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effects due to dead, live and wind load, respectively, YDYL
and are the load factors for the maximum loads ; Yz, 'YI
because the live load which is expected on the member at any particular point in time is less than the maximum live load. The load
combination which involves the wind load thus reflects the fact that it is not
expected that the maximum live load and the maximum wind load will act simultaneously:
Traditionally this unexpected simultaneity has been dealt with by multiplying the
factor of safety by 3/4 or by increasing allowable stresses by 4/3.
suggested here is a better reflection of what actually takes place.
The proposed design process thus defines the appropriate limit states, and hence
it is often named Limit States Design.
Limit states design, in itself, is nothing
fundamentally new but is a procedure which, in effect, requires the designer to
consider explicitly several different modes of possible structural behavior during
design. The particular method above also identifies resistance factors and load
factors, and so it is called Load and Resistance Factor Design; it is one (of several)
limit states design criteria formats.
Broadly speaking, there are two types of limit states:
(1) ultimate limit
states under which the structure or component is judged to have failed in its capacity
to carry load; and (2) serviceability limit states under which the function of the
building is impaired.
The recommendations in this report are confined to the ultimate
limit states as these are of particular concern in standards and specifications which
are intended to protect the public from physical harm.
The recommended load and resistance factor design format which incorporates
limit states, resistance factors, load factors and load combinations is a formalization
of trends evident in many structural specifications in the United States.
It provides a
means whereby it is possible to achieve more uniform performance and reliability in structural
design than is possible with just one factor of safety. This has long been recognized in
reinforced concrete design.
Current research in metal structures has also produced
tentative rules which apply to steel, cold-formed steel, and aluminum structures.
thesis of this report is that it is also desirable to provide common load combinations and
load factors which can be used in connection with all material specifications.
will be elaborated upon subsequently.
The recommended approach requires that procedures be available to determine values
for the resistance factors and the load factors.
The development of the load criterion
is carried out within the context of probabilistic limit states design.
This is because
the reliability of a structure or element is defined in a natural way by the probability
of not achieving any of its limit states.
The procedure used herein is based on modern
engineering reliability analysis methods which have been developed, tested and refined
over the last decade.
The details of the method are described el
re in this report.
For our purposes here it suffices to say that given a structural member or element designed
according to a current structural specification, it is possible to compute the relative
reliability of this design from data defining probability distributions and statistics of
the resistance, the loads and the load effects.
This relative reliability is expressed as
a number called the reliability index, B.
This index usually varies from 2 to 8, depending
on the structure type and loading. By repeatedly determining B for many structural designs,
the relative reliability of different structural members built from different structural
materials can be compared.
If representative values of B are now selected, reflecting the
averaged reliability of satisfactory current designs, it is again possible by using reliability
analysis methods to compute resistance and load factors.
It should be clearly pointed out
that this process is elaborate, and it is performed as a research operation for use by
standard and specification-writing bodies.
The designer would only use the standard
specified values of $ and r in the structural design operation.
The underlying average reliability B is (1) not necessarily the same for all types of
building materials (and there is no reason to force the design profession to adopt a
uniform value), and (2) the values of $ and y depend not only on B but also on the load
and the resistance statistics.
Thus, it is quite likely that if the methodology were
applied to each material separately, different values of the load factors y would be
obtained for, say, steel structures and masonry structures.
This is an entirely logical
consequence of the probabilistic methodology used.
However, the use of different load
factors for different structural material specifications is undesirable in the design
office and results in confusion, especially in structures where the design calls for a mix
of materials, say reinforced concrete, structural steel and aluminum (e.g., slabs, frame
and curtain walls).
It thus was deemed desirable to determine uniform load factors which
could be included in the A58 Standard for all structural materials and to provide a means
whereby individual material specification writing groups could select suitable nominal
resistances and resistance factors corresponding to the load criterion and whatever values
of B they desire.
The use of common load factors would simplify the design process,
particularly when more than one construction material is used in a structure.
standard groups in the United States agree that the A58 Standard is the logical place for
this load criterion ina smuch as it is a national standard and requires consensus approval
and public review of the criteria prior to their implementation.
Summary of Procedure:
The details of achieving the objectives discussed above are given in the body of this
report, with further details and statistics being provided in the Appendices. The following
is only an abbreviated description of the procedure.
This consists basically of using a
probabilistic safety analysis to guide the selection of load factors that produce desired
levels of uniformity in safety which are consistent with existing general practice.
