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1
Basis of Structural Design
Course 13
EN 1990:
The partial factor method (cont.)
Course notes are available for download athttp://www.ct.upt.ro/users/AurelStratan/
Ultimate limit states
The following ultimate limit states shall be verified as relevant:
EQU: Loss of static equilibrium;
STR: Internal failure or excessive deformation;
GEO: Failure or excessive deformation of the ground where the
strengths of soil or rock are significant in providing resistance;
FAT: Fatigue failure of the structure or structural members.
2
Ultimate limit states
EQU: Loss of static equilibrium of the structure or any
part of it considered as a rigid body, where:
minor variations in the value or the spatial distribution of actions
from a single source are significant, and
the strengths of construction materials or ground are generally
not governing;
Example: a bridge deck launched with a counterweight
where loss of static equilibrium may be possible
Ultimate limit states
STR: Internal failure or excessive deformation of the structure or structural members, including footings, piles, basement walls, etc., where the strength of construction materials of the structure governs;
Example: failure of a beam supporting a floor due to excessive stresses
Mmax
3
Ultimate limit states
GEO: Failure or excessive deformation of the ground
where the strengths of soil or rock are significant in
providing resistance;Example: resistance of foundations like footings, piles,
etc.
Ultimate limit states
FAT: Fatigue failure of the structure or structural members.Examples: Cracks developing in steel bridges due to repetitive loading generated by traffic
4
Verifications of static equilibrium and resistance
When considering a limit state of rupture or excessive
deformation of a section, member or connection (STR
and/or GEO), it shall be verified that
Ed Rdwhere:
Ed is the design value of the effect of actions such as
internal force, moment or a vector representing several internal forces or moments;
Rd is the design value of the corresponding resistance.
ULS: Combination of actions
For each critical load case, the design values of the effects of actions (Ed) shall be determined by combining the values of actions that are considered to occur simultaneously
Each combination of actions should include:
a leading variable action, or
an accidental action.
Where the results of a verification are very sensitive to variations of the magnitude of a permanent action from place to place in the structure, the unfavourable and the
favourable parts of this action shall be considered as
individual actions
5
ULS: Combination of actions
Combinations of actions for persistent or transient
design situations (fundamental combinations)
The general format of effects of actions
and can be simplified as:
The combination of action in curly braces {} can be
expressed as:
where "+" implies "to be combined with"
implies "the combined effect of"
ULS: Combination of actions
Gk,j - characteristic permanent action j
G,j - partial safety factor for permanent load Gk,j
P - prestressing
P - partial safety factor for prestressing action P
Qk,1 - leading variable action
Q,1 - partial safety factor for variable load Qk,1
Qk,i - variable action i
Q,i - partial safety factor for variable load Qk,i 0,i - takes into account the reduced probability of the
simultaneous occurrence of two (or more) independent
variable actions
6
ULS: Combination of actions
Combinations of actions for accidental design situations
Ad - design value of the accidental action
Combinations of actions for seismic design situation
AEd - design value of the seismic action
permanent actions are taken with characteristic values
seismic action is taken with design value
variable loads are taken with the quasi-permanent value 2Qk
ULS: Combination of actions
Partial factors for actions and combinations of actions:
and factors are obtained from EN 1990 or CR0-2005:
permanent actions: G,sup = 1.35
permanent actions: G,inf = 0.9
variable actions: Q = 1.5
0,i = 0.7, with the exception of loads in storage facilities, water
pressure, etc, when 0,i = 1.0
Example of fundamental load combinations
The partial factors for properties of materials and products should be obtained from EN 1992 to EN 1999
7
Serviceability limit states
At the SLS it shall be verified that:
Ed Cdwhere:
Cd is the limiting design value of the relevant serviceability
criterion.
Ed is the design value of the effects of actions specified in the
serviceability criterion, determined on the basis of the relevant
combination
Serviceability limit states in buildings should take into
account criteria related, for example, to floor stiffness, differential floor levels, storey sway or/and building sway
and roof stiffness.
Stiffness criteria may be expressed in terms of limits for vertical deflections and for vibrations.
Sway criteria may be expressed in terms of limits for horizontal displacements.
Serviceability limit states
EN 1990: "The serviceability criteria should be specified for each project and agreed with the client".
