the following parameters

AISC DG4 Table 3.1

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

= 4.000

[in]

p_fi

= 1.625

[in]

p_fo

= 1.625

[in]

= 2.742

[in]

Y_p

= 88.61

[in]

Flexure resistance factor-LRFD

φ_b

= 0.90

AISC 14^th F1 (1)

End plate bending strength

φ_bM_pl

= φ_b F_yp t2p Y_p

= 186.90

[kip-ft]

AISC DG4 Table 3.1

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 58.03

[kips]

Flange force provided by end plate bending

φ R_pl

= φ M_pl / d_m

= 189.11

[kips]

AISC DG4 Eq 3.10

ratio

= 0.31

> P_{uf_t}

End Plate Shear Yielding

ratio = 29.02 / 169.20

= 0.17

PASS

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 29.02

[kips]

End plate width

b_plate

= 8.490

[in]

thickness t_p

= 0.750

[in]

Beam flange width

b_fb

= 6.520

[in]

Effective end plate width

b_p

= min ( b_plate , b_fb + 1" )

= 7.520

[in]

AISC DG4 Page 9 item 5

Plate Shear Yielding Check

Plate size

width b_p

= 7.520

[in]

thickness t_p

= 0.750

[in]

Plate yield strength

F_y

= 50.0

[ksi]

Plate gross area in shear

A_gv

= b_p t_p

= 5.640

[in²]

Shear force required

0.5 P_{uf_t}

= 29.02

[kips]

Plate shear yielding strength

R_n

= 0.6 F_y A_gv

= 169.20

[kips]

AISC 14^th Eq J4-3

Resistance factor-LRFD

= 1.00

AISC 14^th Eq J4-3

φ R_n

= 169.20

[kips]

ratio

= 0.17

> 0.5 P_{uf_t}

End Plate Shear Rupture

ratio = 29.02 / 126.58

= 0.23

PASS

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 29.02

[kips]

End plate width

b_plate

= 8.490

[in]

thickness t_p

= 0.750

[in]

Beam flange width

b_fb

= 6.520

[in]

Effective end plate width

b_p

= min ( b_plate , b_fb + 1" )

= 7.520

[in]

AISC DG4 Page 9 item 5

Plate Shear Rupture Check

Bolt hole diameter

bolt dia d_b

= ³⁄₄

[in]

bolt hole dia d_h

= ⁷⁄₈

[in]

AISC 14^th B4.3b

Number of bolt

= 2

Plate size

width b_p

= 7.520

[in]

thickness t_p

= 0.750

[in]

Plate tensile strength

F_u

= 65.0

[ksi]

Plate net area in shear

A_nv

= ( b_p - n d_h ) t_p

= 4.328

[in²]

Shear force required

0.5 P_{uf_t}

= 29.02

[kips]

Plate shear rupture strength

R_n

= 0.6 F_u A_nv

= 168.77

[kips]

AISC 14^th Eq J4-4

Resistance factor-LRFD

= 0.75

AISC 14^th Eq J4-4

φ R_n

= 126.58

[kips]

ratio

= 0.23

> 0.5 P_{uf_t}

Beam Flange Weld Strength

ratio = 58.03 / 120.47

= 0.48

PASS

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 58.03

[kips]

Fillet weld length - double fillet

= [b_fb + ( b_fb - 2k_1b )] /2 as dbl fillet

= 5.770

[in]

Fillet Weld Strength Check

Fillet weld leg size

= ⁵⁄₁₆

[in]

load angle θ

= 90.0

[°]

Electrode strength

F_EXX

= 70.0

[ksi]

strength coeff C₁

= 1.00

AISC 14^th Table 8-3

Number of weld line

= 2 for double fillet

Load angle coefficient

C₂

= ( 1 + 0.5 sin^1.5 θ )

= 1.50

AISC 14^th Page 8-9

Fillet weld shear strength

R_n-w

= 0.6 (C₁ x 70 ksi) 0.707 w n C₂

= 27.838

[kip/in]

AISC 14^th Eq 8-1

Base metal - beam flange

thickness t

= 0.440

[in]

tensile F_u

= 65.0

[ksi]

Base metal - beam flange is in tension, tensile rupture as per AISC 14^th Eq J4-2 is checked

AISC 14^th J2.4

Base metal tensile rupture

R_n-b

= F_u t

= 28.600

[kip/in]

