Yu W., LaBoube R.A. Cold-Formed Steel Design

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WELDED CONNECTIONS 275

Figure 8.19 Example 8.1.

c. Shear Capacity of Welds. By using Eq. (8.26) and

E60 electrodes,

(4πd

/4)(0.75F

)



π(0.4125)

(0.75 ×60)

2.55

= 9.43 kips

d. Strength of Connected Sheets Around Welds

0.675

0.075

= 9 <



0.815



29,500

= 18.07



By using Eq. (8.27a)

4(2.20td

)



4(2.20)(0.075)(0.675)(60)

2.20

= 12.15 kips

On the basis of the above considerations, the allow-

able load for the ASD method is the smallest value,

that is, 9.09 kips, which is governed by the tensile

load for yielding of steel sheets.

B. LRFD Method

As the ﬁrst step of the LRFD method, the AISI requirements

for using arc spot welds should be checked as the ASD

method. From items 1–5 for the ASD method, the layout

of the spot welds are satisﬁed with the AISI requirements.

The design strength φP

for the LRFD method is based

on the following considerations:

a. Tensile Load for Steel Sheets. BasedonSectionC2of

the AISI speciﬁcation:

i. For yielding [Eq. (6.2)],

= φ

)

= (0.90)(4.5 ×0.075)(45) = 13.67 kips

ii. For fracture away from the connections [Eq. (6.3)],

= φ

)

= (0.75)(4.5 ×0.075)(60) = 15.19 kips

Use φ

= 13.67 kips.

b. Tensile Load Based on End Distance (e = 1.25 in.).

Using Eq. (8.25) for four spot welds (F

> 1.08),

φP

= φ(4)(eF

= (0.70)(4)(1.25 × 60 ×0.075) = 15.75 kips

c. Shear Capacity of Welds. By using Eq. (8.26) and E60

electrodes,

φP

= φ(4)



πd



(0.75F

)

= (0.60)(π )(0.4125)

(0.75 × 60) = 14.43 kips

d. Strength of Connected Sheets Around Welds. Since

/t < 0.815

√

E/F

, use Eq. (8.27a),

φP

= φ(4)(2.20td

)

= (0.70)(4)(2.20 ×0.075 × 0.675 ×60)

= 18.71 kips

Based on the above four considerations, the controlling

design strength is 13.67 kips, which is governed by the

tensile load for yielding of steel sheets.

According to the load factors and load combinations

discussed in Section 3.3.2.2, the required strength for the

given dead load–live load ratio of

is computed as follows:

= 1.4P

+ P

= 1.4P

+ 5P

= 6.4P

[Eq. (3.5a)]

where P

= applied load due to dead load

= applied load due to live load

276 8 CONNECTIONS

and

= 1.2P

+ 1.6P

= 1.2P

+ 1.6(5P

) = 9.2P

[Eq. (3.5b)]

Use P

= 9.2P

.Byusing9.2P

= 13.67 kips,

= 1.49 kips

= 5P

= 7.45 kips

The allowable load based on the LRFD method is

+ P

= 1.49 +7.45 = 8.94 kips

It can be seen that the LRFD method permits a slightly

smaller allowable load than the ASD method. The differ-

ence between these two design approaches for this partic-

ular case is less than 2%.

Arc Seam Welds. For arc seam welds (Fig. 8.10), Section

E2.3 of the AISI North American Speciﬁcation speciﬁes

that the nominal shear strength (resistance) P

of an arc

seam weld is the smaller of the values computed by Eqs.

(8.31) and (8.32):

i. Nominal Shear Strength Based on Shear Capacity of

Weld



πd

+ Ld



0.75F

(8.31)

ii. Nominal Shear Strength Based on Strength of

Connected Sheets

= 2.5tF

(0.25L + 0.96d

) (8.32)

For Eqs. (8.31) and (8.32),

 = 2.55 (ASD)

φ = 0.60 (LRFD)

= 0.50 (LSD)

d = width of arc seam weld

L = length of seam weld not including circular ends (for

computation purposes, L should not exceed 3d)

The deﬁnitions of d

, d

, F

,andF

and the require-

ments for minimum edge distance are the same as those for

arc spot welds.

