From: Roger Turk <73527.1356(--nospam--at)compuserve.com>
Date: Wed, 16 Jun 1999 15:16:28 -0400
Charley Hamilton wrote:
. > I think (note the disclaimer!) that the intent of LRFD was to take a
. > step closer to reflecting the "actual" state of uncertainty (partially
. > due to uncertainty of loads, partially due to uncertainty of capacity)
. > from ASD (which seems to be based on empirical design stress limits?
. > What is the basis of ASD?
ASD is not based on "empirical" or "arbitrary" stress limits. ASD is based
on a factor of safety with respect to first yield. LRFD is based on a factor
of safety with respect to a fully plastic (yielded) section.
If we look at a member in pure tension, we can compare the factors of safety
of the two methods rather easily as first yield and a fully plastic (yielded)
section occur at the same load levels.
ASD says that you have a factor of safety of 1.67 wrt yield on the gross
F(t) = .60F(y)
where F(t) is the allowable tension stress.
or a factor of safety of 2.0 wrt ultimate on the effective net area:
F(t) = .50F(u)
With LRFD, figuring out the factor of safety is a little more complex as
there are different load factors for different loadings, however, for dead
load alone, you have a factor of safety of 1.56 wrt yield on the gross area:
phi*P(n)/A(g) = F(y)
where phi = 0.9
phi*P(n) >= 1.4*DL
P(n) >= 1.4*DL/0.9
or a factor of safety of 1.87 wrt ultimate on the net section:
phi*P(n)/A(e) = F(u)
where phi = 0.75
phi*P(n) >= 1.4*DL
P(n) >= 1.4*DL/0.75
For both dead load and live load, you have to consider the relationship of
both to the total load (TL). If both the dead and live loads are each
one-half of the total load, then;
phi*P(n) >= 1.2*TL/2 + 1.6*TL/2
= 1.4 TL
and the factor of safety wrt yield would be 1.56 again, and wrt ultimate it
would again be 1.87.
For bending, the ASD factor of safety wrt first yield on the extreme fiber
varies depending on the shape, but for a compact shape, the FS is 1.52:
F(b) = 0.66 F(y)
For bending in LRFD, I'll let someone else [try to] figure out the factor of
Hope this helps.
A. Roger Turk, P.E.(Structural)