Hancock G.J., Murray Th.M., Ellifritt D.S. Cold-Formed Steel Structures to the AISI Specification
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tions without washers. The resulting empirical formulae
for the nominal tension strength (P
n
) are
With washers P
n
1 ÿ 0:9r
3rd
s
F
u
A
n
4 F
u
A
n
9:30
No washers P
n
1 ÿ r
2:5rd
s
F
u
A
n
4 F
u
A
n
9:31
where r is the ratio of the force transmitted by the bolt or
bolts at the section considered divided by the tension force
in the full cross section at that section. The effect of varying
r by changing the number of bolts at a cross section is
clearly demonstrated in Figure 9.12. It is interesting to
observe that a larger number of bolts in the line of the force
reduces the stress concentration and hence increases the
load capacity on a given net area.
The resistance factor (f) for use in LRFD and the
factor of safety (O) for use in ASD with P
n
speci®ed in
Section E3.2 of the AISI Speci®cation depend on whether
the connection is double or single shear and whether
washers are included, as follows:
With washers double shear f 0:65; O 2:0
and no washers 9:32
With washer single shear f 0:55; O 2:22
9:33
Based on Ref. 9.7, the net section failure of 0.42-mm
(0.016 in.) and 0.60-mm (0.024 in.) G550 (80 ksi) and G300
(44 ksi) sheet steels at connections can be accurately and
reliably predicted with the use of the stress reduction factor
based on the con®guration of bolts and specimen width as
given by Eqs. (9.30) and (9.31), and without the use of the
Chapter 9
278
75% stress reduction factor as speci®ed in Section A3.3.2 of
the AISI Speci®cation for Grade 80 and Grade E steels.
9.5.4 Shear Failure of Bolt (Type IV)
The nominal shear strength (P
n
) of a bolt speci®ed in
Section E3.4 of the AISI Speci®cation is given by
P
n
A
b
F
nv
9:34
where F
nv
is given in Table E3.4-1 of the AISI Speci®cation
A
b
is the gross cross-sectional area of the bolt
The value of F
nv
depends upon whether threads are
excluded from the shear plane. The resistance factor for
LRFD speci®ed in Table E3.4-1 of the AISI Speci®cation is
0.65, and the factor of safety for ASD is 2.4.
The nominal tension strength (P
n
) of a bolt speci®ed in
Section E3.4 of the AISI Speci®cation is
P
n
A
b
F
nt
9:35
where F
nt
is given in Table E3.4-1 of the AISI Speci®cation
A
b
is the gross cross-sectional area of the bolt
The resistance factor for LRFD speci®ed in Table E3.4-1 of
the AISI Speci®cation is 0.75, and the factor of safety for
ASD is generally 2.0, although 2.25 is used for ASTM A307
bolts.
When a combination of shear and tension occurs, the
value of F
nt
in Eq. (9.35) is changed to F
0
nt
. Value of F
0
nt
are
given in Tables E3.4-3 and E3.4-5 for LRFD and E3.4-2 and
E3.4-4 for ASD. They take the form
F
0
nt
101 ÿ 2:4f
v
4 81 ksi 9:36
which is the equation for an ASTM A449 bolt designed by
LRFD with threads not excluded from the shear plane, with
f
v
equal to the shear stress.
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279
9.6 SCREW FASTENERS
Screw fasteners are used very frequently in cold-formed
steel structures, normally to fasten sheeting to thicker
material such as purlins, or to fasten sheets together. A
considerable amount of information is available in the
international literature and has been used to develop
Section E4, Screw Connections of the AISI Speci®cation.
The ECCS document European Recommendations for
the Design of Light Gauge Steel Members (Ref. 9.8) was the
®rst to provide detailed guidance on the design of screw
fasteners and blind rivets. The background research to this
document is set out in Ref. 9.9. Further developments of the
European design rules have been performed to produce the
design requirements in Eurocode 3 Part 1.3 (Ref. 1.7). In
order to apply the methods developed for screwed connec-
tions in Ref. 9.8 to U.S. practice, Peko
È
z (Ref 9.10) modi®ed
the formulae and recalibrated the results to develop speci®c
design rules for use in the American Iron and Steel Insti-
tute Speci®cation. The results are based on a study of screw
diameters ranging from 0.11 in. to 0.28 in. In the study, if
materials of different thickness were connected, the thin-
ner material was assumed to be in contact with the head of
the screw. Two different sets of formulae are provided.
