Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

Limit States
LRFD is based on a limit states philosophy. In this context, the term limit state is used to
describe a condition under which a structure or some portion of the structure ceases to
perform its intended function. Two general kinds of limit states apply to structures:
strength limit states and serviceability limit states. Strength limit states define safety
with regard to extreme load events during which the overriding concern is the protection
of human life from sudden or catastrophic structural failure. Serviceability limit states
pertain to the satisfactory performance of structures under ordinary load conditions. These
limit states include considerations such as excessive deflections, vibrations, cracking, and
other concerns that may have functional or economic consequences but do not threaten
public safety.
81
LOAd ANd RESISTANCE
FACTOR dESIgN
ExAMpLE 4.3
A rectangular steel plate is subjected to an axial dead load of 30 kips and a live load of
48 kips. The yield strength of the steel is 36 ksi.
(a) ASD Method: If a factor of safety of 1.5 with respect to yielding is required,
determine the required cross-sectional area of the plate according to the ASD
method.
(b) LRFD Method: Use the LRFD method to determine the required cross-sectional area
of the plate on the basis of yielding of the gross section. Use a resistance factor φ t =
0.9 and load factors of 1.2 and 1.6 for the dead and live loads, respectively.
Plan the Solution
A simple design problem illustrates how the two methods are used.
SOLUTION
(a) ASD Method
Determine the allowable normal stress from the specified yield stress and the factor of
safety:
σ
allow
σ Y 36 ksi
= = = 24 ksi
FS 1.5
The service load acting on the tension member is the sum of the dead and live compo nents:
P = D + L = 30 kips + 48 kips = 78 kips
The cross-sectional area required to support the service load is computed as
P 78 kips
2
A ≥ = = 3.25 in.
Ans.
σ 24 ksi
allow
(b) LRFD Method
The factored load acting on the tension member is computed as
P = 1.2D + 1.6L
= 1.2(30 kips) + 1.6(48 kips) = 112.8 kips
u
The nominal strength of the tension member is the product of the yield stress and the
cross-sectional area:
P
n
= σ A
Y