Beam to Girder
Clip Angle Shear Connection
Code=AISC 360-10 LRFD
 
Result Summary
geometries & weld limitations = PASS
limit states max ratio 
= 0.95
PASS
 
Sketch
Shear Connection
Code=AISC 360-10 LRFD
 
 
Members & Components Summary
Member
Shear Connection
Code=AISC 360-10 LRFD
 
 
 
Geometry Restriction Checks - Clip Angle to Beam
PASS
Min Bolt Edge Distance - Clip Angle to Beam

Bolt diameter
db
 = 
 = 0.750
[in]

Min edge distance allowed
Le-min
 = 
 = 1.000
[in]
AISC 14th  Table J3.4
Min edge distance in Clip Angle to Beam
Le
 = 
 = 1.375
[in]

 > Le-min
OK
Min Bolt Spacing - Clip Angle to Beam

Bolt diameter
db
 = 
 = 0.750
[in]

Min bolt spacing allowed
Ls-min
 = 2.667 db
 = 2.000
[in]
AISC 14th  J3.3
Min Bolt spacing in Clip Angle to Beam
Ls
 = 
 = 3.000
[in]

 > Ls-min
OK
 
Geometry Restriction Checks - Clip Angle to Girder
PASS
Min Bolt Edge Distance - Clip Angle to Girder Web

Bolt diameter
db
 = 
 = 0.750
[in]

Min edge distance allowed
Le-min
 = 
 = 1.000
[in]
AISC 14th  Table J3.4
Min edge distance in Clip Angle to Girder Web
Le
 = 
 = 1.375
[in]

 > Le-min
OK
Min Bolt Spacing - Clip Angle to Girder Web

Bolt diameter
db
 = 
 = 0.750
[in]

Min bolt spacing allowed
Ls-min
 = 2.667 db
 = 2.000
[in]
AISC 14th  J3.3
Min Bolt spacing in Clip Angle to Girder Web
Ls
 = 
 = 3.000
[in]

 > Ls-min
OK
 
 
W Shape Beam - Tensile Yield
ratio = 25.00 / 111.74
= 0.22
PASS
Gross area subject to tension
Ag
 = 
 = 2.483
[in2]

Steel yield strength
Fy
 = 
 = 50.0
[ksi]

Tensile force required
Pu
 = 
 = 25.00
[kips]

Tensile yielding strength
Rn
 = Fy Ag
 = 124.15
[kips]
AISC 14th  Eq D2-1
Resistance factor-LRFD
φ
 = 0.90
AISC 14th  D2 (a)
φ Rn
 = 
 = 111.74
[kips]
AISC 14th  Eq D2-1
ratio
 = 0.22
 > Pu
OK
 
W Shape Beam - Tensile Rupture
ratio = 25.00 / 87.77
= 0.28
PASS
W beam section
 = W12X30

d
 = 12.300
[in]
bf
 = 6.520
[in]

tf
 = 0.440
[in]
tw
 = 0.260
[in]

Ag
 = 2.483
[in2]


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 7⁄8
[in]
AISC 14th  B4.3b
Number of bolt row
n
 = 3

W section net area
An
 = Ag - n dh tw
 = 1.801
[in2]

Shear lag factor
U
 = 
 = 1.000
AISC 14th  D3

Tensile force required
Pu
 = 
 = 25.00
[kips]

Tensile effective net area
Ae
 = An U
 = 1.801
[in2]

Plate tensile strength
Fu
 = 
 = 65.0
[ksi]

Tensile rupture strength
Rn
 = Fu Ae
 = 117.03
[kips]
AISC 14th  Eq D2-2
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  D2 (b)
φ Rn
 = 
 = 87.77
[kips]
AISC 14th  Eq D2-2
ratio
 = 0.28
 > Pu
OK
 
 
Beam Web - Shear Yielding
ratio = 50.00 / 74.49
= 0.67
PASS
Plate Shear Yielding Check


Plate size
width bp
 = 9.550
[in]
thickness tp
 = 0.260
[in]

Plate yield strength
Fy
 = 50.0
[ksi]

Plate gross area in shear
Agv
 = bp tp
 = 2.483
[in2]

Shear force required
Vu
 = 
 = 50.00
[kips]

Plate shear yielding strength
Rn
 = 0.6 Fy Agv
 = 74.49
[kips]
AISC 14th  Eq J4-3
Resistance factor-LRFD
φ
 = 1.00
AISC 14th  Eq J4-3
φ Rn
 = 
 = 74.49
[kips]

ratio
 = 0.67
 > Vu
OK
 
Beam Web - Shear Rupture
ratio = 50.00 / 52.66
= 0.95
PASS
Plate Shear Rupture Check


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 7⁄8
[in]
AISC 14th  B4.3b
Number of bolt
n
 = 3

Plate size
width bp
 = 9.550
[in]
thickness tp
 = 0.260
[in]

Plate tensile strength
Fu
 = 65.0
[ksi]

Plate net area in shear
Anv
 = ( bp - n dh ) tp
 = 1.801
[in2]

Shear force required
Vu
 = 
 = 50.00
[kips]

Plate shear rupture strength
Rn
 = 0.6 Fu Anv
 = 70.22
[kips]
AISC 14th  Eq J4-4
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-4
φ Rn
 = 
 = 52.66
[kips]

ratio
 = 0.95
 > Vu
OK
 
Beam Web - Bolt Bearing on Beam Web
ratio = 55.90 / 85.56
= 0.65
PASS
The bolt group is oriented so that the shear force V is in ver. direction and the axial force P is in hor. direction
 
Bolt group forces
shear V
 = 50.00
[kips]
axial P
 = -25.00
[kips]