These are
1. Design for shear
2. Design for tension
2.1 Pullout failure
2.2 Pullover failure
Screw connections loaded in shear can fail in one mode or
in a combination of modes, including screw shear, edge
tearing, tilting, and subsequent pullout of the screw and
bearing of the parent plates. The formulae developed only
apply where the edge distance (e
1
), which is the distance
from the center of the screw to the free edge in the direction
of loading, or the pitch, p
1
or p
2
, which is the center-to-
Chapter 9
280
center distance of adjacent screws, as shown in Figure
9.13c, is not less than three times the diameter of the
screw (d). However, the other edge distance in the direction
perpendicular to the load (e
2
) can be 1:5d. The formulae for
the nominal shear strength given in Section E4.3-1 of the
AISI Speci®cation are as follows:
(a) When t
2
4 t
1
, use the smallest of
P
ns
4:2F
u2
t
3
2
d
q
9:37
P
ns
2:7t
1
dF
u1
9:38
P
ns
2:7t
2
dF
u2
9:39
(b) When t
2
5 2:5t
1
, use the smaller of
P
ns
2:7t
1
dF
u1
9:40
P
ns
2:7t
2
dF
u2
9:41
(c) When 2:5t
1
> t
2
> t
1
, use linear interpolation
between (a) and (b), where
t
1
thickness of member in contact with screw head
t
2
thickness of member not in contact with screw head
F
u1
tensile strength of steel sheet with thickness t
1
F
u2
tensile strength of steel sheet with thickness t
2
d nominal screw diameter (see Figure 9.13b)
The resistance factor for LRFD is 0.50, and the factor of
safety for ASD is 3.0. Section E4.3.2 requires that the
nominal shear strength of the screw be at least 1:25P
ns
.
The shear strength of the screw is determined by test,
according to Section F1.
Failure of the net section based on the net cross-
sectional area of the sheet material should also be checked
in the direction of loading according to Sections E3.2 and
C2 of the AISI Speci®cation.
Screw connections loaded in tension can fail by the
screw pulling out of the plate (pullout), by the sheeting
pulling over the screw head and washer if any is present
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281
(pullover), or by tensile failure of the screw. The formulae
for the nominal pullout capacity (P
not
) and pullover capa-
city (P
nov
) are as follows:
P
not
0:85t
c
dF
u2
9:42
where t
c
is the lesser of the depth of penetration and the
thickness (t
2
) and t
2
, F
u2
are the thickness and tensile
strength, respectively, of the sheet not in contact with the
head, as shown in Figure 9.14, and
P
nov
1:5t
1
d
w
F
u1
9:43
FIGURE 9.14 Screws in tension.
FIGURE 9.13 Screws in shear: (a) thickness; (b) nominal screw
diameter (d); (c) minimum edge distances and pitches.
Chapter 9
282
where d
w
is the larger of the screw head diameter or the
washer diameter but not greater than
1
2
in. and t
1
, F
u1
are
the thickness and tensile strength, respectively, of the sheet
adjacent to the head of the screw, as shown in Figure 9.14.
Section E4.4.3 requires the nominal tension strength
of the screw to be at least 1.25 times the lesser of P
not
and
P
nov
. The nominal tension strength of the screw is deter-
mined by test according to Section F1.
9.7 RUPTURE
A mode of failure can occur at bolted connections, where
tearing failure can occur along the perimeter of holes as
shown in Figures 9.15 and 9.16. In some con®gurations,
such as the coped beam with both ¯anges coped as in
Figure 9.15a, the net area of the web in shear resists
rupture, and Section E5.1 of the AISI Speci®cation should
be used. In other cases, such as the coped beam with one
¯ange coped as shown in Figure 9.15b, block shear rupture
occurs where a block is pulled out of the end of the section
with a combination of shear failure on one plane and tensile
failure on the other plane. For the case of tension loading,
block shear rupture planes are shown in Figure 9.16.
