Hancock G.J., Murray Th.M., Ellifritt D.S. Cold-Formed Steel Structures to the AISI Specification
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Now f 0:60 for Eq. (E2.4-3):
fP
n
transverse
7:2 kips
Hence required
T
d
longitudinal
T
d
ÿ fP
n
transverse
12:15 ÿ 7:20 4:95 kips
Try L
l
0:75 in. Hence,
L
l
t
0:75
0:1
7:5 < 25
fP
n
0:60 1 ÿ 0:01
L
l
t
tL
l
F
u
Eq: E2:4-1
0:601 ÿ 0:01 7:50:1 0:75 60 2:50 kips
Hence for a longitudinal ®llet weld each side,
2fP
n
2 2:50 kips 5:0 kips > 4:95 kips
Hence, use 0.75-in. additional ®llet welds on each side in
addition to 2-in. transverse ®llet weld.
D. Arc Spot Weld Design (LRFD Method)
Assume three arc spot welds in line as shown in Figure
9.17c, with visible diameter (d) equal to 1.0 in. each with an
E60 electrode.
Check Shear Strength of Each Arc Spot Weld, Assum-
ing F
xx
60 ksi.
Section E2.2.1
d
e
0:7d ÿ 1:5t 4 0:55d 0:7 1:0 ÿ 1:5 0:1
0:55 in:
Eq: E2:2:1-5
d
e
d
0:55 4 0:55
P
n
p
4
d
e
2
0:75F
xx
Eq: E2:2:1-1
0:7850:55
2
0:75 60 10:68 kips
Chapter 9
288
Now f 0:60 for Eq. (2.2.1-1).
fP
n
0:60 10:68 6:41 kips
For three spot arc welds
3fP
n
19:23 kips > 12:15 kips:
Check Sheet-Tearing Capacity
Section E2.2.1
d
a
d ÿ t 1:0 ÿ 0:1 0:9in:
d
a
t
0:9
0:1
9
0:815
E
F
u
s
0:815
29500
60
r
18:1 > 9
Hence
P
n
2:20td
a
F
u
Eq: E2:2:1-2
2:2 0:1 0:9 60 11:88 kips
Now f 0:60 for Eq. (E2.2.1-2).
fP
n
0:60 11:88 7:13 kips
For three spot arc welds
3fP
n
21:4 kips > 12:15 kips
Minimum-Edge Distance and Spot Spacing
Section E2.2.1
e
min
1:5in: 1:5d
Clear distance between welds 1in: 1:0d.
e
min
P
u
fF
u
t
Eq: 2:2:1-6b
Hence
P
u
e
min
fF
u
t
Now f 0:70 for Eq. (E2.2.1-6b).
Connections
289
Since F
u
=F
sy
1:33 > 1:08
P
u
1:5 0:70 60 0:1 6:3 kips
For three arc spot welds
3P
u
18:9 kips > 12:15 kips
Use 1.5-in. edge distance from the center of the weld to the
edge of the plate and 2 in. between weld centers. The ®nal
detail is shown in Figure 9.17c, and, hence, 1.5-in. edge
distance is satisfactory.
E. Arc Seam Weld Design (LRFD Method)
Use same width (d 1:0 in.) as for the arc spot weld;
hence T
d
12:15 kips remains the same based on section
design strength in tension.
Calculate Length Based on Sheet-Tearing Capacity
Section E2.3
P
n
2:5tF
u
0:25L 0:96d
a
Eq: E2:3-2
Now f 0:60 for Eq. (E2.3-2).
Hence
fP
n
5 T
d
12:15 kips
L 4
T
d
f2:5tF
u
ÿ 0:96d
a
4
12:15
0:60 2:5 0:1 60
ÿ 0:96 0:9
1:94 in:
Hence use L 2 in.
Check Shear Capacity of Spot Weld
Chapter 9
290
Section E2.3
P
n
p
d
2
e
4
Ld
e
0:75F
xx
Eq: E2:3-1
p
0:55
2
2
2 0:55
"#
0:75 60
60:2 kips
Now f 0:60 for Eq. (E2.3-1).