AISC 14^th Eq J4-2

Double fillet linear shear strength

R_n

= min ( R_n-w , R_n-b )

= 27.838

[kip/in]

AISC 14^th Eq 9-2

Resistance factor-LRFD

= 0.75

AISC 14^th Eq 8-1

φ R_n

= 20.879

[kip/in]

Shear resistance required

P_{uf_t}

= 58.03

[kips]

Fillet weld length - double fillet

= 5.770

[in]

Shear resistance provided

φ F_n

= φ R_n x L

= 120.47

[kips]

ratio

= 0.48

> P_{uf_t}

Beam Web Weld Strength

ratio = 30.00 / 38.22

= 0.79

PASS

Beam Web Effective Weld Length Calc

Beam section

d_b

= 12.300

[in]

t_fb

= 0.440

[in]

k_b

= 1.125

[in]

Bolt diameter

d_bolt

= 0.750

[in]

bolt inner pitch p_fi

= 1.625

[in]

Effective weld length case 1

L₁

= 0.5 d_b - k_b

= 5.025

[in]

AISC DG4 Page 38

Effective weld length case 2

L₂

= d_b - 2t_fb - p_fi - 2 d_bolt

= 8.295

[in]

AISC DG4 Page 38

Fillet weld length - double fillet

= min( L₁ , L₂ )

= 5.025

[in]

Fillet Weld Strength Check

Fillet weld leg size

= ⁵⁄₁₆

[in]

load angle θ

= 0.0

[°]

Electrode strength

F_EXX

= 70.0

[ksi]

strength coeff C₁

= 1.00

AISC 14^th Table 8-3

Number of weld line

= 2 for double fillet

Load angle coefficient

C₂

= ( 1 + 0.5 sin^1.5 θ )

= 1.00

AISC 14^th Page 8-9

Fillet weld shear strength

R_n-w

= 0.6 (C₁ x 70 ksi) 0.707 w n C₂

= 18.559

[kip/in]

AISC 14^th Eq 8-1

Base metal - beam web

thickness t

= 0.260

[in]

tensile F_u

= 65.0

[ksi]

Base metal - beam web is in shear, shear rupture as per AISC 14^th Eq J4-4 is checked

AISC 14^th J2.4

Base metal shear rupture

R_n-b

= 0.6 F_u t

= 10.140

[kip/in]

AISC 14^th Eq J4-4

Double fillet linear shear strength

R_n

= min ( R_n-w , R_n-b )

= 10.140

[kip/in]

AISC 14^th Eq 9-2

Resistance factor-LRFD

= 0.75

AISC 14^th Eq 8-1

φ R_n

= 7.605

[kip/in]

Shear resistance required

V_u

= 30.00

[kips]

Fillet weld length - double fillet

= 5.025

[in]

Shear resistance provided

φ F_n

= φ R_n x L

= 38.22

[kips]

ratio

= 0.79

> V_u

Column Flexural Yielding

ratio = 58.03 / 146.53

= 0.40

PASS

Column Flange Bending Strength

See AISC DG4 Table 3.4 for all formulas to derive the following parameters

AISC DG4 Table 3.4

Tension bolt moment arm

h₀

= 13.705

[in]

h₁

= 10.015

[in]

*** Stiffened Column Flange Case ***

Column section

b_fc

= 8.010

[in]

t_fc

= 0.515

[in]

F_yc

= 50.0

[ksi]

bolt gage g

= 4.000

[in]

= 2.830

[in]

= 3.690

[in]

Stiffener plate thickness

t_s

= 0.500

[in]

p_si

= 1.595

[in]

p_so

= 1.595

[in]

Y_c

= 145.6

[in]

Flexure resistance factor-LRFD

φ_b

= 0.90

AISC 14^th F1 (1)

Column flange bending strength

φ_bM_cf

= φ_b F_yc t2fc Y_c

= 144.82

[kip-ft]

AISC DG4 Table 3.4

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force required in tension

P_{uf_t}

= P_u / 2 - M_u / d_m

= 58.03

[kips]

Flange force provided by column flange bending

φ R_cf

= φ M_cf / d_m

= 146.53

[kips]