Estimate the level of reliability implied by the use of the various current
design standards and specifications (e.g. ACI Standard 318, AISC Specifications, etc., and
loads from ANSI Standard A58.1-1972) for various common types of members and elements
(e.g., beams, columns, beam-columns, walls, fillet welds) using
a particular common reliability calculation scheme (Chapter 2);
common and realistic best estimates of distribution types and parameters
(Chapter 3 and Appendices);
the reliability index B as a safety measure for comparison.
Observe the B-levels over ranges of material, limit states, nominal load
ratios (e.g., live-to-dead, wind-to-dead, snow-to-dead), load combinations, and geographical
locations (Chapter 4).
From Steps 1 and 2 it was found that a level of B =
3.0 was consistent with average
current practice for load combinations involving dead plus live or dead plus snow loads,
while B = 2.5 and B = 1.75 were appropriate for combinations containing wind and earthquake
Step 3 Based on the observed B levels, determine load factors consistent with the
implied safety level and the selected safety checking format.
These load factors are
compatible with the nominal load definitions in the proposed ANSI A58.1-1980 Standard
currently being developed.
From Step 3 the following load combinations and load factors were derived (see Chapter
5 for details)
Step 4 Display the relationships between the implied B-levels for these load factors
and nominal loads for the material statistics (mean resistances, coefficients of variation)
against alternate 0-factors.
These charts are given in Chapter 5, together with example
determinations of $ for several structural types and materials.
This information generally
would be sufficient to enable a specification writing group, if it so desires, to select
$-factors without further computer operations.
Some Particular Critical Issues
The selected load factors do not prevent material specification writing groups from
selecting their own $ factors together with their own desired values of B.
There is no
intent here to dictate particular values of 0 or B to be used in material specifications.
Only the load factors are presented along with preliminary resistance variable information
and a method by which B can be estimated for any particular o that might be proposed by
the material groups for their own specifications.
If this procedure is used,
groups do not have to deal with loads to harmonize their own safety levels among their
various limit states.
If desired, for example, different values of B could be used for
bending and shear in concrete structures, or members and connectors in steel structures.
The information given also permits the observation of relative safety levels in current
practice in several material technologies which may assist material specification groups
in selecting their own values of B and $ for design.
The results of this work, as detailed in the main report, show some differences in B
levels from material to material, limit state to limit state, member type to member type,
and especially, from load type to load type.
In particular, reliability with respect to
wind or earthquake loads appears to be relatively low when compared to that for gravity loads
(i.e., dead, live and snow loads), at least according to the methods used for structural
safety checking in conventional design.
These are methods which are simplified representations
of real building behavior and they have presumably given satisfactory performance in the
It was decided to propose load factors for combinations involving wind and earth
quake loads that will give calculated B values which are comparable to those existing in
current practice, and not to attempt to raise these values to those for gravity loads by
increasing the nominal loads or the load factors for wind or earthquake loading.
the information given here the profession may well feel challenged (1) to justify more
explicitly (by analysis or test) why current simplified wind and seismic calculations may
be yielding conservative estimates of loads, resistances and safety; (2) to justify why
current safety levels for gravity loads are higher than necessary if indeed this is true;
(3) to explain why lower safety levels are appropriate for wind and earthquake vis-à-vis
gravity loads, or (4) to agree to raise the wind and seismic loads or load factors to
achieve a similar reliability as that inherent in gravity loads.
While the writers feel
that arguments can be cited in favor and against all four options, they decided that this
report was not the appropriate forum for what should be a profession-wide debate.
The method of obtaining the load factors and resistance factors presented in this
report is general in its applicability. However, the data used herein restrict the utilization
of the results to buildings and similar structures.
They are not intended for vehicular
loads on bridges, transients in reactor containments, and other loads which are considered
to be outside the scope of the A58 Standard.
The writers expect that the loading criterion presented in this report will be carefully
scrutinized by numerous professional organizations and individuals who have interest in or
are affected by the scope and provisions of the A58 Standard.
The writers feel that a
discussion of the recommendations is extremely important, in view of the implications that
the adoption of these recommendations would have on structural design in the United States.
The decision as to whether to incorporate the load criterion in a future edition of
the A58 Standard lies with the A58 Standard Committee.
After an appropriate period of
review and public discussion, a draft provision will be prepared containing the load
combinations and load factors which will be submitted for ballot by the A58 Standard
Committee in accordance with ANSI voluntary consensus standard approval procedures. If
approved, the load criterion will become part of the A58 Standard.
It will then be up to
material specification writing groups to decide whether they wish to adapt their standards
to this load criterion in the interest of harmonizing structural design.