Beam to Girder
End Plate Shear Connection
Code=AISC 360-10 LRFD
 
Result Summary
geometries & weld limitations = PASS
limit states max ratio 
= 0.86
PASS
 
Sketch
Shear Connection
Code=AISC 360-10 LRFD
 
 
Members & Components Summary
Member
Shear Connection
Code=AISC 360-10 LRFD
 
End Plate

Plate
W
 = 6.750
[in]
L
 = 8.750
[in]

t
 = 0.375
[in]

Steel Grade A992
Fy
 = 50.0
[ksi]
Fu
 = 65.0
[ksi]

 
Bolt
end plate bolt

Bolt
dia
 = 0.750
[in]

grade
 = A325-N
Fu
 = 120.0
[ksi]

Fnt
 = 90.0
[ksi]
Fnv
 = 54.0
[ksi]

slip critical
SC
 = No

 
 
 
Geometry Restriction Check - End Plate to Girder
PASS
Min Bolt Edge Distance - End Plate to Girder

Bolt diameter
db
 = 
 = 0.750
[in]

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

 > Le-min
OK
Min Bolt Spacing - End Plate to Girder

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 End Plate to Girder
Ls
 = 
 = 3.000
[in]

 > Ls-min
OK
 
Weld Limitation Check - Beam Web to End Plate
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
 = 
 = 0.313
[in]

 > wmin
OK
Min Fillet Weld Length

Fillet weld size provided
w
 = 
 = 0.313
[in]

Min fillet weld length allowed
Lmin
 = 4 x w
 = 1.250
[in]
AISC 14th  J2.2b
Min fillet weld length
L
 = 
 = 8.750
[in]

 > Lmin
OK
 
 
Beam Web - Shear Yielding
ratio = 35.00 / 74.49
= 0.47
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
 = 
 = 35.00
[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
 = 0.47
 > Vu
OK
 
Beam Web - Shear Rupture
ratio = 35.00 / 72.63
= 0.48
PASS
Plate Shear Rupture Check


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 tp
 = 2.483
[in2]

Shear force in demand
Vu
 = 
 = 35.00
[kips]

Plate shear rupture strength
Rn
 = 0.6 Fu Anv
 = 96.84
[kips]
AISC 14th  Eq J4-4
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-4
φ Rn
 = 
 = 72.63
[kips]

ratio
 = 0.48
 > Vu
OK
 
 
Beam Web - Tensile Yielding
ratio = 25.00 / 102.38
= 0.24
PASS
End Plate Direct Connect Length Calc
Beam web-end plate connect length
L
 = 
 = 8.750
[in]

Beam web thickness
tw
 = 
 = 0.260
[in]

Gross area subject to tension
Ag
 = L tw
 = 2.275
[in2]


Gross area subject to tension
Ag
 = 
 = 2.275
[in2]

Steel yield strength
Fy
 = 
 = 50.0
[ksi]

Tensile force required
Pu
 = 
 = 25.00
[kips]

Tensile yielding strength
Rn
 = Fy Ag
 = 113.75
[kips]
AISC 14th  Eq D2-1
Resistance factor-LRFD
φ
 = 0.90
AISC 14th  D2 (a)
φ Rn
 = 
 = 102.38
[kips]
AISC 14th  Eq D2-1
ratio
 = 0.24
 > Pu
OK
 
Beam Web - Tensile Rupture
ratio = 25.00 / 102.98
= 0.24
PASS
End Plate Direct Connect Length Calc
Beam web-end plate weld length
L
 = 
 = 8.750
[in]

Beam web-end plate fillet weld size
w
 = 
 = 0.313
[in]

Beam web-end plate connect length
Lw
 = L - 2 w
 = 8.125
[in]

Plate Tensile Rupture Check


Plate size
width bp
 = 8.125
[in]
thickness tp
 = 0.260
[in]

Plate tensile strength
Fu
 = 65.0
[ksi]

Plate net area in tension
Ant
 = bp tp
 = 2.113
[in2]

Tensile force in demand
Pu
 = 
 = 25.00
[kips]

Plate tensile rupture strength
Rn
 = Fu Ant
 = 137.31
[kips]
AISC 14th  Eq J4-2
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-2
φ Rn
 = 
 = 102.98
[kips]
AISC 14th  Eq J4-2
ratio
 = 0.24
 > Pu
OK
 
 
Coped Beam - Flexural Rupture
ratio = 35.00 / 44.21
= 0.79
PASS
Beam section & cope side
sect
 = W12X30
cope side
 = double cope
Beam top flange cope
depth dc
 = 1.250
[in]
length Lc
 = 3.983
[in]

Beam bottom flange cope
depth dc
 = 1.500
[in]
length Lc
 = 3.983
[in]


Beam section elastic modulus
Snet
 = 
 = 3.952
[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
 = 
 = 35.00
[kips]