AISC DG4 Eq 3.21

ratio

= 0.40

> P_{uf_t}

Column Web Yielding

ratio = 58.03 / 290.95

= 0.20

PASS

Column web thickness

t_wc

= 0.295

[in]

yield F_y

= 50.0

[ksi]

Doubler plate thickness

t_dp

= 0.375

[in]

yield F_ydp

= 50.0

[ksi]

Equivalent web thickness when considering doubler plate

t_w-eq

= t_wc + t_dp x F_ydp / F_y

= 0.670

[in]

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force in demand

P_uf

= max ( P_{uf_t} , P_{uf_c} )

= 58.03

[kips]

AISC DG13 Eq 4.2-1

Column section

d_c

= 11.900

[in]

t_fc

= 0.515

[in]

t_wc

= 0.295

[in]

k_c

= 1.020

[in]

Column yield strength

F_yc

= 50.0

[ksi]

Top column condition

it's not a top column case

C_t

= 1.0

AISC DG4 Eq 3.24

Beam flange fillet weld size

= 0.313

[in]

beam flange t_fb

= 0.440

[in]

Length of bearing

= t_fb + 2 w

= 1.065

[in]

AISC DG4 Eq 3.24

End plate thickness

t_p

= 0.750

[in]

Column web yielding strength

R_n

= C_t ( 6 k_c + N + 2 t_p ) F_yc t_w-eq

= 290.95

[kips]

AISC DG4 Eq 3.24

Resistance factor-LRFD

= 1.00

AISC 14^th J10.2

φ R_n

= 290.95

[kips]

ratio

= 0.20

> P_uf

Column Web Buckling

ratio = 33.03 / 206.83

= 0.16

PASS

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force required in compression

P_{uf_c}

= P_u / 2 - M_u / d_m

= 33.03

[kips]

Column section

d_c

= 11.900

[in]

t_fc

= 0.515

[in]

t_wc

= 0.295

[in]

k_c

= 1.020

[in]

= d_c - 2 k_c

= 9.860

[in]

Column yield strength

F_yc

= 50.0

[ksi]

E_c

= 29000

[ksi]

Top column condition

it's not a top column case

C_t

= 1.0

AISC 14^th J10.5

Column web buckling strength

R_n1

C_t 24 t3wc √E_c F_yc/h

= 75.25

[kips]

AISC 14^th Eq J10-8

Doubler plate thickness

t_dp

= 0.375

[in]

yield F_ydp

= 50.0

[ksi]

Doubler plate buckling strength

R_n2

C_t 24 t3dp √E_c F_ydp/h

= 154.57

[kips]

AISC 14^th Eq J10-8

Total buckling strength

R_n

= R_n1 + R_n2

= 229.81

[kips]

Resistance factor-LRFD

= 0.90

AISC 14^th J10.5

φ R_n

= 206.83

[kips]

ratio

= 0.16

> P_{uf_c}

Column Web Crippling

ratio = 33.03 / 273.27

= 0.12

PASS

Flange force moment arm

d_m

= d_b - t_fb

= 11.860

[in]

Flange force required in compression

P_{uf_c}

= P_u / 2 - M_u / d_m

= 33.03

[kips]

Column section

d_c

= 11.900

[in]

t_fc

= 0.515

[in]

t_wc

= 0.295

[in]

k_c

= 1.020

[in]

Column yield strength

F_yc

= 50.0

[ksi]

E_c

= 29000

[ksi]

Beam flange fillet weld size

= 0.313

[in]

beam flange t_fb

= 0.440

[in]

End plate thickness

t_p

= 0.750

[in]

Length of bearing

l_b

= t_fb + 2 w + 2 t_p

= 2.565

[in]

Distance from top of column to top of beam flange

d_end-flg

= 4.000

[in]

Top column condition

it's not a top column case, use Eq J10-4

AISC 14^th J10.3 (a)

Column web crippling strength

R_n1

= 0.8 t2wc [1+3

l_b/d_c

(

t_wc/t_fc

)^1.5]x

= 141.82

[kips]

AISC 14^th Eq J10-4

(

E_c F_yc t_fc/t_wc

)^0.5

Doubler plate thickness

t_dp

= 0.375

[in]

yield F_ydp

= 50.0

[ksi]

Doubler plate crippling strength

R_n2

= 0.8 t2dp [1+3

l_b/d_c

(

t_dp/t_fc

)^1.5]x

= 222.54

[kips]