Hence
fP
n
0:60 60:2 36:1 kips > T
d
12:15 kips
Check Minimum-Edge Distance
Section E2.3 (refers to Section E2.2-1)
e
min
3in:>1:5d 1:5in:
e
min
P
u
fF
ut
Eq: E2:2:1-6b
Hence
P
u
e
min
fF
ut
Now f 0:70 since
F
u
F
sy
1:33 > 1:08
P
u
3 0:70 60 0:1
12:6 kips > 12:15 kips
Hence, 3 in. edge distance is satisfactory, and the ®nal
detail is shown in Figure 9.17d.
9.8.2 Bolted Connection Design Example
Problem
Design a bolted connection in single shear to fully develop
the strength of the net section of the sheet in Example
9.8.1, using bolts in the line of action of the force as shown
in Figure 9.9b. Use
1
2
-in. bolts to ASTM A325 with washers
under both head and nut. The example uses the ASD
Connections
291
method. The following section numbers refer to the AISI
Speci®cation.
Solution
A. Plate Strength for Net Plate (ASD Method)
Section C2
d
1
2
in:
d
h
diameter of oversize hole
d
1
8
0:625 in:
Section C2
A
n
b ÿ d
h
t 3 ÿ 0:6250:1 0:2375 in:
2
T
n
is lesser of
T
n
A
g
F
y
3 0:145 13:5 kips Eq: C2-1
Since O 1:67 for Eq. (C2-1),
T
n
O
8:08 kips
T
n
A
n
F
u
0:2375 60 14:25 kips Eq: C2-2
Since O 2:00 for Eq. (C2-2),
T
n
O
7:125 kips
Hence, the required design strength is the lesser of
7.125 kips and 8.08 kips.
T
d
7:125 kips
Section E3.2
Where washers are provided under both the bolt head
and the nut,
P
n
1:0 ÿ 0:9r
3rd
s
F
u
A
n
4 F
u
A
n
Eq: E3:2-1
Chapter 9
292
Now from Figure 9.9b, s 3 in., r
1
3
, assuming three bolts.
Hence
P
n
1:0 ÿ
0:9
3
3
1
3
0:5
3
60 0:2375
12:35 kips < F
u
A
n
14:25 kips
Now O 2:22 for single shear connections in Eq. (E3.2-1).
P
n
O
12:35
2:22
5:56 kips < 7:125 kips
B. Number of Bolts Required (ASD Method)
ASTM A325 bolt F
nv
54:0 (when threads are not
excluded from shear plane)
Section E3.4
A
b
pd
2
4
p0:5
2
4
0:196 in:
2
P
n
A
b
F
nv
0:196 54:0 10:58 kips Eq: E3:4-1
Now
O 2:4
P
n
O
4:41 kips Table E3:4-1
3P
n
O
13:23 kips > T
d
5:56 kips
C. Check Bearing Capacity (ASD Method)
Section E3.3 Table E3.3-1 (with washers under both
bolt head and nut)
For single shear
P
n
3:00F
u
dt 3:00 60 0:5 0:1 9 kips
Connections
293
Now
O 2:22
P
n
O
4:05 kips Table E3:4-1
3
P
n
O
12:16 kips > T
d
5:56 kips
D. Edge Distance (ASD Method)
Section E3.1
Use e 1:0in:>1:5d 0:75 in:
P
n
teF
u
0:1 1:0 60 6 kips Eq: E3:1-1
Now
O 2:0 for
F
u
F
sy
1:33 > 1:08
P
n
O
3:0 kips
3
P
n
O
9:0 kips > 5:56 kips
Also distance between center of bolt holes must be greater
than or equal to 3d 1:5in:>e
1
4
in: 1:25 in. Hence,
bolt hole spacing is governed by the 3d requirement and not
tearout.
Final solution is three
1
2
-in. ASTM A325 bolts in line
spaced 1.5 in. between the centers of the bolt holes and
1.0 in. from the end of the plate to the center of the last bolt
hole. Allowable design load is 5.56 kips, which is controlled
by the plate strength and not the bolt in shear or bearing
strength.
9.8.3 Screw Fastener Design Example (LRFD
Method)
Problem
Determine the design tension strength of a screwed connec-
tion where a No. 12 screw fastens trapezoidal sheeting of
tensile strength (F
u
) equal to 80 ksi and base metal thick-
Chapter 9
294
ness (BMT) of 0.0165 in. to a purlin of ASTM A570 Grade 50
steel and thickness 0.60 in.