Equation (8.31) is derived from Eq. (8.12) and Eq. (8.32)

is based on Eq. (8.13).

Fillet Welds. AccordingtoSectionE2.4oftheAISINorth

American Speciﬁcation, the design strength of a ﬁllet weld

in lap and T-joints should not exceed the values computed

by Eq. (8.33) for the shear strength of the ﬁllet weld and by

Eq. (8.34) or Eq. (8.35) for the strength of the connected

sheets as follows:

i. Nominal Strength Based on Shear Capacity of Weld .

For t > 0.10 in. (3.8 mm),

= 0.75t

(8.33)

 = 2.55 (ASD)

φ =



0.60 (LRFD)

0.50 (LSD)

ii. Nominal Strength Based on Strength of Connected

Sheets

a. Longitudinal Loading.WhenL/t < 25,



1 − 0.01



tLF

(8.34a)

 = 2.55 (ASD)

φ =



0.60 (LRFD)

0.50 (LSD)

When L/t > 25,

= 0.75tLF

(8.34b)

 = 3.05 (ASD)

φ =



0.50 (LRFD)

0.40 (LSD)

b. Transverse Loading

= tLF

(8.35)

 = 2.35 (ASD)

φ =



0.65 (LRFD)

0.60 (LSD)

where P

= nominal strength of a ﬁllet weld

L = length of ﬁllet weld

= effective throat, =0.707w

0.707w

, whichever is smaller

, w

= leg size of ﬁllet weld (Fig. 8.20)

The deﬁnitions of t, F

,andF

are the same as those

used for arc spot welds. It should be noted that Eqs. (8.33),

(8.34), and (8.35) are based on Eqs. (8.14), (8.15), and

(8.16), respectively.

Example 8.2 Use the ASD method to determine the

allowable load for the welded connection using ﬁllet welds,

as shown in Fig. 8.21. Assume that A570 Grade 33 steel

sheets and E60 electrodes are to be used.

WELDED CONNECTIONS 277

Figure 8.20 Leg sizes of ﬁllet welds

1.4

:(a) lap joint; (b) t-joint.

Figure 8.21 Example 8.2.

SOLUTION. From Table 2.1, the yield point and the

tensile strength of A1011 Grade 33 steel are 33 and 52

ksi, respectively. The allowable load P can be determined

as follows:

1. Allowable Tensile Load for Steel Sheet. Based on

Section C2 of the AISI Speciﬁcation:

i. For yielding [Eq. (6.2)],



1.67

(2.0 × 0.105)(33)

1.67

= 4.15 kips

ii. For fracture away from the connections [Eq. (6.3)],



2.00

(2.0 × 0.105)(52)

2.00

= 5.46 kips

Use P

= 4.15 kips.

2. Allowable Load for Longitudinal Fillet Welds. Since

L/t = 2/0.105 = 19.05 < 25, use Eq. (8.34a),

[1 −0.01(L/t)]tLF



[1 −0.01(19.05)](0.105)(2)(52)

2.55

= 3.46 kips per weld

Using two longitudinal welds

= 2P

= 2 × 3.46 = 6.92 kips

Because the thickness of steel sheet is less than 0.10

in., it is not necessary to use Eq. (8.33).

Since P

, the allowable tensile load is governed

by the tensile capacity of steel sheet, that is,

= 4.15 kips

The use of the LRFD method can be handled in the same

way as Example 8.1.

Flare Groove Welds. On the basis of Section E2.5 of the

AISI North American speciﬁcation, the nominal strength of

each ﬂare groove weld should be determined as follows:

i. Nominal Strength Based on Shear Capacity of Weld.

For t > 0.10 in. (3.8 mm),

= 0.75t

(8.36)

 = 2.55 (ASD)

φ =



0.60 (LRFD)

0.50 (LSD)

ii. Nominal Strength Based on Strength of Connected

Sheet

278 8 CONNECTIONS

(

)

Figure 8.22 (a) Shear in longitudinal ﬂare bevel groove

weld.

1.314,1.345

(b) Shear in longitudinal ﬂare V-groove

weld.