AISC 14^th Eq J10-4

(

E_c F_ydp t_fc/t_dp

)^0.5

Total crippling strength

R_n

= R_n1 + R_n2

= 364.36

[kips]

Resistance factor-LRFD

= 0.75

AISC 14^th J10.3

φ R_n

= 273.27

[kips]

ratio

= 0.12

> P_{uf_c}

Column Panel Zone Shear

146.71 / 94.78

N/A

Panel zone shear force

V_p

= P_f-TR - P_f-TL - V_s

= 146.71

[kips]

Column section

d_c

= 11.900

[in]

t_wc

= 0.295

[in]

A_c

= 11.700

[in²]

F_yc

= 50.0

[ksi]

Column axial compression - user input

P_r

= 0.00

[kips]

P_c

= P_y = F_yc A_c

= 585.00

[kips]

AISC 14^th J10.6

P_r ≤ 0.4 P_c , use Eq J10-9

AISC 14^th Eq J10-9

Web panel zone capacity

R_n

= 0.6 F_yc d_c t_wc

= 105.32

[kips]

AISC 14^th Eq J10-9

Resistance factor-LRFD

= 0.90

AISC 14^th J10.6

φ R_n

= 94.78

[kips]

Unbalanced force to be resisted by doubler plate

V_dp

= R_p - φ R_n

= 51.93

[kips]

Doubler Geometry Restriction

PASS

Min Doubler Thickness to Allow for Proper Beveling of Plate

AISC DG13 Eq 4.4-4

Column section

t_fc

= 0.515

[in]

k_c

= 1.020

[in]

Allowed fillet encroachment

r_e

= 0.250

[in]

AISC 14^th Fig 10-3

Min doubler plate thickness

t_pmin

= k_c - t_fc - r_e

= 0.255

[in]

AISC DG13 Eq 4.4-4

Doubler plate thickness

t_dp

= 0.375

[in]

> t_pmin

Min Doubler Thickness to Avoid Shear Buckling of Plate

AISC DG13 Eq 4.4-5

Column section

d_c

= 11.900

[in]

k_c

= 1.020

[in]

= d_c - 2 k_c

= 9.860

[in]

Doubler plate steel

F_y

= 50.0

[ksi]

= 29000

[ksi]

Min doubler plate thickness

t_pmin

= h / 2.24 √E / F_y

= 0.183

[in]

AISC 14^th G2.1 (a)

Doubler plate thickness

t_dp

= 0.375

[in]

> t_pmin

Doubler Plate Shear Yield

ratio = 51.93 / 133.88

= 0.39

PASS

Doubler plate thickness

t_dp

= 0.375

[in]

yield strength F_y

= 50.0

[ksi]

Number of doubler

N_dbl

= 1 for one side

Column depth

d_c

= 11.900

[in]

Area of web

A_w

= t_dp x d_c

= 4.463

[in²]

AISC DG13 Eq 4.4-1

Shear coefficient

C_v

= 1.0

AISC 14^th Eq G2-2

Doubler plate shear in demand

R_dp

= unbalanced force from column

= 51.93

[kips]

panel zone shear calc

Doubler plate shear strength

R_n

= N_dbl 0.6 F_y A_w C_v

= 133.88

[kips]

AISC 14^th Eq G2-1

Resistance factor-LRFD

= 1.00

AISC 14^th G2.1 (a)

φ R_n

= 133.88

[kips]

ratio

= 0.39

> R_dp

Doubler to Column Flange Fillet Weld Limitation

PASS

Min Fillet Weld Size

Thinner part joined thickness

= 0.375

[in]

Min fillet weld size allowed

w_min

= 0.188

[in]

AISC 14^th Table J2.4

Fillet weld size provided

= 0.250

[in]

> w_min

Min Fillet Weld Length

Fillet weld size provided

= 0.250

[in]

Min fillet weld length allowed

L_min

= 4 x w

= 1.000

[in]

AISC 14^th J2.2b

Min fillet weld length

= d_b + ( 3 k_c + t_p )x 2 Ends

= 19.920

[in]

> L_min

Doubler to Column Web Fillet Weld Limitation

PASS

Min Fillet Weld Size

Thinner part joined thickness

= 0.295

[in]

Min fillet weld size allowed

w_min

= 0.188

[in]

