Composite Structures According to Eurocode 4 Work Example
Contents
A Creep and shrinkage
A1 Determination of creep and shrinkage values
- Purpose of example
- Cross-section
- Input data
- Creep coefficients
- Shrinkage strains
- Commentary
A2 Determination of creep and shrinkage values on an example composite highway bridge
- Purpose of example
- Cross-section
- Input data
- Calculation of modular ratio nL for permanent action constant in time
- Calculation of modular ratio nL for shrinkage and shrinkage strains
- Primary effects of shrinkage
- Commentary
A3 Determination of creep and shrinkage values and their effects at calculation of bending moments
- Purpose of example
- Static system, cross-section and actions
- Input data
- Creep and shrinkage
- Effective width of the concrete flange
- Geometrical properties of composite cross-section at mid-span
- Geometrical properties of composite cross-section at support
- Effects of creep and shrinkage
- Commentary
B Composite beams
B1 Effective width of concrete flange
- Purpose of example
- Static system and cross-section
- Calculation of effective width of the concrete flange
- Recapitulation of results
- Commentary
B2 Composite beam – arrangement of shear connectors in solid slab
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Ultimate limit state
- Commentary
B3 Simply supported secondary composite beam supporting composite slab with profiled sheeting
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Ultimate limit state
4.1 Design values of combined actions and of the effects of actions for
the construction stage
4.2 Design values of combined actions and of the effects of actions for the composite stage
4.3 Check for the construction stage
4.4 Check for the composite stage
- Serviceability limit state
5.1 General
5.2 Calculation of deflections
5.2.1 Construction stage deflection
5.2.2 Composite stage deflection
5.3 Simplified calculation of deflections
5.4 Pre-cambering of the steel beam
5.5 Check of vibration of the beam
5.6 Control of crack width
- Commentary
B4 Calculation of simply supported composite beam according to the elastic resistance of the cross-section
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Ultimate limit state
4.1 Design values of the combined actions and of the effects of actions
4.2 Effective width of the concrete flange
4.3 Elastic resistance moment of the composite cross-section
4.4 Vertical shear resistance of the composite cross-section
4.5 Calculation of shear connection
4.6 Check of longitudinal shear resistance of the concrete flange
- Serviceability limit state
5.1 General
5.2 Calculation of deflections
5.3 Pre-cambering of steel beam
5.4 Check of vibration of the beam
5.5 Cracks
5.6 Stresses at the serviceability limit state
- Commentary
B5 Calculation of simply supported composite beam according to the plastic resistance of the cross-section
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Ultimate limit state
4.1 Design values of combined actions and of the effects of actions
4.2 Selection of cross-section
4.3 Effective width of concrete flange
4.4 Classification of the steel cross-section
4.5 Check of shear connection
4.6 Plastic resistance moment of the composite cross-section
4.7 Vertical shear resistance of the composite cross-section
4.8 Check of longitudinal shear resistance of the concrete flange
- Serviceability limit state
5.1 General
5.2 Calculation of deflections
5.3 Pre-cambering of steel beam
5.4 Check of vibration of the beam
5.5 Control of crack width
- Commentary
B6 Calculation of continuous beam over two spans by means of elastic–plastic procedure
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Ultimate limit state
4.1 Design values of combined actions and of the effects of actions for the construction stage
4.2 Design values of combined actions and of the effects of actions for the composite stage
4.3 Check for the construction stage
4.4 Check for the composite stage
- Serviceability limit state
5.1 General
5.2 Calculation of deflections
5.3 Pre-cambering of the steel beam
5.4 Check of vibration of the beam
5.5 Control of crack width
5.5.1 Minimum reinforcement area
5.5.2 Control of cracking of the concrete due to direct loading
- Commentary
B7 Calculation of continuous beam over two spans by means of plastic–plastic procedure
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Ultimate limit state
4.1 Design values of combined actions
4.2 Selection of steel cross-section
4.3 Effective width of concrete flange
4.4 Classification of the composite cross-section
4.5 Calculation of effects of actions
4.6 Check of shear connection
4.7 Resistance moment of composite section at mid-span
4.8 Vertical shear resistance of the cross-section
4.9 Interaction of M-V (bending and shear force)
4.10 Lateral-torsional buckling of the composite beam
4.11 Check of longitudinal shear resistance of the concrete flange
- Serviceability limit state
5.1 General
5.2 Calculation of deflections