1.314,1.345

= R).

1.314,1.345

a. Transverse Loading (Fig. 8.14)

= 0.833tLF

(8.37)

 = 2.55 (ASD)

φ =



0.60 (LRFD)

0.50 (LSD)

b. Longitudinal Loading (Figs. 8.22a–8.22f)

If t ≤ t

< 2t or if the lip height is less than the

weld length L,

= 0.75tLF

(8.38a)

If t

> 2t and the lip height is equal to or greater

than L,

= 1.50tLF

(8.38b)

(d)

Figure 8.22 (d) Flare bevel groove weld (ﬁlled ﬂush to surface,

= R).

1.314

(e) Flare bevel groove weld (not ﬁlled ﬂush to

surface, w

>R).

1.314

(f ) Flare bevel groove weld (not ﬁlled ﬂush

to surface, w

<R).

1.134

Using Eqs. (8.37) and (8.38),

 = 2.80 (ASD)

φ =



0.55 (LRFD)

0.45 (LSD)

In Eqs. (8.36) through (8.38),

= nominal strength (resistance) of ﬂare groove

weld

h = height of lip

L = length of the weld

= effective throat of ﬂare groove weld ﬁlled ﬂush

to surface (Figs. 8.22c and 8.22d)

For ﬂare bevel groove weld t

= 5/16R

For ﬂare V-groove weld t

= 1/2R [3/8R when R >

in. (12.7 mm)]

WELDED CONNECTIONS 279

= effective throat of ﬂare groove weld not ﬁlled

ﬂush to surface = 0.707 w

or 0.707 w

, whichever

is smaller. (Figs. 8.22e and 8.22f )

= larger effective throat than those above shall be

permitted if measurement shows that the welding

procedure to be used consistently yields a large

value of t

R = radius of outside bend surface

= legofweld(seeFigs.8.22e and 8.22f )

, F

were deﬁned previously

It should be noted that Eqs. (8.36), (8.37), and (8.38) are

derived from Eqs. (8.17), (8.18), (8.19), and (8.20).

Example 8.3 Use the ASD method to design a welded

connection as shown in Fig. 8.23 for the applied load of

15 kips. Consider the eccentricity of the applied load. Use

A606 Grade 50 steel (F

= 50 ksi and F

= 70 ksi) and

E70 electrodes.

SOLUTION. Considering the eccentricity of the applied

load, it is desirable to place the welds so that their centroids

coincide with the centroid of the angle section. It should be

noted that weld L

is a ﬂare groove weld, weld L

is a

transverse ﬁllet weld, and weld L

is a longitudinal ﬁllet

weld.

Let P

be the allowable load of end weld L

.Byusing

Eq. (8.35) for transverse ﬁllet welds

tLF



(0.135)(2.0)(70)

2.35

= 8.04 kips

Taking moments about point A,

P(1.502) − P

(2.0) − P

(1.0) = 0

15(1.502) − P

(2.0) − 8.04(1.0) = 0

= 7.25 kips P

= P − (P

+ P

)  0

For the ﬂare groove weld subjected to longitudinal

loading, with the assumption that t ≤ t

< 2t, the allow-

able load according to Eq. (8.38a) is

0.75tLF



0.75(0.135)(1)(70)

2.80

= 2.53 kips/in.

The required length L

7.25

2.53

= 2.87 in.

Use L

= 3in.

For weld length L

, use the minimum length of

in.

speciﬁed in Section 2.3.3.1 of the AWS code, even though

is approximately equal to zero.

8.3.3 Additional Design Information on Welded

Connections

The preceding discussion and design examples were based

on the AISI North American Speciﬁcation. For addi-

tional information concerning details of welded connec-

tions, workmanship, technique, qualiﬁcation, and inspec-

tion, the reader is referred to the AWS code.

8.96

In addition to the research work conducted at Cornell

and the design criteria being used in the United States,

other research projects on welded connections have been

conducted by Baehre and Berggren,

8.4

Stark and Soe-

tens,

8.22

Kato and Nishiyama,

8.23

Snow and Easterling,

8.99

and others. These references also discuss design considera-

tions and testing of welded connections. An economic study

of the connection safety factor has been reported by Lind,

Knab, and Hall in Ref. 8.24. Design information on tubular

joints can be found in Refs. 8.25–8.32 and 8.68–8.70.