Connection tests were performed by Birkemoe and
Gilmor (Ref. 9.11) on coped beams to derive formulae
for shear rupture and block shear rupture. These were
adopted in the American Institute of Steel Construction
FIGURE 9.15 Rupture of coped beam: (a) shear alone; (b) shear
and tension.
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283
Speci®cation in 1978 (Ref. 9.12) and have been used in
various forms in other standards and speci®cations ever
since. They were added to the AISI Speci®cation in 1999.
Test results suggest that it is conservative to predict
the block shear strength by adding the yield strength on
one plane to the rupture strength on the perpendicular
plane. Hence, two possible block shear strengths can be
calculated. These are rupture strength on the net tensile
area with shear yield on the gross area as shown in Figure
FIGURE 9.16 Block shear rupture: (a) small shear force and large
tension force; (b) large shear force and small tension force.
Chapter 9
284
9.16a, and yield on the gross tensile area with shear
rupture on the net shear area as shown in Figure 9.16b.
These form the basis of Eqs. (E5.3-1) and (E5.3-2) of the
AISI Speci®cation, respectively. The controlling equation is
governed by the conditions set out in Section E5.3 and not
the smaller value of Eqs. (E5.3-1) and (E5.3-2), which will
give an erroneous result. In Case (b) in Figure 9.16b, the
total force is controlled mainly by shear so that shear
rupture should control. In Case (a) in Figure 9.16a, the
total force is controlled mainly by tension so that tension
rupture should control.
9.8 EXAMPLES
9.8.1 Welded Connection Design Example
Problem
The 3-in.-wide, 0.1-in.-thick ASTM A570 Grade 45 sheet is
to be welded to the 0.2-in. plate shown in Figure 9.17 by
(a) Longitudinal ®llet welds, or
(b) Combined longitudinal and transverse ®llet
welds, or
(c) An arc spot weld, or
(d) An arc seam weld
Determine the size of each weld to fully develop the design
strength of the plate. The example uses the LRFD method.
The following section numbers refer to the AISI Speci®ca-
tion.
Solution
A. Plate Strength for Full Plate (LRFD Method)
For an ASTM A570 Grade 45 steel
F
y
45 ksi and F
u
60 ksi
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285
Section C2
T
n
A
g
F
y
btF
y
Eq: C2-1
3 0:145 13:5 kips
Since f
t
0:90 for Eq. (C2-1), then
f
t
T
n
12:15 kips
T
n
A
n
F
u
btF
u
Eq: C2-2
3 0:160 18 kips
FIGURE 9.17 Weld design example: (a) longitudinal ®llet welds;
(b) combined longitudinal and transverse ®llet welds; (c) arc spot
weld; (d) arc seam weld.
Chapter 9
286
Since f
t
0:75 for Eq. (C2-2), then
f
t
T
n
0:75 18 13:5 kips
Hence, the design strength of the connection (T
d
) is the
lesser of f
t
T
n
13:5 kips and f
t
T
n
12:5 kips; T
d
12:15 kips.
B. Longitudinal Fillet Weld Design (LRFD Method)
Section E2.4
Assuming L=t > 25,
P
n
0:75tLF
u
Eq: E2:4-2
Now fP
n
4 T
d
, where f 0:55 for Eq. (E2.4-2). Hence,
L
T
d
0:55 0:75tF
u
12:15
0:550:75 0:1 60
4:90 in:
Length of each ®llet
L
2
4:90
2
2:45 in:
Check
L
t
2:45
0:1
24:5 < 25
A slightly shorter length could be used according to Eq.
(E2.4-1), but a 2.5- in.-weld will be used.
C. Combined Longitudinal and Transverse Fillet Weld
Design (LRFD Method)
First locate transverse ®llet weld across 2 in. of end of
plate as shown in Figure 9.17b.
Section E2.4
P
n
transverse
tLF
u
0:1 2 60 12 kips
Eq: E2:4-3
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287