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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
15 kips
for
D
and
45 kips
for
L
.
(1.2 15) (1.6 45)
= 90 kips
u
P= +
Compute the vertical component of factored load using LRFD method.
(2/ 5)
uu
VP=
Here, the factored load is
u
P
and the vertical component of factored load is
u
V
.
Substitute
90 kips
for
u
P
.
(2 / 5) 90
= 80.5 kips
u
V=
Compute the horizontal component of factored load using LRFD method.
(1/ 5)
uu
TP=
Here, the factored load is
u
P
and the horizontal component of factored load is
u
T
.
Substitute
90 kips
for
u
P
.
(1/ 5) 90
= 40.25 kips
u
T=
Calculate the direct tensile load for a single bolt using LRFD method.
/
b u b
V T n=
Here, the direct tensile load for a single bolt using LRFD method is
b
V
, the horizontal
component of factored load is
u
T
and the number of bolts in the connection is
b
n
.
Substitute
40.25 kips
for
u
T
and
6
for
b
n
.
40.25/ 6
= 6.71 kips/bolt
b
V=
Determine the location of centroid of bolt areas measured from top bolts in LRFD.
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 1st row of bolts from the extreme fiber is
1
y
,the number of bolts in the topmost
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 second row from the top is
2
n
and the area of the section of
top bolts is
A
.
.bt
T L V r=+
Here, the direct tensile load for a single bolt using LRFD method is
b
V
, the total tensile load
per bolt using LRFD method is
.TL
and the tensile force of the bolt using LRFD method is
t
r
.
Substitute
6.71 kips/bolt
for
b
V
and
25.5 kips/bolt
for
t
r
.
. 6.71 25.5
= 32.21 kips/bolt
TL=+
Calculate the bearing load per bolt using LRFD method.
. / 6
u
B L P=
Here, the bearing load per bolt using LRFD method is
.BL
, the factored load using LRFD
method is
u
P
.
Substitute
90 kips
for
u
P
.
. 90 / 6
= 15 kips/bolt
BL=
Compute the area of the single bolt using LRFD method.
2
( ) / 4
b
Ad
=
Here, the area of the single bolt using LRFD method is
b
A
and the diameter of the bolt is
d
.
(2/ 5) ( )
aa
VP=
Here, the vertical component of load is
a
V
and the total service load is
a
P
.
Substitute
60 kips
for
a
P
.
(2/ 5) (60)
= 53.67 kips
a
V=
Compute the horizontal component of load using ASD method.
(1/ 5) ( )
aa
HP=
Here, the total service load is
a
P
and the horizontal component of load is
a
H
.
Substitute
60 kips
for
a
P
.
(1/ 5) (60)
= 26.83 kips
a
H=
Compute the direct tensile load for a single bolt using ASD method.
./
a a b
DT H n=
Here, the direct tensile load for a single bolt using ASD method is
.a
DT
, the horizontal
component of factored load using ASD method is
a
H
and the number of bolts in the
connection is
b
n
.
. / 6
aa
B L P=
Here, the bearing load per bolt using ASD method is
.a
BL
, the total service load using ASD
method is
a
P
.
Substitute
60 kips
for
a
P
.
. 60 / 6
= 10 kips/bolt
a
BL =
Compute the area of the single bolt using ASD method.
2
( ) / 4
b
Ad
=
Here, the area of the single bolt using ASD method is
b
A
and diameter of the bolt is
d
.
Substitute
1 in
for
d
.
2
2
( 1 ) / 4
= 0.7854 in
b
A
=
Compute the shear strength of the connection and check the value against bearing load per
bolt using ASD method.
. ( ) /
a nv b
S S F A=
Here, the nominal shear stress in the absence of tension is
nv
F
, the area of a single bolt using
ASD method is
b
A
, the shear strength of the connection using ASD method is
.a
SS
and the
safety factor for ASD is
.