8.3.4 Resistance Welds

Resistance welds (including spot welding and projection

welding) are mostly used for shop welding in cold-formed

steel fabrication (Fig. 8.24).

Figure 8.23 Example 8.3.

280 8 CONNECTIONS

Figure 8.24 Resistance welds.

The nominal shear strengths for spot welding (Table 8.1)

are based on Section E2.6 of the 1996 AISI Speciﬁcation,

which is based on Ref. 8.33 for outside sheets of 0.125 in.

or less in thickness and Ref. 8.34 for outside sheets thicker

than 0.125 in. The safety factor used to determine the

allowable shear strength is 2.5 and the resistance factor used

for the LRFD method is φ = 0.65. Values for intermediate

thicknesses may be obtained by straight-line interpolation.

The above tabulated values may also be applied to

pulsation welding and spot welding medium-carbon and

low-alloy steels with possibly higher shear strengths. It is

interesting to note that if the shear strength speciﬁed in the

AISI Speciﬁcation is used for spot welding galvanized steel

sheets, a relatively larger safety factor may be obtained for

the ASD method.

8.35

It should be noted that special welding procedures may

be required for the welding of low-alloy steels. In all cases,

welding should be performed in accordance with the AWS

recommended practices.

8.33,8.34, 8.104

In 1999, the following equations for the nominal shear

strength of spot welds were developed to replace the tabu-

lated values given in Table 8.1

1.333

1. For 0.01 in. (0.25 mm) ≤ t < 0.14 in. (3.56 mm),

⎧

⎪

⎨

⎪

⎩

144t

1.47

(for t in inches and

in kips) (8.39a)

5.51t

1.47

(for t in mm and

in kN) (8.39b)

2. For 0.14 in. (3.56 mm) ≤ t < 0.18 in. (4.57 mm),

⎧

⎪

⎨

⎪

⎩

43.4t + 1.93 (for t in inches and

in kips) (8.40a)

7.6t + 8.57 (for t in mm and

in kN) (8.40b)

where t is the thickness of the thinnest outside sheet.

The upper limit of Eq. (8.39) was selected to best ﬁt

the data provided in Table 2.1 of Ref. 8.33 and Table 1.3

of Ref. 8.34. Equation (8.40) is limited to t ≤ 0.18 in.

(4.57 mm) due to the thickness limit set forth in the AISI

North American Speciﬁcation.

Table 8.1 and Eqs. (8.39) and (8.40) provide only the

nominal shear strength for spot welding. If the tensile

strength of spot welding is required, it can be obtained

either from tests or from the following empirical formulas

for tensile and shear strengths proposed by Henschkel

8.36

1. Tensile Strength

N = tF



− b

+ c − (f C + gMn)



2. Shear Strength

S = tF



α − β



C +



where N = tensile strength of spot welding

S = shear strength of spot welding

t = sheet thickness

= tensile strength of steel sheet

C = carbon content

Mn = manganese content

D = weld nugget diameter

a, b, c, f , g , α, β = coefﬁcients determined from

test results (see Ref. 8.36 for

detailed information)

It should be noted that Henschkel’s study was based on

the following ranges of material:

1. Thickness of steel sheet: 0.008–0.500 in. (0.2–

12.7 mm)

2. Tensile strength of material: 37,500–163,800 psi

(258–1129 MPa)

3. Carbon content: 0.01–1.09%

4. Manganese content: 0.03–1.37%

From the above two equations, the relationship between

tensile and shear strengths of spot welding can be expressed

as follows:

− b)(α − βC − 0.05βMn)

c − fC− gMn

α − βC − 0.05βMn

Using the constants given in Ref. 8.36, it can be seen

that for the steels speciﬁed in the AISI North American

Speciﬁcation the tensile strength of spot welding is higher

than 25% of the shear strength.

See Example 8.8 for the design of welded connections

using resistance welds.

