Compute the factored load using LRFD method.
(1.2 ) (1.6 )
u
P D L=  +
Here, the dead load is
D
, the live load is
L
and the factored load is
u
P
.
Substitute
10 kips
for
D
and
28 kips
for
L
.
Calculate the bearing load per bolt using LRFD method.
./
ub
B L P n=
Here, the bearing load per bolt using LRFD method is
.BL
, the factored load using LRFD
method is
u
P
and the number of bolts in the connection is
b
n
.
Substitute
56.8 kips
for
u
P
and
6
for
b
n
.
. 56.8/ 6
= 9.47 kips/bolt
BL=
Compute the clear distance in direction of force between edge of hole and edge of adjacent
hole for edge bolts.
(1/16)hd=+
Here, the distance from the centerline of the compression flange to the tension side edge of
the end plate is
h
and the depth of the connecting beam is
d
.
Substitute
3/4 in
for
d
.
(3/ 4) (1/16)
= 13/16 in
h=+
( / 2)
ce
l l h=−
Here, the clear distance in direction of force between edge of hole and edge of adjacent
hole for edge bolts in WT is
c
l
, the effective length of end plate is
e
l
and the distance from
the centerline of the compression flange to the tension side edge of the end plate is
h
.
Substitute
1.5 in
for
e
l
,
0.8125 in
for
h
.
1.5 (0.8125/ 2)
= 1.094 in
c
l=−
Compute the clear distance in direction of force between edge of hole and edge of adjacent
hole for other bolts.
co
l s h=−
Here, the clear distance in direction of force between edge of hole and edge of adjacent
hole for other bolts is
co
l
, distance from centerline of most inside tension bolt row to the
edge of the yield line pattern is
s
and the distance from the centerline of the compression
flange to the tension side edge of the end plate is
h
.
Substitute
3 in
for
s
and
0.8125 in
for
h
.
3 0.8125
= 2.188 in
co
l=−
Check the bearing strength of the connection using LRFD method for edge bolts.
0.560 in
f
t=
for W10 X 49 column.
Here, the thickness of the column flange is
f
t
.
0.620 in
fp
t=
for WT5 X 22.5 end plate.
Here, the thickness of the end plate is
fp
t
.
The end plate controls the bearing strength of the connection of the tee to the column.
min
. 1.2 c fp u
B S l t F
=   
Here, the minimum bearing strength of the connection of the tee to the column using LRFD
method is
min
.BS
, the clear distance in direction of force between edge of hole and edge of
adjacent hole for edge bolts is
c
l
, the thickness of the end plate is
fp
t
,the specified minimum
tensile strength of end plate is
u
F
and the resistance factor for LRFD is
.
Substitute
0.75
for
,
1.094 in
for
c
l
,
0.620 in
for
fp
t
and
65 kips
for
u
F
.
min
. 0.75 1.2 1.094 0.620 65
= 39.7 kips/bolt
BS =  
. 2.4
act fp u
B S d t F
=   
Here, the resistance factor for LRFD is
, the actual bearing strength of the connection of
the tee to the column using LRFD method is
.act
BS
, the depth of the connecting beam is
d
, the thickness of the end plate is
fp
t
and the specified minimum tensile strength of end plate
is
u
F
.
Substitute
0.75
for
,
3/4 in
for
d
,
0.620 in
for
fp
t
and
65 kips
for
u
F
.
. 0.75 2.4 (3/ 4) 0.620 65
= 54.4 kips/bolt
act
BS =  
54.4 39.7
Use
39.7 kips/bolt
as bearing strength of the connection using LRFD method.
39.7 9.47
Hence, O.K.
Check the bearing strength of the connection using LRFD method for other bolts.
0.560 in
f
t=
for W10 X 49 column.
Here, the thickness of the column flange is
f
t
.
0.620 in
fp
t=
for WT5 X 22.5 end plate.
Here, the thickness of the end plate is
fp
t
.
The end plate controls the bearing strength of the connection of the tee to the column.
min
. 1.2
o c f u
B S l t F
=   
Here, the minimum bearing strength of the connection of the tee to the column using LRFD
method for other bolts is
min
.o
BS
, the clear distance in direction of force between edge of
hole and edge of adjacent hole for other bolts is
c
l
, the thickness of the column flange is
f
t
, the specified minimum tensile strength of end plate is
u
F
and the resistance factor for
LRFD is
.