Bolt group resultant force
R
 = ( V2 + P2 )0.5
 = 55.90
[kips]

Resultant force/hor line load angle
θ
 = tan-1 (V / P)
 = 63.43
[°]


Bolt hole diameter
bolt dia db
 = 0.750
[in]
bolt hole dia dbh
 = 0.813
[in]
AISC 14th  B4.3b
Bolt hole ver. dimension
dv
 = 
 = 0.813
[in]

Bolt hole hor. dimension
dh
 = 
 = 0.813
[in]

Bolt center to bolt hole edge dist
dc
 = 0.5 dbh
 = 0.406
[in]


Bolt no in ver & hor direction
Bolt Row nv
 = 3
Bolt Col nh
 = 1

Bolt spacing
ver sv
 = 3.000
[in]

Bolt edge distance
ver ev
 = 1.750
[in]
hor eh
 = 1.500
[in]


Bolt clear dist - bot right corner bolt
LcA
 = min (
ev/sin θ
,
eh/cos θ
) - dc
 = 1.550
[in]

Bolt clear dist - right side edge bolt
LcB
 = min (
sv - 0.5dv/sin θ
,
eh/cos θ
) - dc
 = 2.494
[in]

Single Bolt Shear Strength

Bolt shear stress
bolt grade
 = A325-N
Fnv
 = 54.0
[ksi]
AISC 14th  Table J3.2
bolt dia db
 = 0.750
[in]
bolt area Ab
 = 0.442
[in2]

Single bolt shear strength
Rn-bolt
 = 2 x Fnv Ab
 = 47.71
[kips]
AISC 14th  Eq J3-1

Bolt bearing on plate
thick t
 = 0.260
[in]
tensile Fu
 = 65.0
[ksi]

Bolt bearing strength
Rn-br
 = 3.0 db t Fu
 = 38.03
[kips]
AISC 14th  Eq J3-6b

Type A - Bolt Group Bottom Right Corner Bolt
Number of bolt
nA
 = 1

Bolt tear out strength
Rn-tA
 = 1.5 LcA t Fu
 = 39.30
[kips]
AISC 14th  Eq J3-6b
Bolt bearing strength
RnA
 = min ( Rn-tA , Rn-br , Rn-bolt )
 = 38.03
[kips]


Type B - Bolt Group Right Side Edge Bolt
Number of bolt
nB
 = 2

Bolt tear out strength
Rn-tB
 = 1.5 LcB t Fu
 = 63.21
[kips]
AISC 14th  Eq J3-6b
Bolt bearing strength
RnB
 = min ( Rn-tB , Rn-br , Rn-bolt )
 = 38.03
[kips]


Bolt bearing strength for all bolts
Rn
 = nA RnA + nB RnB + nC RnC + nD RnD
 = 114.08
[kips]

Bolt resistance factor-LRFD
φ
 = 0.75
AISC 14th  J3-10
φ Rn
 = 
 = 85.56
[kips]

ratio
 = 0.65
 > R
OK
 
Beam Web - Shear - Block Shear - 1-Side Strip
ratio = 50.00 / 55.77
= 0.90
PASS
Plate Block Shear - Side Strip


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 7⁄8
[in]
AISC 14th  B4.3b
Plate thickness
tp
 = 0.260
[in]

Plate strength
Fy
 = 50.0
[ksi]
Fu
 = 65.0
[ksi]

Bolt no in ver & hor dir
nv
 = 1
nh
 = 3

Bolt spacing in hor dir
sh
 = 3.000
[in]

Bolt edge dist in ver & hor dir
ev
 = 1.500
[in]
eh
 = 1.750
[in]


Gross area subject to shear
Agv
 = [ (nh - 1) sh + eh ] tp
 = 2.015
[in2]

Net area subject to shear
Anv
 = Agv - [ (nh - 1) + 0.5 ] dh tp
 = 1.446
[in2]

Net area subject to tension
Ant
 = ( ev - 0.5 dh ) tp
 = 0.276
[in2]


Block shear strength required
Vu
 = 
 = 50.00
[kips]

Uniform tension stress factor
Ubs
 = 1.00
AISC 14th  Fig C-J4.2
Bolt shear resistance provided
Rn
 = min (0.6Fu Anv , 0.6Fy Agv ) +
 = 74.36
[kips]
AISC 14th  Eq J4-5
Ubs Fu Ant

Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-5
φ Rn
 = 
 = 55.77
[kips]

ratio
 = 0.90
 > Vu
OK
 
Beam Web - Axial Tearout - Block Shear - Center Strip
ratio = 25.00 / 70.03
= 0.36
PASS
Plate Block Shear - Center Strip


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 7⁄8
[in]
AISC 14th  B4.3b
Plate thickness
tp
 = 0.260
[in]

Plate strength
Fy
 = 50.0
[ksi]
Fu
 = 65.0
[ksi]

Bolt no in ver & hor dir
nv
 = 3
nh
 = 1

Bolt spacing in ver & hor dir
sv
 = 3.000
[in]
sh
 = 1.750
[in]

Bolt edge dist in ver & hor dir
ev
 = 3.000
[in]
eh
 = 1.500
[in]


Gross area subject to shear
Agv
 = [ (nh - 1) sh + eh ] tp x 2
 = 0.780
[in2]

Net area subject to shear
Anv
 = Agv - [(nh - 1)+ 0.5] dh tp x2
 = 0.553
[in2]

Net area subject to tension
when sheared out by center strip
Ant
 = ( nv - 1) ( sv - dh ) tp
 = 1.105
[in2]


Block shear strength required
Vu
 = 
 = 25.00
[kips]

