Hancock G.J., Murray Th.M., Ellifritt D.S. Cold-Formed Steel Structures to the AISI Specification

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typical of a cold-rolled and annealed low-carbon steel. A

linear region is followed by a distinct plateau at 60 ksi, then

strain hardening up to the ultimate tensile strength at

75 ksi. Stopping the testing machine for 1 min during the

yield plateau, as shown at point A in Figure 2.1, allows

relaxation to the static yield strength of 57.7 ksi. This

reduction is a result of decreasing the strain rate to zero.

The plateau value of 60 ksi is in¯ated by the effect of strain

rate. The elongation on a 2-in. gauge length at fracture is

approximately 23%. A typical measured stress-strain curve

for a 0.06-in. cold-rolled sheet is shown in Figure 2.2. The

steel has undergone cold-reducing (hard rolling) during the

manufacturing process and therefore does not exhibit a

yield point with a yield plateau as for the annealed steel in

Figure 2.1. The initial slope of the stress-strain curve may

be lowered as a result of the prework. The stress-strain

curve deviates from linearity (proportional limit) at

FIGURE 2.1 Stress-strain curve of a cold-rolled and annealed

sheet steel.

Chapter 2

approximately 36 ksi, and the yield point has been deter-

mined from 0.2% proof stress [as speci®ed in AISI Manual

(Ref. 1.2)] to be 65 ksi. The ultimate tensile strength is

76 ksi, and the elongation at fracture on a 2-in. gauge

length is approximately 10%. The value of the elongation

at fracture shown on the graph is lower as a result of the

inability of an extensometer to measure the strain during

local elongation to the point of fracture without damage.

The graph in the falling region has been plotted for a

constant chart speed.

Typical stress-strain curves for a 0.08-in.-thick tube

steel are shown in Figure 2.3. The stress-strain curve in

Figure 2.3a is for a tensile specimen taken from the ¯ats,

and the curve in Figure 2.3b is for a tensile specimen taken

from the corner of the section. The ¯at specimen displays a

yield plateau, probably as a result of strain aging (see

Section 2.4) following manufacture, whereas the corner

FIGURE 2.2 Stress-strain curve of a cold-rolled sheet steel.

Materials and Cold Work of Forming

specimen exhibits the characteristics of a cold worked steel.

The Young's modulus (E

meas

) of the corner specimen is

lower than that of the ¯at specimen as a result of greater

prework.

FIGURE 2.3 Stress-strain curves of a cold-formed tube: (a) stress-

strain curve (¯at); (b) stress-strain curve (corner).

Chapter 2

2.3 DUCTILITY

A large proportion of the steel used for cold-formed steel

structures is of the type shown in Figures 2.2 and 2.3. These

steels are high tensile and often have limited ductility as a

result of the manufacturing processes. The question arises

as to what is an adequate ductility when the steel is used in

a structural member including further cold-working of the

corners, perforations such as bolt holes, and welded connec-

tions. Two papers by Dhalla and Winter (Refs. 2.2, 2,3)

attempt to de®ne adequate ductility in this context.

Ductility is de®ned as the ability of a material to

undergo sizable plastic deformation without fracture. It

reduces the harmful effects of stress concentrations and

permits cold-forming of a structural member without

impairment of subsequent structural behavior. A conven-

tional measure of ductility, according to ASTM A370, is the

percent permanent elongation after fracture in a 2-in.

gauge length of a standard tension coupon. For conven-

tional hot-rolled and cold-rolled mild steels, this value is

approximately 20±30%.

A tensile specimen before and after a simple tension

test is shown in Figures 2.4a and 2.4b, respectively. After

testing, the test length of approximately 3 in. has under-

gone a uniform elongation as a result of yielding and strain

hardening. The uniform elongation is taken from the yield

point up to the tensile strength as shown in Figure 2.4c.