Substitute
0.75
for
,
2.188 in
for
c
l
,
0.560 in
for
fp
t
and
65 kips
for
u
F
.
min
. 0.75 1.2 2.188 0.560 65
= 71.7 kips/bolt
o
BS =   
. 2.4
acto f u
B S d t F
=   
Here, the resistance factor for LRFD is
, the actual bearing strength of the connection of
the tee to the column using LRFD method for other bolts is
.acto
BS
, the depth of the
connecting beam is
d
, the thickness of the column flange is
f
t
and the specified minimum
tensile strength of end plate is
u
F
.
Substitute
0.75
for
,
3/4 in
for
d
,
0.560 in
for
f
t
and
65 kips
for
u
F
.
. 0.75 2.4 (3/ 4) 0.560 65
= 49.14 kips/bolt
acto
BS =  
49.14 71.7
Use
49.14 kips/bolt
as bearing strength of the connection using LRFD method for other
bolts.
49.14 9.47
Hence, O.K.
Compute the area of a single bolt using LRFD method.
2
( ) / 4
bb
Ad
=
Here, the area of a single bolt using LRFD method is
b
A
and the diameter of a single bolt
is
b
d
.
Substitute
3/ 4 in
for
b
d
.
2
2
( (3/ 4) ) / 4
= 0.4418 in
b
A
=
Check shear strength of the connection and check the value against bearing load per bolt
b
A
56.8 3
= 170.4 in-kips
u
M=
= 170.4 in–kips
u
M
…… (3)
Equate (1) and (3).
15 170.4
t
r=
Solve for
t
r
.
170.4 /15
11.36 kips
t
r=
=
Check for upper limit on nominal tensile stress in the presence of shear in LRFD.
‘ (1.3 ) ( )
nt
nt nt rv
nv
nt
F
F F f
F
F
=  −
Here, the nominal tensile stress in the presence of shear is
‘
nt
F
, the nominal tensile stress in
the absence of shear is
nt
F
, the nominal shear stress in the absence of tension is
nv
F
,the
required shear stress using LRFD method is
rv
f
and the resistance factor for LRFD is
.
Substitute
90 kips
for
nt
F
,
0.75
for
,
54 kips
for
nv
F
and
21.44 ksi
for
rv
f
.
90
‘ (1.3 90) (( ) 21.44)
0.75 54
= 69.35 ksi
nt
F=  −
69.35 < 90
Hence, O.K.
co
l s h=−
Here, the clear distance in direction of force between edge of hole and edge of adjacent
hole for other bolts is
co
l
, distance from centerline of most inside tension bolt row to the
edge of the yield line pattern is
s
and the distance from the centerline of the compression
flange to the tension side edge of the end plate is
h
.
Substitute
3 in
for
s
and
0.8125 in
for
h
.
3 0.8125
= 2.188 in
co
l=−
Check the bearing strength of the connection using ASD method.
0.560 in
f
t=
for W10 X 49 column.
Here, the thickness of the column flange is
f
t
.
0.620 in
fp
t=
for WT5 X 22.5 end plate.
Here, the thickness of the end plate is
fp
t
.
The end plate controls the bearing strength of the connection of the tee to the column in
ASD.
min
. (1.2 ) /
a c fp u
B S l t F=  
Here, the minimum bearing strength of the connection of the tee to the column in ASD for
edge bolts is
min
.a
BS
, the clear distance in direction of force between edge of hole and edge
of adjacent hole for edge bolts is
c
l
, the thickness of the end plate is
fp
t
,the specified
minimum tensile strength of end plate is
u
F
and the safety factor for ASD is
.
Substitute
2
for
,
1.094 in
for
l
,
0.620 in
for
t
and
65 kips
for
F
.
f
t
Check shear strength of the connection and check the value against bearing load per bolt
using ASD method.
Assume that the threads are in the plane of shear.
. ( ) /
a nv b
S S F A= 
Here, the shear strength of the connection using ASD method is
.a
SS
, the safety factor for
ASD is
, the nominal shear stress in the absence of tension is
nv
F
and the area of a single
bolt is
b
A
.
Substitute
2
for
,
54 kips
for
nv
F
and
2
0.4418 in
for
b
A
.
. (54 0.4418) / 2
= 11.93 kips/bolt
a
SS =
11.93 > 6.33
Hence, O.K.
Compute the location of centroid of bolt areas measured from top bolts.
1 1 2 2
(( ) ( ))/y y n y n A=  +
Here, the location of centroid of bolt areas measured from top bolts is
y
, the vertical
distance of 2nd row of bolts from the extreme fiber is
1
y
,the number of bolts in the second
row is
1
n
,the vertical distance between the centroidal section from the extreme fiber is
2
y
and the number of bolts in the third row from the top is
2
n
and the area of the section of
top bolts is
A
.
1
n
2
n
15.29 7.6
Hence, O.K.
Therefore, the number of bolts provided are adequate using ASD method.