Uniform tension stress factor
Ubs
 = 1.00
AISC 14th  Fig C-J4.2
Bolt shear resistance provided
Rn
 = min (0.6Fu Anv , 0.6Fy Agv ) +
 = 93.37
[kips]
AISC 14th  Eq J4-5
Ubs Fu Ant

Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-5
φ Rn
 = 
 = 70.03
[kips]

ratio
 = 0.36
 > Vu
OK
 
 
Coped Beam - Flexural Rupture
ratio = 50.00 / 240.69
= 0.21
PASS
Beam section & cope side
sect
 = W12X30
cope side
 = double cope
Beam top flange cope
depth dc
 = 1.250
[in]
length Lc
 = 3.858
[in]

Beam bottom flange cope
depth dc
 = 1.500
[in]
length Lc
 = 3.858
[in]


Snet of Coped Beam With Hor Reinforcing Stiffener Plates
Beam sect W12X30
d
 = 12.300
[in]
bf
 = 6.520
[in]

tf
 = 0.440
[in]
tw
 = 0.260
[in]

 
Stiffener plate size
wp
 = 3.000
[in]
tp
 = 0.375
[in]

 
Flange cope depth-top & bot flange
dct
 = 1.250
[in]
dcb
 = 1.500
[in]

 
Properties of Coped W Sect With Hor Reinforcing Stiffener Plates
Top flange
bft
 = 6.260
[in]
tft
 = 0.375
[in]

Bottom flange
bfb
 = 6.260
[in]
tfb
 = 0.375
[in]

W sect depth
d
 = 8.800
[in]
web tw
 = 0.260
[in]

 
Dist from sect centroid to T&B flange face
xt
 = 4.400
[in]
xb
 = 4.400
[in]

Max dist sect centroid to T&B flange face
xmax
 = max ( xt , xb )
 = 4.400
[in]

 
W sect moment of inertia
Ix
 = 
 = 94.7
[in4]

W sect elastic modulus
Snet
 = Ix / xmax
 = 21.52
[in3]


Beam section tensile strength
Fu
 = 
 = 65.0
[ksi]

Distance from face of cope to the point of inflection of beam
e
 = 
 = 4.358
[in]
AISC 14th  Page 9-6

Beam end shear force
Vu
 = 
 = 50.00
[kips]

Beam end shear resistance
Rn
 = Fu Snet / e
 = 320.92
[kips]
AISC 14th  Eq 9-4
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq 9-4
φ Rn
 = 
 = 240.69
[kips]

ratio
 = 0.21
 > Vu
OK
 
Coped Beam - Local Web Buckling
ratio = 50.00 / 222.17
= 0.23
PASS
Beam section & cope side
sect
 = W12X30
cope side
 = double cope
Beam top flange cope
depth dct
 = 1.250
[in]
length Lct
 = 3.858
[in]

Beam bottom flange cope
depth dcb
 = 1.500
[in]
length Lcb
 = 3.858
[in]


Snet of Coped Beam With Hor Reinforcing Stiffener Plates
Beam sect W12X30
d
 = 12.300
[in]
bf
 = 6.520
[in]

tf
 = 0.440
[in]
tw
 = 0.260
[in]

 
Stiffener plate size
wp
 = 3.000
[in]
tp
 = 0.375
[in]

 
Flange cope depth-top & bot flange
dct
 = 1.250
[in]
dcb
 = 1.500
[in]

 
Properties of Coped W Sect With Hor Reinforcing Stiffener Plates
Top flange
bft
 = 6.260
[in]
tft
 = 0.375
[in]

Bottom flange
bfb
 = 6.260
[in]
tfb
 = 0.375
[in]

W sect depth
d
 = 8.800
[in]
web tw
 = 0.260
[in]

 
Dist from sect centroid to T&B flange face
xt
 = 4.400
[in]
xb
 = 4.400
[in]

Max dist sect centroid to T&B flange face
xmax
 = max ( xt , xb )
 = 4.400
[in]

 
W sect moment of inertia
Ix
 = 
 = 94.7
[in4]

W sect elastic modulus
Snet
 = Ix / xmax
 = 21.52
[in3]


Distance from face of cope to the point of inflection of beam
e
 = 
 = 4.358
[in]
AISC 14th  Page 9-6

Beam section
depth d
 = 12.300
[in]
web tw
 = 0.260
[in]

Fy
 = 50.0
[ksi]
E
 = 29000
[ksi]

fd
 = 3.5 - 7.5 (dct / d)
 = 2.738
AISC 14th  Eq 9-13
Reduced beam depth
h0
 = d - dct - dcb
 = 9.550
[in]

Plate local buckling stress
Fcr
 = 0.62 π E
t2w/Lct h0
fd
 = 283.7
[ksi]
AISC 14th  Eq 9-12
Fcr
 = Fcr   ≤  Fy
 = 50.0
[ksi]
AISC 14th  Eq 9-12

Beam end shear force
Vu
 = 
 = 50.00
[kips]

Beam end shear resistance
Rn
 = Fcr Snet / e
 = 246.86
[kips]
AISC 14th  Eq 9-6
Resistance factor-LRFD
φ
 = 0.90
AISC 14th  Eq 9-6
φ Rn
 = 
 = 222.17
[kips]

ratio
 = 0.23
 > Vu
OK
 
 
Hor Stiffener to Coped Beam Web Fillet Weld Limitation
PASS
Min Fillet Weld Size

Thinner part joined thickness
t
 = 
 = 0.260
[in]

Min fillet weld size allowed
wmin
 = 
 = 0.188
[in]
AISC 14th  Table J2.4
Fillet weld size provided
w
 = 
 = 0.250
[in]