AISC 14^th Table J2.4

Fillet weld size provided

= 0.250

[in]

> w_min

Min Fillet Weld Length

Fillet weld size provided

= 0.250

[in]

Min fillet weld length allowed

L_min

= 4 x w

= 1.000

[in]

AISC 14^th J2.2b

Min fillet weld length

= d_c - 2 x k_c

= 9.860

[in]

> L_min

Doubler Weld Strength at Column Flange

ratio = 51.93 / 110.91

= 0.47

PASS

Doubler Plate to Column Flange Weld Length Calc

Beam section

d_b

= 12.300

[in]

column section k_c

= 1.020

[in]

End plate thickness

t_p

= 0.750

[in]

Doubler plate to column flange weld length - single fillet

= d_b +(3 k_c + t_p ) x 2 ends

= 19.920

[in]

AISC DG13 Fig 4-3

Fillet Weld Strength Check

Fillet weld leg size

= ¹⁄₄

[in]

load angle θ

= 0.0

[°]

Electrode strength

F_EXX

= 70.0

[ksi]

strength coeff C₁

= 1.00

AISC 14^th Table 8-3

Number of weld line

= 1 for single fillet

Load angle coefficient

C₂

= ( 1 + 0.5 sin^1.5 θ )

= 1.00

AISC 14^th Page 8-9

Fillet weld shear strength

R_n-w

= 0.6 (C₁ x 70 ksi) 0.707 w n C₂

= 7.424

[kip/in]

AISC 14^th Eq 8-1

Base metal - doubler plate

thickness t

= 0.375

[in]

tensile F_u

= 65.0

[ksi]

Base metal - doubler plate is in shear, shear rupture as per AISC 14^th Eq J4-4 is checked

AISC 14^th J2.4

Base metal shear rupture

R_n-b

= 0.6 F_u t

= 14.625

[kip/in]

AISC 14^th Eq J4-4

Single fillet linear shear strength

R_n

= min ( R_n-w , R_n-b )

= 7.424

[kip/in]

AISC 14^th Eq 9-2

Resistance factor-LRFD

= 0.75

AISC 14^th Eq 8-1

φ R_n

= 5.568

[kip/in]

Shear resistance required

R_dp

= 51.93

[kips]

Fillet weld length - single fillet

= 19.920

[in]

Shear resistance provided

φ F_n

= φ R_n x L

= 110.91

[kips]

ratio

= 0.47

> R_dp

Doubler Weld Strength at Column Web

ratio = 51.93 / 54.90

= 0.95

PASS

Doubler Plate to Column Web Weld Length Calc

Column section

d_c

= 11.900

[in]

k_c

= 1.020

[in]

Doubler plate to column web weld length - single fillet

= d_c - 2 x k_c

= 9.860

[in]

Fillet Weld Strength Check

Fillet weld leg size

= ¹⁄₄

[in]

load angle θ

= 0.0

[°]

Electrode strength

F_EXX

= 70.0

[ksi]

strength coeff C₁

= 1.00

AISC 14^th Table 8-3

Number of weld line

= 1 for single fillet

Load angle coefficient

C₂

= ( 1 + 0.5 sin^1.5 θ )

= 1.00

AISC 14^th Page 8-9

Fillet weld shear strength

R_n-w

= 0.6 (C₁ x 70 ksi) 0.707 w n C₂

= 7.424

[kip/in]

AISC 14^th Eq 8-1

Base metal - doubler plate

thickness t

= 0.375

[in]

tensile F_u

= 65.0

[ksi]

Base metal - doubler plate is in shear, shear rupture as per AISC 14^th Eq J4-4 is checked

AISC 14^th J2.4

Base metal shear rupture

R_n-b

= 0.6 F_u t

= 14.625

[kip/in]

AISC 14^th Eq J4-4

Single fillet linear shear strength

R_n

= min ( R_n-w , R_n-b )

= 7.424

[kip/in]

AISC 14^th Eq 9-2

Resistance factor-LRFD

= 0.75

AISC 14^th Eq 8-1

φ R_n

= 5.568

[kip/in]

Shear resistance required

R_dp

= 51.93

[kips]

Fillet weld length - single fillet

= 9.860

[in]

Shear resistance provided

φ F_n

= φ R_n x L

= 54.90

[kips]

ratio

= 0.95

> R_dp