II n

two sets of R were combined and the optimization was performed over both sets of data.

The optimal ☀, YL and YE for steel and concrete beams assuming Yo = 1.2 are shown in the

The YE

༥

= 0.0

0.82

0.80

factor then was adjusted so as to force the down to the same range as for the

other load combinations.

It was found that by making Y,

= 0.2 and

=

YE

1.5, the corresponding optimal (listed in the last columns of Table 5.5) is about the same as for the other load combinations. However the factored load 0.2 L would be less than the mean of L

E

many instances, and it was decided to raise in which Υπ = 1.3 also was carefully considered because of the consistency with the treatment of wind loads. With this alternative, the optimal factors were much less than 0.80; conversely, if the same used with the gravity and wind load combinations were to be used in combinations with earthquake load the reliability indices would be less than B = 1.75. There is simply too great a difference in c.o.v. in wind load (0.30 - 0.40) and earthquake load (greater than 1.00) to warrant the same load factor for each.

A similar analysis with the combination D + S + E showed that the necessary snow load factor was close to zero, implying that snow and earthquake loads in combination could be = 0.2 for conservatism in areas

neglected. Nevertheless, it seems sensible to specify S

subject to heavy snow and to earthquake hazards.

Counteracting Loads Common instances in which loads counteract one another include cases where load effects due to wind or earthquake act in a sense opposing gravity load effects. This case is extremely difficult to handle using mean-value reliability analysis methods but is relatively straightforward using the advanced procedure. The two cases U = WD and U = E D are considered.

Constraints placed on the minimization simplify the problem. First, since the probability density function of dead load is symmetrical about D/D = 1.05 and since loads are additive, it is reasonable that YD = 0.9 when loads counteract. factor for a particular material and limit state should be the same, regardless of the

load combination.

Accordingly, YW (and

= 0.9 and

=

n n

The same

n n

0.85, and selecting the Y(and Yg) which minimizes Eq. 5.9. characterizations of the wind and earthquake environments are used here as for the combinations where the load effects are additive. It was assumed that values of W/D E /D between 2 and 5 were equally probable. The optimal value of Yw (and YE) depends on the choice of ; for example, Y varied from 1.22 to 1.26 for steel beams as & was increased from 0.85 to 0.90. In the interest of consistency with the additive combinations involving these

=

Ο

It is interesting to note that if Yw is selected to best achieve ß 2.5, the same as for the additive combination D + W, then YW

=

1.5.

This would result in additional

conservatism against counteracting forces over existing practice.

Other combinations may be treated similarly. For example, a combination of live plus snow load may be important in design of upper story columns. Similarly, a combination of wind and snow load may be important for certain roof structures. These cases involve considering the combinations

In sum, the load combinations and load factors recommended for use by the individual material specification writers in their design specifications are:

It should be noted that the designer may have to consider other loading combinations in

certain unusual situations.

While this could be done using the methodology described in

this report if data on the individual loads were available, appropriate factors also could

be estimated by noting whether any similarities exist between the load in question and the loads in Eqs. 5.16. For example, it might be appropriate to select a factor of 1.6 for

rain loads.

W /D

In Fig. 5.7, the resulting B's for various combinations of the ratios L/D S/D = 1000 ft2 (93 m2) and for the case of compact

n

n'

n

n

n

R

= 0.13. This case represents a representative

are given for an influence area A steel beams for which R/R = 1.07 and V,

structural type which is performing satisfactorily in current design. The ranges of Bvalues inherent in current design practice (AISC Specification, Part 1) are given in

Tables C-7.2 and C-7.3. Following is a representative set of values:

According to the new design procedure with the proposed load factors (Fig. 5.7), the These values are, for of 0.85, equal to (for an

values of B are much more condensed.

influence area of 1000 ft2)

0.65). In the most practical range of load ratios, B is close to 3 for beams and is about 3.25 for columns. The values of B are considerably more uniform for different design

situations than is the case with current criteria.

5.6 Recommendations to Material Specification Groups

It is anticipated that material specification groups will want to experiment in selecting resistance factors to use along with the load criterion in the previous section.