 > wmin
OK
Min Fillet Weld Length

Fillet weld size provided
w
 = 
 = 0.250
[in]

Min fillet weld length allowed
Lmin
 = 4 x w
 = 1.000
[in]
AISC 14th  J2.2b
Min fillet weld length
L
 = 
 = 5.858
[in]

 > Lmin
OK
Hor Reinforcing Stiffener Extension Beyond Cope

To prevent local crippling of the beam web, the longitudinal stiffening must be extended
min a distance of dc beyond the cope
AISC 14th  Fig 9-10 (b)
 
Flange cope depth-top & bot flange
dct
 = 1.250
[in]
dcb
 = 1.500
[in]

Max cope depth - top & bot flange
dc
 = max ( dct , dcb )
 = 1.500
[in]

 
Hor stiffener plate extension beyond cope
Le
 = 
 = 2.000
[in]

 > dc
OK
 
Hor Stiffener to Coped Beam Web Fillet Weld Strength
ratio = 5.22 / 10.97
= 0.48
PASS
Stiffener to Coped Beam Web Weld Line Force Calc

Refer to AISC Design Example v15 Page IIA-78 for the formula used below on how to get the stiffener weld line forces
 
From Snet calc in Coped Beam - Local Web Buckling check above, the properties of stiffener reinforced W section
 
Reinforced W sect moment of inertia
Inet
 = 
 = 94.7
[in4]

Reinforced stiffener plate area
Ap
 = 
 = 2.348
[in2]

 
Dist from centroid of reinforced sect to centroid of stiffener plate
y
 = 
 = 4.213
[in]

 
First moment of reinforced stiffener plate
Q
 = Ap y
 = 9.892
[in3]

 
Beam end shear force
Vu
 = 
 = 50.00
[kips]


Weld line shear stress
ru1
 = 
Vu Q/Inet
 = 5.223
[kip/in]


Distance from face of cope to the point of inflection of beam
e
 = 
 = 4.358
[in]
AISC 14th  Page 9-6
 
Beam web hor coped length
Lc
 = 
 = 3.858
[in]

Hor stiffener plate extension beyond the cope
Le
 = 
 = 2.000
[in]

 
Stiffener to beam web weld length
Lw
 = Lc + Le
 = 5.858
[in]

Weld line shear stress
ru2
 = 
Vu e Q/Inet Lw
 = 3.886
[kip/in]


Weld line shear stress - max
ru
 = max ( ru1 , ru2 )
 = 5.223
[kip/in]

Fillet Weld Strength Calc
Fillet weld leg size
w
 = 1⁄4
[in]
load angle θ
 = 0.0
[°]

Electrode strength
FEXX
 = 70.0
[ksi]
strength coeff C1
 = 1.00
AISC 14th  Table 8-3
Number of weld line
n
 = 2   for double fillet

Load angle coefficient
C2
 = ( 1 + 0.5 sin1.5 θ )
 = 1.00
AISC 14th  Page 8-9
Fillet weld shear strength
Rn-w
 = 0.6 (C1 x 70 ksi) 0.707 w n C2
 = 14.847
[kip/in]
AISC 14th  Eq 8-1

Base metal - stiffener
thickness t
 = 0.375
[in]
tensile Fu
 = 65.0
[ksi]

Base metal - stiffener is in shear, shear rupture as per AISC 14th  Eq J4-4 is checked
AISC 14th  J2.4
Base metal shear rupture
Rn-b
 = 0.6 Fu t
 = 14.625
[kip/in]
AISC 14th  Eq J4-4

Double fillet linear shear strength
Rn
 = min ( Rn-w , Rn-b )
 = 14.625
[kip/in]
AISC 14th  Eq 9-2
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq 8-1
φ Rn
 = 
 = 10.969
[kip/in]

ratio
 = 0.48
 > ru
OK
 
 
Clip Angle - Beam Side - Shear Yielding
ratio = 25.00 / 131.25
= 0.19
PASS
Plate Shear Yielding Check


Plate size
width bp
 = 8.750
[in]
thickness tp
 = 0.500
[in]

Plate yield strength
Fy
 = 50.0
[ksi]

Plate gross area in shear
Agv
 = bp tp
 = 4.375
[in2]

Shear force required
Vu
 = 
 = 25.00
[kips]

Plate shear yielding strength
Rn
 = 0.6 Fy Agv
 = 131.25
[kips]
AISC 14th  Eq J4-3
Resistance factor-LRFD
φ
 = 1.00
AISC 14th  Eq J4-3
φ Rn
 = 
 = 131.25
[kips]

ratio
 = 0.19
 > Vu
OK
 
Clip Angle - Beam Side - Shear Rupture
ratio = 25.00 / 89.58
= 0.28
PASS
Plate Shear Rupture Check


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 7⁄8
[in]
AISC 14th  B4.3b
Number of bolt
n
 = 3

Plate size
width bp
 = 8.750
[in]
thickness tp
 = 0.500
[in]

Plate tensile strength
Fu
 = 65.0
[ksi]

Plate net area in shear
Anv
 = ( bp - n dh ) tp
 = 3.063
[in2]

Shear force required
Vu
 = 
 = 25.00
[kips]

Plate shear rupture strength
Rn
 = 0.6 Fu Anv
 = 119.44
[kips]
AISC 14th  Eq J4-4
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-4
φ Rn
 = 
 = 89.58
[kips]

ratio
 = 0.28
 > Vu
OK
 
Clip Angle - Beam Side - Axial Tensile Yield
ratio = 12.50 / 196.88
= 0.06
PASS
Plate Tensile Yielding Check