BOLTED CONNECTIONS 281

Table 8.1 Nominal Shear Strength for Spot Welding

1.314

Thickness of Nominal Shear Thickness of Nominal Shear

Thinnest Outside Strength per Thinnest Outside Strength per

Sheet (in.) Spot (kips) Sheet (in.) Spot (kips)

0.010 0.13 0.080 3.33

0.020 0.48 0.090 4.00

0.030 1.00 0.100 4.99

0.040 1.42 0.110 6.07

0.050 1.65 0.125 7.29

0.060 2.28 0.190 10.16

0.070 2.83 0.250 15.00

8.3.5 Shear Lag Effect in Welded Connections of

Members

When a tension member is not connected through all

elements, such as when an angle is connected through

only one leg, the stress distribution in the cross section

is nonuniform. This phenomenon is referred to as “shear

lag,” which has a weakening effect on the tensile capacity

of the member.

For the design of hot-rolled steel shapes, the AISC

Speciﬁcation uses the effective net area A

for determining

the nominal strength. The effective net area is computed as

= UA

in which U is the reduction factor and A

is the net area.

For cold-formed steel design, the following Speciﬁ-

cation Section E2.7 was added in the Supplement in

1999

1.333

and has been retained for subsequent editions of

the Speciﬁcation

1.345

E2.7 Shear Lag Effect in Welded Connections of

Members Other Than Flat Sheets

The nominal strength of a welded member shall be determined

in accordance with Section C2. For fracture and/or yielding

in the effective net section of the connected part, the nominal

tensile strength, P

, shall be determined as follows:

= A

(8.41)

 = 2.50 (ASD)

φ =



0.60 (LRFD)

0.50 (LSD)

where F

is the tensile strength of the connected part as

speciﬁedinSectionA2.1orA2.3.2andA

= AU is the

effective net area with U deﬁned as follows:

1. When the load is transmitted only by transverse welds:

A = area of directly connected elements

U = 1.0

2. When the load is transmitted only by longitudinal welds

or by longitudinal welds in combination with transverse

welds:

A = gross area of member, A

U = 1.0 for members when the load is transmitted directly

to all of the cross sectional elements

Otherwise, the reduction coefﬁcient U is determined

as follows:

(a) For angle members:

U = 1.0 −

1.20 ¯x

< 0.9 (8.42)

but U shall not be less than 0.4

(b) For channel members:

U = 1.0 −

0.36 ¯x

< 0.9 (8.43)

but U shall not be less than 0.5

where ¯x = distance from shear plane to centroid of the

cross section (Fig. 8.25)

L = length of longitudinal welds (Fig. 8.25)

The above design provisions were adapted from the AISC

design approach. Equations (8.42) and (8.43) are based

on the research work conducted by Holcomb, LaBoube,

and Yu at the University of Missouri-Rolla on bolted

connections.

6.24,6.25

8.4 BOLTED CONNECTIONS

The structural behavior of bolted connections in cold-

formed steel construction is somewhat different from that in

hot-rolled heavy construction, mainly because of the thin-

ness of the connected parts. Prior to 1980, the provisions

included in the AISI Speciﬁcation for the design of bolted

connections were developed on the basis of the Cornell tests

conducted under the direction of George Winter.

8.37–8.40

These provisions were updated in 1980

1.4

to reﬂect the

results of additional research performed in the United

282 8 CONNECTIONS

Figure 8.25 Determination of ¯x for sections using ﬁllet welds.

1.333,1.346

States

4.30,8.41–8.46

and to provide a better coordination with

the speciﬁcations of the Research Council on Structural

Connections

8.47

and the AISC.

1.148

In 1986, design provi-

sions for the maximum size of bolt holes and the allowable

tension stress for bolts were added in the AISI Speciﬁca-

tion. The 1996 edition of the Speciﬁcation combined the

ASD and LRFD design provisions with minor revisions.

The shear lag effect on bolted connections were considered

in the Supplement to the 1996 Speciﬁcation. New bearing

equations were adopted in the 2001 edition

1.336

and retained

in the 2007 edition of the Speciﬁcation.