Beam end shear resistance
Rn
 = Fu Snet / e
 = 58.95
[kips]
AISC 14th  Eq 9-4
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq 9-4
φ Rn
 = 
 = 44.21
[kips]

ratio
 = 0.79
 > Vu
OK
 
Coped Beam - Local Web Buckling
ratio = 35.00 / 40.81
= 0.86
PASS
Beam section & cope side
sect
 = W12X30
cope side
 = double cope
Beam top flange cope
depth dct
 = 1.250
[in]
length Lct
 = 3.983
[in]

Beam bottom flange cope
depth dcb
 = 1.500
[in]
length Lcb
 = 3.983
[in]


Beam section elastic modulus
Snet
 = 
 = 3.952
[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
 = 274.8
[ksi]
AISC 14th  Eq 9-12
Fcr
 = Fcr   ≤  Fy
 = 50.0
[ksi]
AISC 14th  Eq 9-12

Beam end shear force
Vu
 = 
 = 35.00
[kips]

Beam end shear resistance
Rn
 = Fcr Snet / e
 = 45.34
[kips]
AISC 14th  Eq 9-6
Resistance factor-LRFD
φ
 = 0.90
AISC 14th  Eq 9-6
φ Rn
 = 
 = 40.81
[kips]

ratio
 = 0.86
 > Vu
OK
 
 
End Plate - Shear Yield
ratio = 17.50 / 98.44
= 0.18
PASS
Plate Shear Yielding Check


Plate size
width bp
 = 8.750
[in]
thickness tp
 = 0.375
[in]

Plate yield strength
Fy
 = 50.0
[ksi]

Plate gross area in shear
Agv
 = bp tp
 = 3.281
[in2]

Shear force required
Vu
 = 
 = 17.50
[kips]

Plate shear yielding strength
Rn
 = 0.6 Fy Agv
 = 98.44
[kips]
AISC 14th  Eq J4-3
Resistance factor-LRFD
φ
 = 1.00
AISC 14th  Eq J4-3
φ Rn
 = 
 = 98.44
[kips]

ratio
 = 0.18
 > Vu
OK
 
End Plate - Shear Rupture
ratio = 17.50 / 67.18
= 0.26
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
 = 0.375
[in]

Plate tensile strength
Fu
 = 65.0
[ksi]

Plate net area in shear
Anv
 = ( bp - n dh ) tp
 = 2.297
[in2]

Shear force required
Vu
 = 
 = 17.50
[kips]

Plate shear rupture strength
Rn
 = 0.6 Fu Anv
 = 89.58
[kips]
AISC 14th  Eq J4-4
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-4
φ Rn
 = 
 = 67.18
[kips]

ratio
 = 0.26
 > Vu
OK
 
End Plate - Block Shear - Center Strip
ratio = 35.00 / 170.93
= 0.20
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
 = 0.375
[in]

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

Bolt no in ver & hor dir
nv
 = 2
nh
 = 3

Bolt spacing in ver & hor dir
sv
 = 4.000
[in]
sh
 = 3.000
[in]

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


Gross area subject to shear
Agv
 = [ (nh - 1) sh + eh ] tp x 2
 = 5.531
[in2]

Net area subject to shear
Anv
 = Agv - [(nh - 1)+ 0.5] dh tp x2
 = 3.891
[in2]

Net area subject to tension
when sheared out by center strip
Ant
 = ( nv - 1) ( sv - dh ) tp
 = 1.172
[in2]


Block shear strength required
Vu
 = 
 = 35.00
[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 ) +
 = 227.91
[kips]
AISC 14th  Eq J4-5
Ubs Fu Ant

Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-5
φ Rn
 = 
 = 170.93
[kips]

ratio
 = 0.20
 > Vu
OK
 
End Plate - Block Shear - 2-Side Strip
ratio = 35.00 / 148.08
= 0.24
PASS
Plate Block Shear - 2 Side Strips


Bolt hole diameter
bolt dia db
 = 3⁄4
[in]
bolt hole dia dh
 = 7⁄8
[in]
AISC 14th  B4.3b
Plate thickness
tp
 = 0.375
[in]

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

Bolt no in ver & hor dir
nv
 = 2
nh
 = 3

Bolt spacing in ver & hor dir
sv
 = 4.000
[in]
sh
 = 3.000
[in]

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


Gross area subject to shear
Agv
 = [ (nh - 1) sh + eh ] tp x 2
 = 5.531
[in2]

Net area subject to shear
Anv
 = Agv - [(nh - 1)+ 0.5] dh tp x2
 = 3.891
[in2]

Net area subject to tension
when sheared out by 2 side strips
Ant
 = ( ev - 0.5 dh ) tp x 2
 = 0.703
[in2]


Block shear strength required
Vu
 = 
 = 35.00
[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 ) +
 = 197.44
[kips]
AISC 14th  Eq J4-5
Ubs Fu Ant

Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq J4-5
φ Rn
 = 
 = 148.08
[kips]

ratio
 = 0.24
 > Vu
OK
 
End Plate - Bolt Bearing on End Plate
ratio = 35.00 / 107.35
= 0.33
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
 = 0.375
[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
 = 79.98 ≤ 54.84
 = 54.84
[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
 = 35.42 ≤ 54.84
 = 35.42
[kips]