5.2.1 Construction stage deflection
5.2.2 Composite stage deflection
5.3 Pre-cambering of the steel beam
5.4 Check of vibration of the beam
5.5 Control of crack width
- Commentary
B8 Two-span composite beam – more detailed explanations of provisions of EN 1994-1-1
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Properties of cracked and uncracked cross-sections
- Ultimate limit state
5.1 Design values of the combined actions and of the effects of the actions for the construction stage
5.2 Design values of the combined actions and of the effects of the actions for the composite stage
5.3 Check for the construction stage
5.4 Check for the composite stage
- Serviceability limit sate
6.1 General
6.2 Stress limits
6.3 Calculation of deflections
- Commentary
Composite Structures According to Eurocode 4
C Composite columns
C1 Composite column with concrete-filled circular hollow section subject to axial compression and verified using European buckling curves
- Purpose of example
- Static system, cross-section and design action effects
- Properties of materials
- Geometrical properties of the cross-section
4.1 Selection of the steel cross-section and reinforcement
4.2 Cross-sectional areas
4.3 Second moments of area
- Steel contribution ratio
- Local buckling
- Effective modulus of elasticity for concrete
- Resistance of the cross-section to compressive axial force
8.1 Plastic resistance of the cross-section without confinement effect
8.2 Plastic resistance of the cross-section taking into account confinement effect
- Resistance of the member in axial compression
9.1 Verification of conditions for using simplified design method
9.2 Check of resistance of the member in axial compression
- Commentary
C2 Composite column with concrete-filled circular hollow section subject to axial compression, verified using European buckling curves and using second-order analysis taking into account member imperfections
- Purpose of example
- Static system, cross-section and design action effects
- Properties of materials
- Geometrical properties of the cross-section
4.1 Selection of the steel cross-section and reinforcement
4.2 Cross-sectional areas
4.3 Second moments of area
4.4 Plastic section moduli
- Steel contribution ratio
- Local buckling
- Effective modulus of elasticity for concrete
- Resistance of the cross-section to compressive axial force
8.1 Plastic resistance of the cross-section without confinement effect
8.2 Plastic resistance of the cross-section taking into account the confinement effect
- Resistance of the member in axial compression – using European buckling curves
9.1 Verification of conditions for using the simplified design method
9.2 Check of resistance of the member in axial compression
- Resistance of the member in axial compression – using second-order analysis, taking into account member imperfections
10.1 General
10.2 Verification of conditions for using the simplified design method
10.3 Resistance of the cross-section in combined compression and uniaxial bending
10.4 Calculation of action effects according to second-order analysis
10.5 Check of the resistance of the member in combined compression and uniaxial bending
- Commentary
C3 Composite column with concrete filled circular hollow section subject to axial compression and uniaxial bending
- Purpose of example
- Static system, cross-section and design action effects
- Properties of materials
- Geometrical properties of the cross-section
- Steel contribution ratio
- Local buckling
- Effective modulus of elasticity for concrete
- Resistance of the cross-section to compressive axial force
- Verification of conditions for using the simplified design method
- Resistance of the member in axial compression
- Resistance of the member in combined compression and uniaxial bending
- Check of the load introduction
- Commentary
C4 Composite column with concrete-filled rectangular hollow section subject to axial compression and uniaxial bending
- Purpose of example
- Static system, cross-section and design action effects
- Properties of materials
- Geometrical properties of the cross-section
- Steel contribution ratio
- Local buckling
- Effective modulus of elasticity for concrete
- Resistance of the cross-section to compressive axial force
- Verification of conditions for using the simplified design method
- Resistance of the member in axial compression
- Resistance of the member in combined compression and uniaxial bending
- Commentary
C5 Composite column with partially concrete-encased H-section subject to axial compression and uniaxial bending
- Purpose of example
- Static system, cross-section and design action effects
- Properties of materials
- Geometrical properties of the cross-section
4.1 Selection of the steel cross-section and reinforcement
4.2 Cross-sectional areas
4.3 Second moments of area
4.4 Plastic section moduli
- Steel contribution ratio
- Local buckling
- Effective modulus of elasticity for concrete
- Resistance of the cross-section to compressive axial force
