Eccentric Connections – Shear

Eccentrically loaded bolt groups

Ultimate Strength (Plastic Analysis)

Uses Instantaneous Center of Rotation (I.C.)

“most rational method”

Elastic (Vector) Analysis Assumed rotation about the C.G. of bolt group

Pu

CG

Instantaneous Center (I.C.)

Accounts for translation and rotation

Pu

CG CG IC?

CG IC?

Pu

CG

P

IC?

d

d

e

xo

yo

CG

P

IC

Ri

di qi

CG

P

IC

d

d

e

xo

yo

Ri

di qi

0)sincos(

0

0coscos

0

0sinsin

0

1

1

1

dd

dq

dq

o

n

i

oii

n

i

ii

y

n

i

ii

x

yxePdR

M

PR

F

PR

F

How do we know if our guess

for the I.C. is correct?

Load-Deformation (AISC Fig. 7-3)

55.010)1(

eRR ulti

2.718

tuAb

where tu is ~70% of Fub

(from experiments)

Alternatively, use shear

strength of bolt as calculated

by LRFD for Rult

Fig. 7-3, for one ¾” ASTM A325 bolt

in single shear, from tests (Fisher)

NOTE max

CG

P

IC

d

d

e

xo

yo

Ri

di qi

Iterative process required to solve!

55.010)1(

eRR ulti

0)sincos(

0

0coscos

0

0sinsin

0

1

1

1

dd

dq

dq

o

n

i

oii

n

i

ii

y

n

i

ii

x

yxePdR

M

PR

F

PR

F

CG

P

IC

d

d

e

xo

yo

Ri

di qi

Eccentric Connections (Shear) - Ultimate Strength Method

Bolt properties Eccentricity (in) Spacing (in)

Fub 120 ksi Dia. 0.875 in e 7.5 x 3

N or X 1 N=1, X=0 y 3

x y max 0.34

IC -1.7 -1.5 dmax 6.80

Bolt x y xi yi di i Ri Rixi/di Ridi

1 -1.5 -4.5 0.2 -3 3.01 0.15 25.13 1.67 75.57

2 -1.5 -1.5 0.2 0 0.20 0.01 7.92 7.92 1.58

3 -1.5 1.5 0.2 3 3.01 0.15 25.13 1.67 75.57

4 -1.5 4.5 0.2 6 6.00 0.30 28.07 0.93 168.49

5 1.5 4.5 3.2 6 6.80 0.34 28.33 13.33 192.64

6 1.5 1.5 3.2 3 4.39 0.22 27.05 19.73 118.63

7 1.5 -1.5 3.2 0 3.20 0.16 25.50 25.50 81.59

8 1.5 -4.5 3.2 -3 4.39 0.22 27.05 19.73 118.63

SUM 90.5 832.7

Pu = 67.86

Pu = 67.88

diff -0.03%

wrt CG wrt IC

Pu

e

CGIC

x

y

1

2

3

4

8

7

6

5

max

max

d

di

From tests

~ 0.34” cos q

Fy and M

Salmon et al., 4.11 (b)

Pu 6”

3”

3 @

3”

½” Plate

A36 Plate

Calculate maximum

load, Pu

Use ultimate

strength method

7/8” A325N bolts

Suppose, for this example, that we

have determined that bolt shear

capacity controls over bolt bearing

Spreadsheet

Define bolt group, etc.

Pu

e

CG IC

x

y

1

2

3

4

8

7

6

5

?

Bolt Properties, define bolt group, eccentricity, etc.

Locate bolts wrt C.G. Calculate wrt guess for I.C.

Note, maximum defined as 0.34, as shown in tests

Note: Ri calculated based on Rn according to AISC

0.563Fub for X or 0.450Fu

b for N (instead of tu)

M =

(Pu)(e+xocosd+yosind)

Fy, M, Fx

f applied here

Note: this spreadsheet set up for yo = 0 and d = 0

AISC Table 7-7 (Tables 7-6 to 7-13 for Bolt Groups)

Interpolate for ex = 7.5 in C=3.1

Interpolation within tables OK; interpolation between

tables not OK (use next lower angle of loading)

3.1 24.3 75.3

n n

n

R C r

R x kips

f f

f

Pu 6”

3”

3 @

3”

½” Plate

7/8” A325N bolts