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


Number of bolt
interior nin
 = 4
edge ned
 = 2

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

Required shear strength
Vu
 = 
 = 35.00
[kips]

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

ratio
 = 0.33
 > Vu
OK
 
 
End Plate / Girder - Bolt Shear
ratio = 35.00 / 107.35
= 0.33
PASS
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
 = 6.0
shear plane m
 = 1

Bolt group eccentricity coefficient
Cec
 = 
 = 1.000

Required shear strength
Vu
 = 
 = 35.00
[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
 = 0.33
 > Vu
OK
 
End Plate / Girder - Bolt Bearing on Girder
ratio = 35.00 / 107.35
= 0.33
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
 = 
 = 35.00
[kips]

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

ratio
 = 0.33
 > Vu
OK
 
 
Bolt Tensile Prying Action on End Plate
ratio = 4.17 / 6.91
= 0.60
PASS
Bolt group forces
shear V
 = 35.00
[kips]
axial P
 = -25.00
[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
 = 35.00
[kips]
no of bolt n
 = 6

Shear stress required
frv
 = V / ( n Ab )
 = 13.20
[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
 = 87.66
[ksi]
AISC 14th  Eq J3-3a
Bolt norminal tensile strength
rn
 = F'nt Ab
 = 38.73
[kips]
AISC 14th  Eq J3-1
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  J3.6
Single bolt tensile capacity
φ rn
 = 
 = 29.04
[kips]


Single Bolt Tensile Capacity After Considering Prying
End plate
width w
 = 6.750
[in]
bolt gage g
 = 4.000
[in]

web tw
 = 0.260
[in]


Dist from bolt center to plate edge
a
 = 0.5 (w - g)
 = 1.375
[in]

a'
 = a + 0.5 db ≤ (1.25 b + 0.5 db )
 = 1.750
[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 face of web
b
 = 0.5(g - tw )
 = 1.870
[in]

b'
 = b - 0.5 db
 = 1.495
[in]
AISC 14th  Eq 9-21

Bolt pitch spacing
sv
 = 3.000

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

ρ
 = b' / a'
 = 0.854
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
 = 29.04
[kips]

Resistance factor-LRFD
φ
 = 0.90
AISC 14th  Page 9-10
End plate thickness
t
 = 0.375
[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
 = 1.009
[in]
AISC 14th  Eq 9-30a
α'
 = 
1/δ (1 + ρ )
[ (
tc/t
)2 - 1 ]
 = 4.664
AISC 14th  Eq 9-35
when  α' > 1
Q
 = (
t/tc
)2 (1 + δ )
 = 0.238
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
 = 6.91
[kips]
AISC 14th  Eq 9-31
ratio
 = 0.60
 > T
OK

Calculate Max Single Bolt Tensile Load
Bolt group force
axial P
 = 25.00
[kips]

 
Bolt number
Bolt Row nh
 = 2
Bolt Col nv
 = 3

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

 
 
Beam Web to End Plate Weld Strength
ratio = 5.29 / 7.61
= 0.70
PASS
Weld Group Forces
shear V
 = 35.00
[kips]
axial P
 = -25.00
[kips]   in tension
 
Beam web-end plate weld length
L
 = 
 = 8.750
[in]

Beam web-end plate fillet weld size
w
 = 
 = 0.313
[in]

Beam web-end plate weld length used for design
Lw
 = L - 2 w
 = 8.125
[in]

 
Combined Weld Stress
Weld stress from axial force
fa
 = P / L
 = -3.077
[kip/in]
in tension
Weld stress from shear force
fv
 = V / L
 = 4.308
[kip/in]

Weld stress combined - max
fmax
 = ( f2a + f2v )0.5
 = 5.294
[kip/in]
AISC 14th  Eq 8-11
Weld stress load angle
θ
 = tan-1 (
fa/fv
)
 = 35.5
[°]

Fillet Weld Strength Calc
Fillet weld leg size
w
 = 5⁄16
[in]
load angle θ
 = 35.5
[°]

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 )
 = 1.22
AISC 14th  Page 8-9
Fillet weld shear strength
Rn-w
 = 0.6 (C1 x 70 ksi) 0.707 w n C2
 = 22.671
[kip/in]
AISC 14th  Eq 8-1

Base metal - beam web
thickness t
 = 0.260
[in]
tensile Fu
 = 65.0
[ksi]

Base metal - beam web 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
 = 10.140
[kip/in]
AISC 14th  Eq J4-4

Double fillet linear shear strength
Rn
 = min ( Rn-w , Rn-b )
 = 10.140
[kip/in]
AISC 14th  Eq 9-2
Resistance factor-LRFD
φ
 = 0.75
AISC 14th  Eq 8-1
φ Rn
 = 
 = 7.605
[kip/in]

ratio
 = 0.70
 > fmax
OK