Plate size
width bp
 = 8.750
[in]
thickness tp
 = 0.500
[in]

Plate yield strength
Fy
 = 50.0
[ksi]

Plate gross area in shear
Ag
 = bp tp
 = 4.375
[in2]

Tensile force required
Pu
 = 
 = 12.50
[kips]

Plate tensile yielding strength
Rn
 = Fy Ag
 = 218.75
[kips]
AISC 14th  Eq J4-1
Resistance factor-LRFD
φ
 = 0.90
AISC 14th  Eq J4-1
φ Rn
 = 
 = 196.88
[kips]

ratio
 = 0.06
 > Pu
OK
 
Clip Angle - Beam Side - Axial Tensile Rupture
ratio = 12.50 / 149.30
= 0.08
PASS
Plate Tensile Rupture Check


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 7⁄8
[in]
AISC 14th  B4.3b
Number of bolt
n
 = 3

Plate size
width bp
 = 8.750
[in]
thickness tp
 = 0.500
[in]

Plate tensile strength
Fu
 = 65.0
[ksi]

Plate net area in tension
Ant
 = ( bp - n dh ) tp
 = 3.063
[in2]

Tensile force required
Pu
 = 
 = 12.50
[kips]

Plate tensile rupture strength
Rn
 = Fu Ant
 = 199.06
[kips]
AISC 14th  Eq J4-2
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-2
φ Rn
 = 
 = 149.30
[kips]
AISC 14th  Eq J4-2
ratio
 = 0.08
 > Pu
OK
 
 
Clip Angle - Beam Side - Bolt Bearing on Clip Angle
ratio = 27.95 / 53.68
= 0.52
PASS
The bolt group is oriented so that the shear force V is in ver. direction and the axial force P is in hor. direction
 
Bolt group forces
shear V
 = 50.00
[kips]
axial P
 = -25.00
[kips]

Bolt group resultant force
R
 = ( V2 + P2 )0.5
 = 55.90
[kips]

Each angle or plate takes
R
 = 0.50 x R
 = 27.95
[kips]

Resultant force/hor line load angle
θ
 = tan-1 (V / P)
 = 63.43
[°]


Bolt hole diameter
bolt dia db
 = 0.750
[in]
bolt hole dia dbh
 = 0.813
[in]
AISC 14th  B4.3b
Bolt hole ver. dimension
dv
 = 
 = 0.813
[in]

Bolt hole hor. dimension
dh
 = 
 = 0.813
[in]

Bolt center to bolt hole edge dist
dc
 = 0.5 dbh
 = 0.406
[in]


Bolt no in ver & hor direction
Bolt Row nv
 = 3
Bolt Col nh
 = 1

Bolt spacing
ver sv
 = 3.000
[in]

Bolt edge distance
ver ev
 = 1.375
[in]
hor eh
 = 1.500
[in]


Bolt clear dist - bot right corner bolt
LcA
 = min (
ev/sin θ
,
eh/cos θ
) - dc
 = 1.131
[in]

Bolt clear dist - right side edge bolt
LcB
 = min (
sv - 0.5dv/sin θ
,
eh/cos θ
) - dc
 = 2.494
[in]

Single Bolt Shear Strength

Bolt shear stress
bolt grade
 = A325-N
Fnv
 = 54.0
[ksi]
AISC 14th  Table J3.2
bolt dia db
 = 0.750
[in]
bolt area Ab
 = 0.442
[in2]

Single bolt shear strength
Rn-bolt
 = Fnv Ab
 = 23.86
[kips]
AISC 14th  Eq J3-1

Bolt bearing on plate
thick t
 = 0.500
[in]
tensile Fu
 = 65.0
[ksi]

Bolt bearing strength
Rn-br
 = 3.0 db t Fu
 = 73.13
[kips]
AISC 14th  Eq J3-6b

Type A - Bolt Group Bottom Right Corner Bolt
Number of bolt
nA
 = 1

Bolt tear out strength
Rn-tA
 = 1.5 LcA t Fu
 = 55.14
[kips]
AISC 14th  Eq J3-6b
Bolt bearing strength
RnA
 = min ( Rn-tA , Rn-br , Rn-bolt )
 = 23.86
[kips]


Type B - Bolt Group Right Side Edge Bolt
Number of bolt
nB
 = 2

Bolt tear out strength
Rn-tB
 = 1.5 LcB t Fu
 = 121.57
[kips]
AISC 14th  Eq J3-6b
Bolt bearing strength
RnB
 = min ( Rn-tB , Rn-br , Rn-bolt )
 = 23.86
[kips]


Bolt bearing strength for all bolts
Rn
 = nA RnA + nB RnB + nC RnC + nD RnD
 = 71.57
[kips]

Bolt resistance factor-LRFD
φ
 = 0.75
AISC 14th  J3-10
φ Rn
 = 
 = 53.68
[kips]

ratio
 = 0.52
 > R
OK
 
Clip Angle - Beam Side - Block Shear - 1-Side Strip
ratio = 25.00 / 101.77
= 0.25
PASS
Plate Block Shear - Side Strip


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 7⁄8
[in]
AISC 14th  B4.3b
Plate thickness
tp
 = 0.500
[in]

Plate strength
Fy
 = 50.0
[ksi]
Fu
 = 65.0
[ksi]

Bolt no in ver & hor dir
nv
 = 1
nh
 = 3

Bolt spacing in hor dir
sh
 = 3.000
[in]

Bolt edge dist in ver & hor dir
ev
 = 1.500
[in]
eh
 = 1.375
[in]


Gross area subject to shear
Agv
 = [ (nh - 1) sh + eh ] tp
 = 3.688
[in2]