8.4.1 Research Work and Types of Failure Mode

Since 1950, numerous bolted connections using thin sheets

with A307 bolts and A325 high-strength bolts have been

tested at Cornell University and other institutions. The

purposes of these research projects were to study the struc-

tural performance of bolted connections and to provide

necessary information for the development of reliable

design methods. A summary of this research is provided

by Yu

1.354

Results of tests indicate that the following four basic

types of failure usually occur in the cold-formed steel bolted

connections:

1. Longitudinal shearing of the sheet along two parallel

lines (Fig. 8.26a)

2. Bearing or piling up of material in front of the bolt

(Fig. 8.26b)

3. Tearing of the sheet in the net section (Fig. 8.26c)

4. Shearing of the bolt (Fig. 8.26d)

These four failure modes are also illustrated in Fig.

8.27. In many cases, a joint is subject to a combination of

different types of failure modes. For example, the tearing

of the sheet is often caused by the excessive bolt rotation

and dishing of the sheet material.

8.45,6.23

8.4.1.1 Longitudinal Shearing of Steel Sheets (Type

I Failure) When the edge distance e as shown in

Figure 8.26 Types of failure of bolted connections.

8.37

Figs. 8.27a and 8.28 is relatively small, connections

usually fail in longitudinal shearing of the sheet along two

parallel lines.

Research

1.354

has shown that for bolted connections

having small e/d ratios the bearing stress at failure can

be predicted by

(8.44)

where σ

= ultimate bearing stress between bolt and

connected part, ksi

= tensile strength of connected part, ksi

e = edge distance, in.

d = bolt diameter, in.

Equation (8.44) is based on the results of bolted connec-

tion tests with the following parameters

8.46

Diameter of bolt d :

–1 in. (4.8–25.4 mm)

Thickness of connected part t: 0.036–0.261 in. (0.9–

6.6 mm)

BOLTED CONNECTIONS 283

Figure 8.27 Types of failure of bolted connections: (a) longitu-

dinal shear failure of sheet (type I); (b) bearing failure of sheet

(type II); (c) tensile failure of sheet (type III); (d ) shear failure of

bolt (type IV).

Figure 8.28 Dimensions s and e used in bolted connections.

Edge distance e: 0.375–2.5 in. (9.5–63.5 mm)

Yield point of steel F

: 25.60–87.60 ksi (177–604 MPa,

1800–6150 kg/cm

)

Tensile strength of steel F

: 41.15–91.30 ksi (284–630 MPa,

2890–6420 kg/cm

)

e/d ratio: 0.833–3.37

d/t ratio: 2.61–20.83

ratio: 1.00–1.63

The dimension of the specimens and the test results are

given in Ref. 8.45.

By substituting σ

= P

/dt into Eq. (8.44), Eq. (8.45)

can be obtained for the required edge distance e,

e =

(8.45)

This equation was also used for the speciﬁcations of the

Research Council on Structural Connections

8.47,8.48

and the

AISC.

1.148

8.4.1.2 Bearing or Piling Up of Steel Sheet (Type II

Failure) When the edge distance is sufﬁciently large (i.e.,

for large e/d ratios), the connection may fail by bearing

or piling up of steel sheet in front of the bolt, as shown

in Fig. 8.27b. Additional studies indicate that the bearing

strength of bolted connections depends on several param-

eters, including the tensile strength of the connected part,

the thickness of the connected part, the types of joints (lap

joints or butt joint), single-shear or double-shear conditions,

the diameter of the bolt, the F

ratio of the connected

part, the use of washers, the “catenary action” of steel

sheets, and the rotation of fasteners. Equation (8.46) was

developed for determining the ultimate bearing capacity on

the basis of the applicable parameters. This equation was

developed from the available test data

8.105, 8.106

= Cm

dtF

(8.46)

where C = bearing factor, determined in accordance

with Table 8.2

= modiﬁcation factor for type of bearing

connection determined in accordance with

Table 8.3

d = nominal bolt diameter

t = uncoated sheet thickness

= tensile strength of sheet.