After the tensile strength has been reached, necking of the

material occurs over a much shorter length (typically

in.

approximately) as shown in Figure 2.4b and ends when

fracture of the test piece occurs. Elongation in the necking

region is called local elongation. An alternative estimate of

local ductility can be provided by calculating the ratio of the

reduced area at the point of fracture to the original area.

This measure has the advantage that it does not depend on

a gauge length as does local elongation. However, it is more

dif®cult to measure.

Materials and Cold Work of Forming

Dhalla and Winter investigated a range of steels which

had both large and small ratios of uniform elongation to

local elongation. The purpose of the investigation was to

determine whether uniform or local elongation was more

FIGURE 2.4 Ductility measurement: (a) tensile specimen before

test; (b) tensile specimen after test; (c) stress-strain curve for hot

formed steel.

Chapter 2

bene®cial in providing adequate ductility and to determine

minimum values of uniform and local ductility. The steels

tested ranged from cold-reduced steels, which had a

uniform elongation of 0.2% and a total elongation of 5%,

to annealed steels, which had a uniform elongation of 36%

and a total elongation of 50%. In addition, a steel which had

a total elongation of 1.3% was tested. Further, elastic-

plastic analyses of steels containing perforations and

notches were performed to determine the minimum

uniform ductility necessary to ensure full yield of the

perforated or notched section without the ultimate tensile

strength being exceeded adjacent to the notch or perfora-

tion.

The following ductility criteria have been suggested to

ensure satisfactory performance of thin steel members

under essentially static load. They are included in Section

A3.3 of the AISI Speci®cation. The ductility criterion for

uniform elongation outside the fracture is

 3:0% 2:1

The ductility criterion for local elongation in a

in. gauge

length is

 20% 2:2

The ductility criterion for the ratio of the tensile strength

F

 to yield strength F

 is

 1:05 2:3

In the AISI Speci®cation, Section A3.3, 1.05 in Eq. (2.3) has

been changed to 1.08.

The ®rst criterion for uniform elongation is based

mainly on elastic-plastic analyses. The second criterion

for local elongation is based mainly on the tests of steels

with low uniform elongation and containing perforations

where it was observed that local elongations greater than

20% allowed complete plasti®cation of critical cross

Materials and Cold Work of Forming

sections. The third criterion is based on the observation

that there is a strong correlation between uniform elonga-

tion and the ratio of the ultimate tensile strength to yield

strength of a steel F

.

The requirements expressed by Eqs. (2.1) and (2.2) can

be transformed into the conventional requirement speci®ed

in ASTM A370 for total elongation at fracture. Using a 2-in.

gauge length and assuming necking occurs over a

in.

length, we obtain

2in:

 E



0:5E

ÿ E



2:0

2:4

Substitution of Eqs. (2.1) and (2.2) in Eq. (2.4) produces

2in:

 7:25% 2:5

This value can be compared with those speci®ed on a 2-in.

gauge length in ASTM A570, which is 11% for a Grade 50

steel, and ASTM 607, which is 12% for a Grade 70 steel, as

set out in Table 2.1.

Section A3.3.2 of the AISI Speci®cation states that

steels conforming to ASTM A653 SS Grade 80, A611

Grade E, A792 Grade 80, and A875 SS Grade 80, and

other steels which do not comply with the Dhalla and

Winter requirements may be used for particular multiple

web con®gurations provided the yield point F

 used for

design is taken as 75% of the speci®ed minimum or 60 ksi,

whichever is less, and the tensile strength F

 used for

design is 75% of the speci®ed minimum or 62 ksi, whichever

is less.

