Basis of Structural Design.pdf

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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.

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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


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

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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.


FAT: Fatigue failure of the structure or structural members.Examples: Cracks developing in steel bridges due to repetitive loading generated by traffic

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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

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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"


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

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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


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

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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.


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

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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

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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

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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

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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)


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

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Load cases (combinations of actions)

Persistent design situation



Seismic design situation


Serviceability limit states (SLS) see EN 1998-1





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

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(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


(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

Documents

Basis of Structural Design.pdf