It should be noted that the Eq. 8.46 is applicable only

when the deformation around the bolt holes is not a design

consideration. If the deformation around the bolt holes

is a design consideration, research has determined that

the nominal bearing strength is given by the following

Table 8.2 Bearing Factor C

1.345

Thickness, td/tC

0.024 ≤ t < 0.1875 d/t < 10 3.0

10 ≤ d/t ≤ 22 4 − 0.1(d /t)

d/t > 22 1.8

284 8 CONNECTIONS

Table 8.3 Modiﬁcation Factor m

forTypeofBearing

Connection

1.345

Type of Bearing Connection m

Single-shear and outside sheets of double-shear

connection with washers under both bolt head

and nut

1.00

Single-shear and outside sheets of double-shear

connection without washers under both bolt

head and nut or only one washer

0.75

Inside sheet of double-shear connection with or

without washers

1.33

equation

6.25

= (4.64t +1.53) dtF

(with t in inches) (8.47a)

ForSIunits:

= (0.183t +1.53) dtF

(with t in mm) (8.47b)

All symbols were deﬁned previously.

The above design equations were developed from the

research conducted at the University of Missouri-Rolla to

recognize the hole elongation prior to reaching the limited

bearing strength of a bolted connection.

6.24,6.25

The move-

ment of the connection was limited to 0.25 in. (6.4 mm),

which is consistent with the permitted elongation prescribed

in the AISC speciﬁcation for hot-rolled steel shapes and

built-up members.

8.4.1.3 Tearing of Sheet in Net Section (Type III

Failure) In bolted connections, the type of failure by

tearing of the sheet in the net section is related to the stress

concentration caused by

1. The presence of holes

2. The concentrated localized force transmitted by the

bolt to the sheets

Previous tests conducted at Cornell University for

connections using washers under the bolt head and nut

have indicated that plastic redistribution is capable of

eliminating the stress concentration caused by the presence

of holes even for low-ductility steel.

8.39

However, if

the stress concentration caused by the localized force

transmitted by the bolt to the sheet is pronounced, the

strength of the sheet in the net section was found to

be reduced for connections having relatively wide bolt

spacing in the direction perpendicular to the transmitted

force. The effects of the d/s ratio on the tensile strength of

bolted connections with washers is discussed in Ref. 1.354.

An additional study conducted at Cornell on connections

using multiple bolts has shown that the sharp stress concen-

tration is much relieved when more than one bolt in line is

used and the failure in the net section in two-bolt (r =

)

and three-bolt (r =

) tests occurred at a much higher stress

than in a single-bolt (r = 1) connection. The following

formulas have been developed to predict the failure stress

in the net section:

net



1 − 0.9r +3r





≤ F

when

≤ 0.3

(8.48)

net

= F

when

> 0.3 (8.49)

where σ

net

= failure stress in net section, ksi

r = force transmitted by bolt or bolts at the

section considered divided by the force in

the member at that section

d = bolt diameter, in.

s = spacing of bolts perpendicular to line of

stress, in.

= ultimate tensile strength of steel sheets, ksi

The correlations between Eq. (8.48) and the test data is

discussed by Yu in Ref. 1.354. The test data reﬂects the

following parameters

8.46

Diameter of bolt d :

–1

in. (6.4–28.6 mm)

Thickness of steel sheet t: 0.0335–0.191 in. (0.9–4.9 mm)

Width of steel sheet s: 0.872–4.230 in. (22–107 mm)

Yield point of steel F

: 26.00–99.40 ksi (179–685 MPa,

1830–6990 kg/cm

)

Tensile strength of steel F

: 41.15–99.80 ksi (284–688 MPa,

2890–7020 kg/cm

)

d/s ratio: 0.063–0.50

d/t ratio: 3.40–21.13

When washers are not used and when only one washer

is used in bolted connections, the failure stress in the net

section σ

net

can be determined by

net



1.0 −r + 2.5r





≤ F

(8.50)

The correlation between Eq. (8.50) and the test data is

presented by Yu in Ref. 1.354.

Research conducted at the University of Sydney revealed

that for ﬂat sheet connections having multiple rows of bolts

in the line of force the strength reduction represented by

Eqs. (8.48) and (8.50) is not required.

8.107

8.4.1.4 Shearing of Bolt (Type IV Failure) A number

of double-shear and single-shear tests were performed at