September 8, 2020

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

.

Substitute

3 in

for

1

y

,

2

for

1

n

,

9 in

for

2

y

,

2

for

2

n

and

2

6 in

for

A

.

((3 2) (9 2)) / 6

= 4 in

y= +

Compute the tensile force of the bolt using LRFD method.

t

M n r d=

Here, the resisting moment is

M

, the number of bolts above the neutral axis is

n

, the tensile

force of the bolt using LRFD method is

t

r

and the distance between the centroid of the

tension bolts and the centroid of the compression bolts is

d

.

Substitute

4

for

n

,

7.5 in

for

d

.

4 7.5

= 30

t

t

Mr

r

=

30 t

Mr=

…… (1)

( ) ( )

u u v u h

M V e T e= +

…… (2)

Here, the applied moment on the connection is

u

M

, the vertical component of the factored

load is

u

V

and the eccentricity of the vertical component of the factored load is

v

e

, the

horizontal component of the factored load is

u

T

and the eccentricity of the horizontal

component of the factored load is

h

e

.

Substitute

80.5 kips

for

u

V

,

6 in

for

v

e

,

40.25 kips

for

u

T

and

7 in

for

h

e

80.5 6 (40.25 7)

= 764.75 in-kips

u

M= +

= 764.75 in-kips

u

M

…… (3)

Equate (1) and (3).

30 764.75

t

r=

Solve for

t

r

.

764.75/ 30

= 25.5 kips/bolt

t

r=

Compute the total tensile load per bolt using LRFD method.

.bt

T L V r=+

Here, the direct tensile load for a single bolt using LRFD method is

b

V

, the total tensile load