- Verification of the conditions for using simplified design method
- Resistance of the member in axial compression
- Resistance of the member in combined compression and uniaxial bending
11.1 Resistance of the member about the y–y axis taking into account the equivalent member imperfection e0,z
11.2 Resistance of the member about the z-z axis taking into account the equivalent member imperfection e0,y
- Check of the longitudinal shear outside the area of load introduction
- Check of the load introduction
13.1 Load introduction for combined compression and bending
13.2 Calculation of the stud resistance
13.3 Calculation of the shear forces on the studs based on elastic theory
13.4 Calculation of the shear forces on the studs based on plastic theory
- Commentary
C6 Composite column with fully concrete-encased H-section subject to axial compression and biaxial bending
- Purpose of example
- Static system, cross-section and design action effects
- Properties of materials
- Geometrical properties of the cross-section
- Steel contribution ratio
- Local buckling
- Effective modulus of elasticity for concrete
- Resistance of the cross-section to compressive axial force
- Verification of the conditions for using the simplified design method
- Resistance of the member in axial compression
- Resistance of the member in combined compression and uniaxial bending
- Resistance of the member in combined compression and biaxial bending
- Commentary
D Composite slabs
D1 Two-span composite slab unpropped at the construction stage
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Structural details of composite slab
4.1 Slab thickness and reinforcement
4.2 Largest nominal aggregate size
4.3 Minimum value for nominal thickness of steel sheet
4.4 Composite slab bearing requirements
- Ultimate limit state
5.1 Construction stage
5.2 Composite stage
- Serviceability limit state
6.1 Control of cracking of concrete
6.2 Limit of span/depth ratio of slab
6.3 Calculation of deflections
- Commentary
D2 Three-span composite slab propped at the construction stage
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Structural details of composite slab
4.1 Slab thickness and reinforcement
4.2 Largest nominal aggregate size
4.3 Minimum value for nominal thickness of steel sheet
4.4 Composite slab bearing requirements
- Ultimate limit state
5.1 Construction stage
5.2 Composite stage
- Serivceability limit state
6.1 Control of cracking of concrete
6.2 Limit of span/depth ratio of slab
6.3 Calculation of deflections
- Commentary
D3 Three-span composite slab propped at the construction stage end anchorage and additional reinforcement
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Structural details of composite slab
4.1 Slab thickness and reinforcement
4.2 Largest nominal aggregate size
4.3 Minimum value for nominal thickness of steel sheet
4.4 Composite slab bearing requirements
- Ultimate limit state
5.1 Construction stage
5.2 Composite stage
5.3 Composite stage – alternatively, the composite slab is designed as continuous
- Serviceability limit state
6.1 Control of cracking of concrete
6.2 Limit of span/depth ratio of slab
6.3 Calculation of deflections
- Commentary
D4 Two-span composite slab unpropped at the construction stage – commentaries on EN 1994-1-1
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Structural details of composite slab
4.1 Slab thickness and reinforcement
4.2 Largest nominal aggregate size
4.3 Minimum value for nominal thickness of steel sheet
4.4 Composite slab bearing requirements
- Ultimate limit state
5.1 Construction stage
5.2 Composite stage
- Serviceability limit state
6.1 Control of cracking of concrete
6.2 Limit of span/depth ratio of slab
6.3 Calculation of deflections
- Commentary
D5 Hoesch Additive Floor
- Purpose of example
- Generally about the Hoesch Additive Floor system
- Structural system and cross-section
- Properties of materials
- Selection of effective span length without supporting at the construction stage
- Ultimate limit state
6.1 Calculation at the construction stage
6.2 Calculation for final stage
- Serviceability limit state
7.1 Cracking of concrete
7.2 Deflections
- Commentary
E Fatigue
E1 Fatigue verification for composite highway bridge
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Global analysis
- Fatigue assessment
5.1 Assessment of structural steel details
5.1.4 Design stress ranges – cross-section 3-3
5.2 Assessment of reinforcing steel
5.3 Assessment of shear connection
- Commentary
E2 Fatigue assessment for a composite beam of a floor structure
- Purpose of example
- Static system, cross-section and actions
- Properties of materials
- Properties of the IPE 450 cross-section
- Effective widths of concrete flange
- Classification of composite cross-section
- Flexural properties of elastic cross-section
- Global analysis
- Fatigue assessment
- Commentary
Composite Structures According to Eurocode 4
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