# The Direct Strength Method of Cold

```Product Development and DSM
Rational Analysis vs. Chapter F
• For a new section, outside the boundaries of the
pre-qualified limits of DSM you begin with two
options for the resistance (safety) factor
A1.1(b):
F:
Members
USA and Mexico
 (ASD)
 (LRFD)
2.00
0.80
  C  M m Fm Pm  e
 (LSD)
0.75
2
o VM
 VF2 CP VP2  VQ2
Rational analysis incentive
VP=6.5% (minimum value)
0.9
VP=10% (low scatter)

0.85
VP=15% (typical scatter)
0.8
rational analysis  value
0.75
0.7
5
10
15
20
number of tests (n)
25
30
New pre-qualified members, or extending
the bounds on pre-qualified members
• “No formal method yet exists in the Specification
for extending the Direct Strength Method to
extending the bounds for existing pre-qualified
members. Currently, to extend the bounds or add
an additional cross-section, a formal ballot vote
of the AISI Committee on Specifications is
required.” (DSM Guide page 75)
New Cross-section
• Consider the case where
– one is interested in pre-qualifying a new cross-section.
• Suggested procedure
– Do three or more tests.
– Generate a  using Chapter F, but use the test-to-predicted
ratio with DSM as the prediction to generate the professional
factor Pm, and the C.O.V. VP.1
– If  is greater than a DSM pre-qualified cross-section (=0.9
for beams, =0.85 for columns) this is strong evidence that
the cross-section should be pre-qualified.
– The proposed bounds for the new cross-section would be the
bounds of the testing.
(1) (In a method relying solely on testing PM is 1.0 and VP is the scatter in the test results,
here Pm is the mean accuracy of the predicting method, and VP is the scatter in the predicting
method).
Extending the bounds
• Consider the case where
– engineering judgment makes it clear that a cross-section fits in one
of the pre-qualified categories, but geometric bounds are violated.
– a large battery of tests cannot be performed
• Suggested Procedure
– Perform at least three tests and determine the average test-topredicted ratio for DSM (Pm*)1.
– If the Pm* of the three tests is equal to or greater1 than the
comparable pre-qualified category (see table on next slide), then
the bounds should likely be extended.
(1) Estimating the mean with a small number of tests is more reliable than estimating VP, so this
method assures that the reliability (in essence, ) is met, by assuming that the variation (VP) in
the new cross-sections is equal to that of the underlying category.
(2) In no way does a lower Pm* preclude that the cross-section should be pre-qualified, but
additional testing will likely be required.
The existing statistics
Beams
C-sections
C-sections with web stiffeners
Z-sections
Hat sections
Trapezoidal sections
ALL BEAMS
Columns
C-sections
n
Pm
VP
185
42
48
186
98
559
1.10
1.12
1.13
1.10
1.01
1.09
0.11
0.07
0.13
0.15
0.13
0.12
114
1.01
0.15
C-sections with web stiffeners1
29
0.88
0.14
Z-sections
85
0.96
0.13
Rack sections
17
1.02
0.05
Hat sections
4
0.98
0.02
ALL COLUMNS
249
0.98
0.14
(1) Thomasson's (1978) tests contribute to the low Pm, more recent tests
by Kwon and Hancock (1992) showed much better agreement.
Rational analysis incentive
VP=6.5% (minimum value)
0.9
VP=10% (low scatter)

0.85
VP=15% (typical scatter)
0.8
rational analysis  value
0.75
0.7
5
10
15
20
number of tests (n)
25
30
Pilot tests for a new cross-section
• Consider the case where
– Pilot tests on a new cross-section are being considered
– A large battery of tests cannot be performed at the time.
• Suggested procedure
–
–
–
–
–
Perform at least 3 tests
get average test-to-predicted ratio for DSM (Pm*).
For the C.O.V. (VP) assume the worst VP observed, 15%1.
Set the correction for sample size, Cp to 1.0.
Find  via Chapter F. If the  produced is greater than or equal to
DSM pre-qualified ( =0.9 for beams,  =0.85 for columns) this is
evidence that the cross-section should be pre-qualified.2
(1) Estimating the mean with a small number of tests is more reliable than estimating VP, so this method
attempts to assure that the reliability is met, by assuming that VP is the most conservative observed to
date.
(2) A lower  is not cause for immediate rejection, but does suggest more tests may be needed.
Notes: The preceding procedures do not guarantee the
cross-section will be pre-qualified; they are an attempt
to provide manufacturers with the best current advice.
Currently, testing and calculation evidence would need
to be taken to the AISI Committee on Specifications in
the form of a ballot for consideration to extend prequalified cross-sections. All test results would need to
be available to the public. All quantities should be
measured, not nominal. The thickness should be the
measured base metal thickness, the yield stress should
be based on tensile coupons from the as-formed crosssection, and the dimensions should be based on direct
measurement.
Other bugaboos
• Shear
– If the webs are flat existing AISI main Spec. will do, DSM
Design Guide gives rational analysis options for avoiding
testing, but it is more involved than just the finite strip method
at this point
• Web crippling
– Depends greatly on the details you use, but the AISI Spec.
method is highly empirical and likely not readily extended –
may have to perform tests
• System issues (how you brace etc.)
– How you brace, how you ship, etc. etc. all have a large
impact on what you do and what you want – many of which
clearly drive things more than just what we discussed today
```