Net area subject to shear
Anv
 = Agv - [ (nh - 1) + 0.5 ] dh tp
 = 2.594
[in2]

Net area subject to tension
Ant
 = ( ev - 0.5 dh ) tp
 = 0.531
[in2]


Block shear strength required
Vu
 = 
 = 25.00
[kips]

Uniform tension stress factor
Ubs
 = 1.00
AISC 14th  Fig C-J4.2
Bolt shear resistance provided
Rn
 = min (0.6Fu Anv , 0.6Fy Agv ) +
 = 135.69
[kips]
AISC 14th  Eq J4-5
Ubs Fu Ant

Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-5
φ Rn
 = 
 = 101.77
[kips]

ratio
 = 0.25
 > Vu
OK
 
Clip Angle - Beam Side-Axial Tearout - Block Shear - Center Strip
ratio = 12.50 / 134.67
= 0.09
PASS
Plate Block Shear - Center Strip


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 7⁄8
[in]
AISC 14th  B4.3b
Plate thickness
tp
 = 0.500
[in]

Plate strength
Fy
 = 50.0
[ksi]
Fu
 = 65.0
[ksi]

Bolt no in ver & hor dir
nv
 = 3
nh
 = 1

Bolt spacing in ver & hor dir
sv
 = 3.000
[in]
sh
 = 1.750
[in]

Bolt edge dist in ver & hor dir
ev
 = 1.375
[in]
eh
 = 1.500
[in]


Gross area subject to shear
Agv
 = [ (nh - 1) sh + eh ] tp x 2
 = 1.500
[in2]

Net area subject to shear
Anv
 = Agv - [(nh - 1)+ 0.5] dh tp x2
 = 1.063
[in2]

Net area subject to tension
when sheared out by center strip
Ant
 = ( nv - 1) ( sv - dh ) tp
 = 2.125
[in2]


Block shear strength required
Vu
 = 
 = 12.50
[kips]

Uniform tension stress factor
Ubs
 = 1.00
AISC 14th  Fig C-J4.2
Bolt shear resistance provided
Rn
 = min (0.6Fu Anv , 0.6Fy Agv ) +
 = 179.56
[kips]
AISC 14th  Eq J4-5
Ubs Fu Ant

Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-5
φ Rn
 = 
 = 134.67
[kips]

ratio
 = 0.09
 > Vu
OK
 
Clip Angle - Beam Side - Block Shear - Shear/Tensile Interact
ratio =
= 0.07
PASS
Shear block shear strength required
Vu
 = 
 = 25.00
[kips]

Axial block shear strength required
Pu
 = 
 = 12.50
[kips]

 
Shear block shear strength available
φ Rnv
 = from calc shown above
 = 101.77
[kips]

Axial block shear strength available
φ Rnt
 = from calc shown above
 = 134.67
[kips]

 
Block shear shear/tensile interaction
ratio
 = (
Vu/φ Rnv
)2 + (
Pu/φ Rnt
)2
 = 0.07
AISC 14th  Eq 10-5
 < 1.0
OK
 
 
Clip Angle - Girder Side - Shear Rupture
ratio = 25.00 / 89.58
= 0.28
PASS
Plate Shear Rupture Check


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 7⁄8
[in]
AISC 14th  B4.3b
Number of bolt
n
 = 3

Plate size
width bp
 = 8.750
[in]
thickness tp
 = 0.500
[in]

Plate tensile strength
Fu
 = 65.0
[ksi]

Plate net area in shear
Anv
 = ( bp - n dh ) tp
 = 3.063
[in2]

Shear force required
Vu
 = 
 = 25.00
[kips]

Plate shear rupture strength
Rn
 = 0.6 Fu Anv
 = 119.44
[kips]
AISC 14th  Eq J4-4
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-4
φ Rn
 = 
 = 89.58
[kips]

ratio
 = 0.28
 > Vu
OK
 
Clip Angle - Girder Side - Bolt Bearing on Clip Angle
ratio = 25.00 / 53.68
= 0.47
PASS
Single Bolt Shear Strength

Bolt shear stress
bolt grade
 = A325-N
Fnv
 = 54.0
[ksi]
AISC 14th  Table J3.2
bolt dia db
 = 0.750
[in]
bolt area Ab
 = 0.442
[in2]

Single bolt shear strength
Rn-bolt
 = Fnv Ab
 = 23.86
[kips]
AISC 14th  Eq J3-1
Bolt Bearing/TearOut Strength on Plate


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 13⁄16
[in]
AISC 14th  Table J3.3
Bolt spacing & edge distance
spacing Ls
 = 3.000
[in]
edge distance Le
 = 1.375
[in]

Plate tensile strength
Fu
 = 65.0
[ksi]

Plate thickness
t
 = 0.500
[in]

Interior Bolt


Bolt hole edge clear distance
Lc
 = Ls - dh
 = 2.188
[in]

Bolt tear out/bearing strength
Rn-t&b-in
 = 1.5 Lc t Fu ≤ 3.0 db t Fu
AISC 14th  Eq J3-6b
 = 106.64 ≤ 73.13
 = 73.13
[kips]

Bolt strength at interior
Rn-in
 = min ( Rn-t&b-in , Rn-bolt )
 = 23.86
[kips]

Edge Bolt


Bolt hole edge clear distance
Lc
 = Le - dh / 2
 = 0.969
[in]

Bolt tear out/bearing strength
Rn-t&b-ed
 = 1.5 Lc t Fu ≤ 3.0 db t Fu
AISC 14th  Eq J3-6b
 = 47.23 ≤ 73.13
 = 47.23
[kips]

Bolt strength at edge
Rn-ed
 = min ( Rn-t&b-ed , Rn-bolt )
 = 23.86
[kips]


