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Basis of Structural Design 结构设计基础


Basis of Structural Design

Course 13 EN 1990: The partial factor method (cont.)

Course notes are available for download at http://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.

1

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

2

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

3

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 ≤ Rd where: 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

4

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" Σ implies "the combined effect of"

ULS: Combination of actions
Gk,j - characteristic permanent action j γG,j - partial safety factor for permanent load Gk,j P - prestressing γP - partial safety factor for prestressing action P Qk,1 - leading variable action γQ,1 - partial safety factor for variable load Qk,1 Qk,i - variable action i γQ,i - partial safety factor for variable load Qk,i ψ0,i - takes into account the reduced probability of the simultaneous occurrence of two (or more) independent variable actions

5

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 ψ2Qk

ULS: Combination of actions
Partial factors for actions and combinations of actions:

γ and ψ factors are obtained from EN 1990 or CR0-2005:
– – – – permanent actions: γG,sup = 1.35 permanent actions: γG,inf = 0.9 variable actions: γQ = 1.5 ψ0,i = 0.7, with the exception of loads in storage facilities, water pressure, etc, when ψ0,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

6

Serviceability limit states
At the SLS it shall be verified that: Ed ≤ Cd where:
– 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

7

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

8

SLS: Combination of actions
Characteristic combination Frequent combination Quasi-permanent combination

For serviceability limit states the partial factors γM 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

9

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

10

Example: multistorey frame
Self-weight (Gk,1) Dead load on floors (Gk,2) Exterior cladding (Gk,3)

The following actions can be identified:
– – – – – Permanent loads Gk Imposed loads Qk Snow load Sk Wind load Wk Seismic action Aed
Imposed load (Qk,1) Snow load (Sk ) Wind load (Wk )

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.

most relevant

Two categories of limit states need to be considered:
– Ultimate limit states (ULS) – Serviceability limit states (SLS)

Persistent design situation

Seismic design situation

ULS

SLS

ULS

SLS

11

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

12

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

check beam deflections check lateral storey deformations

Seismic design situation
– Ultimate limit states (ULS)
? (Gk,1 + Gk,2 + Gk,3) + 0.4(Qk,1 + Sk) + Aed

check strength, stability and ductility of members and connections

– Serviceability limit states (SLS) → check lateral storey displacements determined according to specific requirements of EN 1998-1

13



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