Solution
Pullout Screw
Section E4.4.1
No. 12 screw:
d 0:21 in:
F
u2
purlin65 ksi
P
not
0:85t
c
dF
u2
0:85 0:060 0:21 65 Eq: E4:4:4:1
0:696 kips
f 0:5 Section E4
fP
not
0:5 0:696 0:348 kips
Static Capacity of Sheathing Limited by Pullover
Section E4.4.2
P
nov
1:5t
1
d
w
F
u1
Eq: 4:4:2:1
t
1
0:0165 in:
F
u1
80 ksi
d
w
0:375 in:
P
nov
1:5 0:0165 0:375 80 0:742 kips
f 0:5 for Section E4
fP
nov
0:5 0:742 0:371 kips
Hence, pullout rather than pullover controls the design.
REFERENCES
9.1 Peko
È
z, T. and McGuire, W., Welding of Sheet Steel,
Proceedings, Fifth International Specialty Confer-
ence on Cold-Formed Steel Structures, St Louis,
MO, November, 1980.
9.2 Stark, J. W. B. and Soetens, F., Welded Connections in
Cold-Formed Sections, Fifth International Specialty
Connections
295
Conference on Cold-Formed Steel Structures, St
Louis, MO, November, 1980.
9.3 American Welding Society, ANSI=AWS D1.3-98,
Structural Welding CodeÐSheet Steel, American
Welding Society, Miami, FL, 1998.
9.4 American Welding Society, AWS C1.3-70, Recom-
mended Practises for Resistance Welding Coated
Low-Carbon Steels, Miami, FL, 1970 (reaf®rmed
1987).
9.5 American Welding Society, AWS C1.1-66, Recom-
mended Practice for Resistance Welding, Miami, FL.
9.6 Yu, Wei-Wen, AISI Design Criteria for Bolted Connec-
tions, Proceedings Sixth International Specialty
Conference on Cold-Formed Steel Structures, St
Louis, MO, November, 1982.
9.7 Rogers, C. A and Hancock, G. J., Bolted connection
tests of thin G550 and G300 sheet steels, Journal of
Structural Engineering, ASCE, Vol. 124, No. 7, 1998,
798±808.
9.8 European Convention for Constructional Steelwork,
European Recommendations for the Design of Light
Gauge Steel Members, Technical Committee 7, Work-
ing Group 7.1, 1987.
9.9 Stark, J. W. B. and Toma, A. W., Connections in thin-
walled structures, Developments in Thin-Walled
Structures, Chapter 5, Eds. Rhodes, J. and Walker,
A. C., Applied Science Publishers, London, 1982.
9.10 Peko
È
z. T., Design of Cold-Formed Steel Screw
Connections, Tenth International Specialty Confer-
ence on Cold-Formed Steel Structures, St Louis,
November, 1990.
9.11 Birkemoe, P. C. and Gilmor, M. I., Behaviour of
bearing-critical double angle beam connections, Engi-
neering Journal, AISC, Fourth Quarter, 1978.
9.12 American Institute of Steel Construction, Speci®ca-
tion for the Design, Fabrication and Erection of
Structural Steel for Buildings, Chicago, AISC, 1978.
Chapter 9
296
10
Metal Building Roof and Wall Systems
10.1 INTRODUCTION
Metal building roof and wall systems are generally
constructed with cold-formed C- and Z-sections. Roof
members are called purlins, and wall members are referred
to as girts, although the sections may be identical. Gener-
ally, purlins are lapped, as shown in Figure 10.1, to provide
continuity and, therefore, greater ef®ciency. The lap
connection is usually made with two machine-grade bolts
through the webs of the lapped purlins at each end of the
lap as shown in the ®gure. In addition, the purlins are
¯ange-bolted to the supporting rafter or web-bolted to a
web clip or an antiroll device. Z-section purlins are gener-
ally point symmetric; however, some manufacturers
produce Z-sections with unequal-width ¯anges to facilitate
nesting in the lapped region. Girts are generally not lapped
but can be face- or ¯ush-mounted as shown in Figure 10.2.
297