A recent study of G550 steel to AS 1397 (Ref. 2.4) in

0.42-mm (0.016 in.) and 0.60-mm (0.024 in.) thicknesses has

been performed by Rogers and Hancock (Ref. 2.5) to ascer-

tain the ductility of G550 steel and to investigate the

validity of Section A3.3.2. This steel is very similar to

ASTM A653 SS Grade 80, A611 Grade E, A792 Grade 80,

and A875 SS Grade 80. Three representative elongation

distributions are shown in Figure 2.5 for unperforated

Chapter 2

tensile coupons taken from 0.42-mm (0.016 in.) G550 steel

in (a) the longitudinal rolling direction of the steel strip, (b)

the transverse direction, and (c) the diagonal direction. The

coupons were each taken to fracture. In general, G550

FIGURE 2.5 Elongation of 0.42-mm (0.016 in.) G550 (Grade 80)

steel: (a) longitudinal specimen; (b) transverse specimen; (c)

diagonal specimen.

Materials and Cold Work of Forming

coated longitudinal specimens have constant uniform elon-

gation for each 0.10-in. gauge with an increase in percent

elongation at the gauge in which fracture occurs as shown

in Figure 2.5a. Transverse G550 specimens show almost no

uniform elongation, but do have limited elongation at the

fracture as shown in Figure 2.5b. The diagonal test speci-

men results in Figure 2.5c indicate that uniform elongation

is limited outside of a

in. zone around the fracture, while

local elongation occurs in the fracture gauge as well as in

the adjoining gauges. These results show that the G550

steel ductility depends on the direction from which the

tensile coupons are obtained. The steel does not meet the

Dhalla and Winter requirements described above except for

uniform elongation in the longitudinal direction.

The study by Rogers and Hancock (Ref. 2.5) also

investigated perforated tensile coupons to determine

whether the net section fracture capacity could be devel-

oped at perforated sections. Coupons were taken in the

longitudinal, transverse, and diagonal directions as

described in the preceding paragraph. Circular, square,

and diamond-shaped perforations of varying sizes were

placed in the coupons. It was found that despite the low

values of elongation measured for this steel, as shown in

Figure 2.5, the load carrying capacity of G550 steel as

measured in concentrically loaded perforated tensile

coupons can be adequately predicted by using existing

limit states design procedures based on net section fracture

without the need to limit the tensile strength to 75% of

80 ksi as speci®ed in Section A3.3.2 of the AISI Speci®ca-

tion.

2.4 EFFECTS OF COLD WORK ON

STRUCTURAL STEELS

Chajes, Britvec, and Winter (Ref. 2.6) describes a detailed

study of the effects of cold-straining on the stress-strain

characteristics of various mild carbon structural sheet

Chapter 2

steels. The study included tension and compression tests of

cold-stretched material both in the direction of prior

stretching and transverse to it. The material studied

included

1. Cold-reduced annealed temper-rolled killed sheet

coil

2. Cold-reduced annealed temper-rolled rimmed

sheet coil

3. Hot-rolled semikilled sheet coil

4. Hot-rolled rimmed sheet coil

The terms rimmed, killed, and semikilled describe the

method of elimination or reduction of the oxygen from the

molten steel. In rimmed steels, the oxygen combines with

the carbon during solidi®cation and the resultant gas rises

through the liquid steel so that the resultant ingot has a

rimmed zone which is relatively purer than the center of

the ingot. Killed steels are deoxidized by the addition of

silicon or aluminum so that no gas is involved and they

have more uniform material properties. Most modern

steels are continuously cast and are aluminum or silicon

killed.

A series of signi®cant conclusions were derived in Ref.

2.6 and can be explained by reference to Figure 2.6. The

major conclusions are the following:

1. Cold work has a pronounced effect on the mechan-

ical properties of the material both in the direction

of stretching and in the direction normal to it.

2. Increases in the yield strength and ultimate

tensile strength as well as decreases in the ducti-

lity were found to be directly dependent upon the

amount of cold work. This can be seen in Figure

2.6a where the curve for immediate reloading

returns to the virgin stress-strain curve in the

strain-hardening region.

3. A comparison of the yield strength in tension with

that in compression for specimens taken both

Materials and Cold Work of Forming