04-LRFD Concept (Steel Structural Design & Prof. Shehab Mourad)

1. 1 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
SSTTEEEELL DDEESSIIGGNN MMEETTHHOODDSS
1. Allowable stress method (ASD): focuses on conditions
at service loads:
stresses at combined service loads £ Allowable stresses
2. Load and Resistance Factor Design (LRFD): based on
limit state philosophy. It focuses on conditions at loads
greater than the service loads when failure is close to
happen:
factored resistance ³ sum of factored load effects
or
fRn ³ SaI Qi
f : resistance factor
Rn: nominal resistance
a: load factors
Qi: load effect
The LRFD method is deemed conceptually more realistic to
establish structural safety.
SSttrruuccttuurraall SSaaffeettyy
Structures and structural members must always be designed to
carry some reserve load above what is expected under normal
use.
There are three main reasons why some sort of safety factor is
necessary in structural design.
[1] Variability in resistance.
[2] Variability in loading.
[3] Consequences of failure

2. 2 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Philosophy of Loads & Resistance Factored
Design (LRFD)
1- Loads
Loads Specifications
In U.S., Loadings are specified in building codes such as
n Uniform Building Code (UBC)
n Basic Building Code (BOCA)
n Standard Building Code
These codes have been consolidated in the International Building Code (IBC).
Loadings in these codes are mainly based on ASCE Minimum Design
Loads for Buildings and Other Structures (ASCE 7-02)
In Saudi Arabia, Loadings specifications are given in SBC 301
which is mainly based on (ASCE 7-02).
2- are different in;
Dead loads (D) : are constant in magnitude and remain in one
direction, consist of own weight of structure (steel weight, walls,
floors, roof, utility pipes, etc), DDeeaadd LLooaaddss ((SSBBCC 330011 cchhaapptteerr 33))
Live loads (L) : may change in position and magnitude, also
can be movable loads as trucks and cranes.
LLiivvee LLooaaddss ((SSBBCC 330011 cchhaapptteerr 44))
Environmental loads: caused by the environment in which a
particular structure is located and it varied with time and may
not all act all together, as;
(a) Snow (S)
(b) Rain (R), can cause roof failure due to roof ponding
(c) Temperature change (T)
(d) Wind loads (W) (SBC 301 Chapters 6 and 7)
(e) Earthquake loads (E) ((SSBBCC 330011 CChhaapptteerrss 99 aanndd 1144))
Nature and type

3. 3 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
The minimum design loads for buildings
and other structures are specified by the
applicable codes, as the American Society of Civil
Engineering (ASCE 7-02) and SBC 301
Load factors are used to increase the
magnitude of the calculated loads to
account for the uncertainties involved in estimating the
magnitude of different loads as, dead, live, wind and
earthquake loads. Load factors are different according to
the load nature, and its applied period.
For Example, dead load factor = 1.4
Live load factor = 1.6
Different types of loads can be
combined since it can be applied simultaneously, however
they may not be with the same magnitudes and factors.
For example, it is very rarely that the structure will be
subjected to the total factored dead and live loads at the
same instant the factored wind load or the earthquake loads
will be maximum.
The following load combinations ((ASCE 7-02) are used to
investigate the critical combination of factored loads
(ultimate loads = Pu):
1- 1.4D
2- 1.2D + 1.6 (L, or S or R)
3- 1.2D + 1.6 (Lr, or S or R) + (0.5L or 0.8W)
4- 1.2D ± 1.6W + 0.5L + 0.5 (Lr, or S or R)
5- 1.2D ± 1.0E + 0.5L + 0.2S
6- 0.9D ± ( 1.6 W or 1.0E)
See Load Combinations in SBC 301 Sec 2.3, to
discover the difference
- Magnitude
- Load Factors
- Load Combinations

4. 4 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
2- Resistance
Resistance of a member is it's nominal strength based on
it' s nominal dimensions, and material properties.
Are used to reduce the nominal
strength (Pn) to account for the
uncertainties in the material strength, dimensions,
workmanship and consequences of failure.
11.. VVaarriiaabbiilliittyy iinn RReessiissttaannccee
w Variability of the strengths.
w Differences between the as-built dimensions and those found in
structural drawings.
w Effects of simplification made in the derivation of the members
resistance.
22.. VVaarriiaabbiilliittyy iinn LLooaaddiinngg
(see Section 2-10 in the book)
33.. CCoonnsseeqquueenncceess ooff FFaaiilluurree
A number of subjective factors must be considered in determining an
acceptable level of safety.
w Potential loss of life.
w Cost of clearing the debris and replacement of the structure
and its contents.
w Cost to society.
w Type of failure: Beam vs. column, warning (ductile) vs.
sudden (brittle), existence of alternative load paths.
LRFD Resistance Factors, f (SBC 306)
Some examples of the strength reduction factor (resistance
factor), Ф, are:
1. Фc = 0.85 for axial compression and columns
2. Фv = 0.90 for shear in beams
3. Фb = 0.90 for flexure in beams ( bending moment )
4. Фt = 0.90 for yielding in a tension member
5. Фt = 0.75 for fracture in a tension member, welds & bolts
- Resistance Factors

5. 5 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
3- Reliability and LRFD Specification
is refered to the estimated percentage of times
that the resistance of a structure will equal or
exceed the maximum loading combination applied to the structure
during its estimated life ( say 50 years)
Usually steel structures are designed to be 99.7% reliable, then
only a probability of 0.3% the strength will be lower than the
applied loads, but it doesn’t mean failure !!!
The typical distribution of the Resistance (R) of a member and
the applied loads (Q) are varied and as shown to be normal
distribution
b : reliability Index = number of standard deviations from the mean
22
)/(ln
Q
VV
m
Q
m
R
R +
=b
b= 1.75 for member subjected to gravity loads and earthquake loads
b = 2.50 for member subjected to gravity loads and wind loads
b = 3.00 for members subjected to gravity loads
b = 4.50 for connections (bolts and weld)
Therefore the resistance factors (Ф) for different members and load
factors for different load combinations are adjusted accordingly to be as
mentioned before.
- Reliability
LRFD target is to satisfy the following condition
Factored Resistance ≥ Factored Loads
Ф Pn ≥ Pu

6. 6 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Example 2
The axial loads on a building column resulting from the code specified
service loads have been calculated as :
PD=445 kN
PL=667 kN
PLr=133 kN
PW=267 kN (can be positive or negative)
PE=222 kN (can be positive or negative)
Determine the required strength for this column.
Solution:
Combination Pu (kN)
Comb1: 1.4 D 623
Comb2: 1.2 D + 1.6 L + 0.5 Lr 1668
Comb3a: 1.2 D + 1.6 Lr +0.5 L 1080
Comb3b: 1.2 D + 1.6 Lr +0.8 W 960
Comb4: 1.2D + 1.6W + 0.5 L + 0.5 Lr 1361
Comb5a: 1.2D + 1.0 E + 0.5 L 1090
Comb5b: 1.2D - 1.0 E + 0.5 L 646
Comb6a: 0.9D + 1.6W 828
Comb6b: 0.9D - 1.6W -27
Comb7a: 0.9D + 1.0E 623
Comb7b: 0.9D - 1.0E 179
Based on combination results, the required strength of the column is
1668 kN in compression and 27 kN in tension. In other words, the
column needs to be designed for compression and tension.