Number of bolt
interior nin
 = 2
edge ned
 = 1

Bolt bearing strength for all bolts
Rn
 = nin Rn-in + ned Rn-ed
 = 71.57
[kips]

Required shear strength
Vu
 = 
 = 25.00
[kips]

Bolt resistance factor-LRFD
φ
 = 0.75
AISC 14th  J3-10
φ Rn
 = 
 = 53.68
[kips]

ratio
 = 0.47
 > Vu
OK
 
Clip Angle - Girder Side - Block Shear - 1-Side Strip
ratio = 25.00 / 101.77
= 0.25
PASS
Plate Block Shear - Side Strip


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 7⁄8
[in]
AISC 14th  B4.3b
Plate thickness
tp
 = 0.500
[in]

Plate strength
Fy
 = 50.0
[ksi]
Fu
 = 65.0
[ksi]

Bolt no in ver & hor dir
nv
 = 1
nh
 = 3

Bolt spacing in hor dir
sh
 = 3.000
[in]

Bolt edge dist in ver & hor dir
ev
 = 1.500
[in]
eh
 = 1.375
[in]


Gross area subject to shear
Agv
 = [ (nh - 1) sh + eh ] tp
 = 3.688
[in2]

Net area subject to shear
Anv
 = Agv - [ (nh - 1) + 0.5 ] dh tp
 = 2.594
[in2]

Net area subject to tension
Ant
 = ( ev - 0.5 dh ) tp
 = 0.531
[in2]


Block shear strength required
Vu
 = 
 = 25.00
[kips]

Uniform tension stress factor
Ubs
 = 1.00
AISC 14th  Fig C-J4.2
Bolt shear resistance provided
Rn
 = min (0.6Fu Anv , 0.6Fy Agv ) +
 = 135.69
[kips]
AISC 14th  Eq J4-5
Ubs Fu Ant

Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-5
φ Rn
 = 
 = 101.77
[kips]

ratio
 = 0.25
 > Vu
OK
 
 
Clip Angle / Beam Web - Bolt Shear
ratio = 55.90 / 107.35
= 0.52
PASS
Bolt group forces
shear V
 = 50.00
[kips]
axial P
 = -25.00
[kips]

Bolt group resultant force
R
 = ( V2 + P2 )0.5
 = 55.90
[kips]


Bolt shear stress
bolt grade
 = A325-N
Fnv
 = 54.0
[ksi]
AISC 14th  Table J3.2
bolt dia db
 = 0.750
[in]
bolt area Ab
 = 0.442
[in2]

Number of bolt carried shear
ns
 = 3.0
shear plane m
 = 2


Beam Side Bolt Group Eccentricity
 
Eccentricity in double angle connection can be neglected when bolt group has single vertical row of bolt and
the distance from face of angle OSL to bolt group CG is less than 3 inch
AISC 14th  Page 10-8
 
Bolt group eccentricity coefficient
Cec
 = 
 = 1.000
AISC 14th  Page 10-8

Required shear strength
Vu
 = 
 = 55.90
[kips]

Bolt shear strength
Rn
 = Fnv Ab ns m Cec
 = 143.14
[kips]
AISC 14th  Eq J3-1
Bolt resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J3-1
φ Rn
 = 
 = 107.35
[kips]

ratio
 = 0.52
 > Vu
OK
 
 
Clip Angle / Girder - Bolt Shear
ratio = 25.00 / 53.68
= 0.47
PASS
Bolt group forces
shear V
 = 25.00
[kips]
axial P
 = 12.50
[kips]

Bolt shear stress
grade
 = A325-N
Fnv
 = 54.0
[ksi]
AISC 14th  Table J3.2
bolt dia db
 = 0.750
[in]
bolt area Ab
 = 0.442
[in2]

Number of bolt carried shear
ns
 = 3.0
shear plane m
 = 1

Bolt group eccentricity coefficient
Cec
 = 
 = 1.000

Required shear strength
Vu
 = 
 = 25.00
[kips]

Bolt shear strength
Rn
 = Fnv Ab ns m Cec
 = 71.57
[kips]
AISC 14th  Eq J3-1
Bolt resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J3-1
φ Rn
 = 
 = 53.68
[kips]

ratio
 = 0.47
 > Vu
OK
 
Clip Angle / Girder - Bolt Bearing on Girder
ratio = 50.00 / 107.35
= 0.47
PASS
Single Bolt Shear Strength

Bolt shear stress
bolt grade
 = A325-N
Fnv
 = 54.0
[ksi]
AISC 14th  Table J3.2
bolt dia db
 = 0.750
[in]
bolt area Ab
 = 0.442
[in2]

Single bolt shear strength
Rn-bolt
 = Fnv Ab
 = 23.86
[kips]
AISC 14th  Eq J3-1
Bolt Bearing/TearOut Strength on Plate


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 13⁄16
[in]
AISC 14th  Table J3.3
Bolt spacing
spacing Ls
 = 3.000
[in]

Plate tensile strength
Fu
 = 65.0
[ksi]

Plate thickness
t
 = 0.295
[in]

Interior Bolt


Bolt hole edge clear distance
Lc
 = Ls - dh
 = 2.188
[in]

Bolt tear out/bearing strength
Rn-t&b-in
 = 1.5 Lc t Fu ≤ 3.0 db t m Fu
AISC 14th  Eq J3-6b
 = 62.92 ≤ 43.14
 = 43.14
[kips]

Bolt strength at interior
Rn-in
 = min ( Rn-t&b-in , Rn-bolt )
 = 23.86
[kips]