Schematic representation of vertical deflections:
wc - Precamber in the unloaded structural member
w1 - Initial part of the deflection under permanent loads of the
relevant combination of actions
w2 - Long-term part of the deflection under permanent loads
w3 - Additional part of the deflection due to the variable actions of
the relevant combination of actions
wtot - Total deflection as sum of w1, w2, w3 wmax - Remaining total deflection taking into account the
precamber
8
Serviceability limit states
Horizontal displacements can be
represented schematically:
u - Overall horizontal displacement
over the building height H
ui - Horizontal displacement over a
storey height Hi
SLS: Combination of actions
Three categories of combinations of actions are proposed in EN:
characteristic (normally used for irreversible limit states, e.g. for
exceeding of some cracking limits in concrete)
frequent (is normally used for reversible limit states) and
quasi-permanent (is normally used for assessment of long-term
effects)
The appropriate combinations of actions should be selected depending on serviceability requirements and performance criteria imposed for the particular project, the client or the relevant national authority
9
SLS: Combination of actions
Characteristic
combination
Frequent
combination
Quasi-permanent combination
For serviceability limit states the partial factors M for the properties of materials should be taken as 1.0 except if differently specified in EN 1992 to EN 1999.
Examples of limiting values for vertical
deflections
10
Examples of limiting values for horizontal deflections
Example: multistorey frame
Objective: design using the partial factor method a steel multistorey frame
For the design of the structure, the STR category of limit
states is relevant
11
Example: multistorey frame
The following
actions can be
identified:
Permanent loads Gk
Imposed loads Qk
Snow load Sk
Wind load Wk
Seismic action Aed
Self-weight (Gk,1
) Dead load on floors (Gk,2
) Exterior cladding (Gk,3
)
Snow load (Sk) Wind load (Wk)
Imposed load (Qk,1
)Imposed load -
chessboard (Qk,2
)Seismic load (Aed)
Example: multistorey frame
Of the four possible design situations,
Persistent design situations,
Transient design situations,
Accidental design situations,
Seismic design situations.
Two categories of limit states need to be considered:
Ultimate limit states (ULS)
Serviceability limit states (SLS)
Seismic design
situation
ULS SLS
Persistent design
situation
ULS SLS
most
relevant
12
Example: multistorey frame
Load cases (combinations of actions)
Persistent design situation
Ultimate limit states (ULS)
Serviceability limit states (SLS)
Seismic design situation
Ultimate limit states (ULS)
Serviceability limit states (SLS) see EN 1998-1
Example: multistorey frame
Load cases (combinations of actions)
Persistent design situation
Ultimate limit states (ULS)
1.35(Gk,1 + Gk,2 + Gk,3) + 1.5Qk,1 1.35(Gk,1 + Gk,2 + Gk,3) + 1.5Qk,2 1.35(Gk,1 + Gk,2 + Gk,3) + 1.5Sk,1 1.35(Gk,1 + Gk,2 + Gk,3) + 1.5Wk 0.9(Gk,1 + Gk,2 + Gk,3) + 1.5Wk 1.35(Gk,1 + Gk,2 + Gk,3) + 1.5Qk,1 + 1.05Sk 1.35(Gk,1 + Gk,2 + Gk,3) + 1.5Sk + 1.05Qk,1 1.35(Gk,1 + Gk,2 + Gk,3) + 1.5Qk,1 + 1.05Sk + 1.05Wk 1.35(Gk,1 + Gk,2 + Gk,3) + 1.5Sk + 1.05Qk,1 + 1.05Wk 1.35(Gk,1 + Gk,2 + Gk,3) + 1.5Wk + 1.05Qk,1 + 1.05Sk
check
strength and
stability of
members
and
connections
13
Example: multistorey frame
Load cases (combinations of actions)
Persistent design situation
Serviceability limit states (SLS)
(Gk,1 + Gk,2 + Gk,3) + Qk,1 (Gk,1 + Gk,2 + Gk,3) + Qk,2 (Gk,1 + Gk,2 + Gk,3) + Sk,1 (Gk,1 + Gk,2 + Gk,3) + Wk (Gk,1 + Gk,2 + Gk,3) + Wk + 0.7Qk,1 + 0.7Sk
Seismic design situation
Ultimate limit states (ULS)
(Gk,1 + Gk,2 + Gk,3) + 0.4(Qk,1 + Sk) + Aed
Serviceability limit states (SLS) check lateral storey displacements determined according to specific requirements of
EN 1998-1
check beam
deflections
check lateral storey
deformations
check strength, stability
and ductility of members
and connections