Number of bolt
interior nin
 = 6

Bolt bearing strength for all bolts
Rn
 = nin Rn-in
 = 143.14
[kips]

Required shear strength
Vu
 = 
 = 50.00
[kips]

Bolt resistance factor-LRFD
φ
 = 0.75
AISC 14th  J3-10
φ Rn
 = 
 = 107.35
[kips]

ratio
 = 0.47
 > Vu
OK
 
Clip Angle / Girder - Angle Leg Bending
ratio = 1.11 / 2.67
= 0.42
PASS
Angle leg on beam
width b
 = 8.750
[in]
thickness t
 = 0.500
[in]

tensile Fu
 = 65.0
[ksi]
bolt gage g
 = 2.000
[in]

Beam web thickness
tp
 = 0.260
[in]

 
The angle leg bending moment is derived based on the assumption that the 2L legs to form a single
span L=2d beam with both ends fixed and tensile point load 2P imposed at mid span of this beam,
so the moment M=(1/8) x 2P x 2d = 0.5 P d
 
1/2 beam span - distance from bolt center to gusset plate center
d
 = g + 0.5 tp
 = 2.130
[in]

Axial tensile load on single angle
P
 = 
 = 12.50
[kips]

Moment in demand
Mr
 = 0.5 P d
 = 1.11
[kip-ft]

Moment capacity
Mn
 = ( t2 b ) / 4 x Fu
 = 2.96
[kip-ft]
AISC 14th  Eq 15-21
Resistance factor-LRFD
φ
 = 0.90
AISC 14th  Eq 15-21
φ Mn
 = 
 = 2.67
[kip-ft]

ratio
 = 0.42
 > Mr
OK
 
 
Bolt Tensile Prying Action on Clip Angle
ratio = 4.17 / 13.35
= 0.31
PASS
For 2L clip angle, all loads to be x 0.5 for single angle
Bolt group forces
shear V
 = 25.00
[kips]
axial P
 = -12.50
[kips]


Single Bolt Tensile Capacity Without Considering Prying
Bolt grade
grade
 = A325-N

Nominal tensile/shear stress
Fnt
 = 90.0
[ksi]
Fnv
 = 54.0
[ksi]
AISC 14th  Table J3.2
bolt dia db
 = 0.750
[in]
bolt area Ab
 = 0.442
[in2]

Bolt group shear force
shear V
 = 25.00
[kips]
no of bolt n
 = 3

Shear stress required
frv
 = V / ( n Ab )
 = 18.86
[ksi]

Resistance factor-LRFD
φ
 = 0.75
AISC 14th  J3.7
Modified nominal tensile stress
F'nt
 = 1.3 Fnt -
Fnt/φ Fnv
frv ≤ Fnt
 = 75.08
[ksi]
AISC 14th  Eq J3-3a
Bolt norminal tensile strength
rn
 = F'nt Ab
 = 33.17
[kips]
AISC 14th  Eq J3-1
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  J3.6
Single bolt tensile capacity
φ rn
 = 
 = 24.88
[kips]


Single Bolt Tensile Capacity After Considering Prying
Clip angle
leg width L
 = 3.500
[in]
bolt gage g
 = 2.000
[in]

leg t
 = 0.500
[in]


Dist from bolt center to leg edge
a
 = L - g
 = 1.500
[in]

a'
 = a + 0.5 db ≤ (1.25 b + 0.5 db )
 = 1.875
[in]
AISC 14th  Eq 9-27

Bolt hole diameter
bolt dia db
 = 0.750
[in]
bolt hole dia dh
 = 0.813
[in]
AISC 14th  B4.3b
Dist from bolt center to centerline of angle leg
b
 = g - 0.5 t
 = 1.750
[in]

b'
 = b - 0.5 db
 = 1.375
[in]
AISC 14th  Eq 9-21

Angle length
L
 = 8.750
[in]
Bolt Col nv
 = 3

Bolt spacing
sv
 = 3.000

Bolt tributary length
p
 = L / nv     p ≤ 2b  and p ≤ sv
 = 2.917
[in]
AISC 14th  Page 9-11

ρ
 = b' / a'
 = 0.733
AISC 14th  Eq 9-26
δ
 = 1 - dh / p
 = 0.721
AISC 14th  Eq 9-24
Tensile capacity per bolt before considering prying
B
 = from calc shown in above section
 = 24.88
[kips]

Resistance factor-LRFD
φ
 = 0.90
AISC 14th  Page 9-10
Clip angle leg thickness
t
 = 0.500
[in]
tensile Fu
 = 65.0
[ksi]

Plate thickness req'd to develop bolt tensile capacity without prying
tc
 = (
4 B b'/φ p Fu
)0.5
 = 0.896
[in]
AISC 14th  Eq 9-30a
α'
 = 
1/δ (1 + ρ )
[ (
tc/t
)2 - 1 ]
 = 1.765
AISC 14th  Eq 9-35
when  α' > 1
Q
 = (
t/tc
)2 (1 + δ )
 = 0.537
AISC 14th  Eq 9-34
 
Bolt tensile force per bolt in demand
T
 = from calc shown below
 = 4.17
[kips]

 
Tensile strength per bolt after considering prying
φ rn
 = B x Q
 = 13.35
[kips]
AISC 14th  Eq 9-31
ratio
 = 0.31
 > T
OK

Calculate Max Single Bolt Tensile Load
For 2L clip angle, all loads to be x 0.5 for single angle
Bolt group force
axial P
 = 12.50
[kips]

 
Bolt number
Bolt Row nh
 = 1
Bolt Col nv
 = 3

Bolt tensile force per bolt
T
 = P / ( nv nh )
 = 4.17
[kips]