Reference problem ===================== Geometry --------- We consider a square plate with side :math:`1m` and thickness :math:`\mathrm{0,2}m`. Material properties ---------------------- Nil. Boundary conditions and loads ------------------------------------- A mechanical resolution operator is not called; generalized analytical effort fields are given at the input of CALC_FERRAILLAGE, corresponding to one of the following configurations: Case of loading at ELU ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1. compression force of :math:`1000000\text{N}` exerted along the :math:`\text{Y}` axis, and a shear force of :math:`100000\text{N}` along :math:`\text{Y}` 2. traction force of :math:`1000000\text{N}` exerted along the :math:`\text{X}` axis, and a shear force of :math:`-600000\text{N}` along :math:`\text{X}` 3. tractive force of :math:`1000000\text{N}` exerted along the :math:`\text{Y}` axis, and a shear force of :math:`-20000\text{N}` along :math:`\text{X}` and :math:`80000\text{N}` along :math:`\text{Y}` 4. bending moment of :math:`100000\text{Nm}` around the :math:`\text{Y}` axis. 5. Bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis. 6. bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis and :math:`100000\text{N}` compression force exerted along the :math:`\text{X}` axis 7. bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis and :math:`100000\text{N}` traction force exerted along the :math:`\text{X}` axis 8. bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis and :math:`2000000\text{N}` traction force exerted along the :math:`\text{X}` axis 9. bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis and :math:`-75000\text{Nm}` bending moment around the :math:`\text{Y}` axis 10. bending moment of :math:`-150000\text{Nm}` around the :math:`\text{Y}` axis. 11. bending moment of :math:`-260000\text{Nm}` around the :math:`\text{Y}` axis. 12. bending moment of :math:`-380000\text{Nm}` around the :math:`\text{Y}` axis. 13. compression force of :math:`1500000\text{N}` exerted along the :math:`\text{Y}` axis, and a shear force of :math:`800000\text{N}` along :math:`\text{Y}` 14. bending moment of :math:`380000\text{Nm}` around the axis :math:`\text{X}`, compression force of :math:`4500000\text{N}` exerted along the axis :math:`X`, and a shear force of :math:`100000\text{N}` following :math:`\text{Y}` Load cases with the ELS Feature ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1. compression force of :math:`1000000\text{N}` exerted along the :math:`\text{Y}` axis, and a shear force of :math:`100000\text{N}` along :math:`\text{Y}` 2. traction force of :math:`1000000\text{N}` exerted along the :math:`\text{X}` axis, and a shear force of :math:`-600000\text{N}` along :math:`\text{X}` 3. tractive force of :math:`1000000\text{N}` exerted along the :math:`\text{Y}` axis, and a shear force of :math:`-20000\text{N}` along :math:`\text{X}` and :math:`80000\text{N}` along :math:`\text{Y}` 4. bending moment of :math:`100000\text{Nm}` around the :math:`\text{Y}` axis. 5. Bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis. 6. bending moment of :math:`300000\text{Nm}` around the :math:`\text{X}` axis and :math:`20000\text{N}` compression force exerted along the :math:`\text{X}` axis 7. bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis and :math:`100000\text{N}` traction force exerted along the :math:`\text{X}` axis 8. bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis and :math:`2000000\text{N}` traction force exerted along the :math:`\text{X}` axis 9. bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis and :math:`-75000\text{Nm}` bending moment around the :math:`\text{Y}` axis 10. bending moment of :math:`-300000\text{Nm}` around the :math:`\text{Y}` axis. Case of loading at the ELS Quasi-Permanent ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1. compression force of :math:`1000000\text{N}` exerted along the :math:`\text{Y}` axis, and a shear force of :math:`100000\text{N}` along :math:`\text{Y}` 2. traction force of :math:`1000000\text{N}` exerted along the :math:`\text{X}` axis, and a shear force of :math:`-600000\text{N}` along :math:`\text{X}` 3. tractive force of :math:`1000000\text{N}` exerted along the :math:`\text{Y}` axis, and a shear force of :math:`-20000\text{N}` along :math:`\text{X}` and :math:`80000\text{N}` along :math:`\text{Y}` 4. bending moment of :math:`100000\text{Nm}` around the :math:`\text{Y}` axis. 5. Bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis. 6. bending moment of :math:`300000\text{Nm}` around the :math:`\text{X}` axis and :math:`15000\text{N}` compression force exerted along the :math:`\text{X}` axis 7. bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis and :math:`100000\text{N}` traction force exerted along the :math:`\text{X}` axis 8. bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis and :math:`2000000\text{N}` traction force exerted along the :math:`\text{X}` axis 9. bending moment of :math:`100000\text{Nm}` around the :math:`\text{X}` axis and :math:`-75000\text{Nm}` bending moment around the :math:`\text{Y}` axis 10. bending moment of :math:`-125000\text{Nm}` around the :math:`\text{Y}` axis. Other calculation parameters --------------------------- Settings at ELU ~~~~~~~~~~~~~~~~~~~ In ELU, we will consider 9 configurations on which we will start the calculation of the 14 load cases presented in §1.3.1: * Setup 1- Basic calculation: - calculation at EC2 - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of steel fyk= 500 MPa - Young's modulus of Eys steel = 210,000 MPa - type diagram (sant-901) for steel = 'B2' - characteristic strength of concrete fck= 35 MPa - density of the steel = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Configuration 2- Taking into account compression reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of steel fyk= 500 MPa - Young's modulus of Eys steel = 210,000 MPa - type diagram (sant-901) for steel = 'B2' - characteristic strength of concrete fck= 35 MPa - density of the steel = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Configuration 3- Taking into account the minimum reinforcement see EC2: - calculation at EC2 - **FERR_COMP = 'OUI '** - **FERR_MIN = 'CODE '** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of steel fyk= 500 MPa - Young's modulus of Eys steel = 210,000 MPa - type diagram (sant-901) for steel = 'B2' - characteristic strength of concrete fck= 35 MPa - density of the steel = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Configuration 4- Taking into account a minimum reinforcement provided by the user: - calculation at EC2 - **FERR_COMP = 'OUI '** - **FERR_MIN = 'OUI '** - **RHO_LONGI_MIN = 0.0013,** - **RHO_TRNSV_MIN = 0. ,** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of fyk steel = 500 MPa - Young's modulus of Eys steel = 210,000 MPa - type diagram (sant-901) for steel = 'B2' - characteristic strength of concrete fck = 35 MPa - density of the steel [s] = 7800 kg/m3 - αcc = 1.0/γc = 1.5/γs = 1.15 * Configuration 5- Change in the type of the diagram (ys−e) for steel: - calculation at EC2 - **FERR_COMP = 'OUI '** - **FERR_MIN = 'CODE '** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of steel fyk= 500 MPa - Young's modulus of Eys steel = 210,000 MPa - type diagram (sant-901) for steel = 'B1' - characteristic strength of concrete fck= 35 MPa - density of the steel = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Configuration 6- Taking into account the impact of compression on the shear force resistance: - calculation at EC2 - **FERR_COMP = 'OUI '** - **FERR_MIN = 'CODE '** - **UTIL_COMPR = 'OUI '** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of steel fyk= 500 MPa - Young's modulus of Eys steel = 210,000 MPa - type diagram (sant-901) for steel = 'B2' - characteristic strength of concrete fck= 35 MPa - density of the steel = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Configuration 7- Taking into account the impact of shear force and torsion on the longitudinal reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - **FERR_MIN = 'CODE '** - **EPURE_CISA = 'OUI '** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of steel fyk= 500 MPa - Young's modulus of Eys steel = 210,000 MPa - type diagram (sant-901) for steel = 'B2' - characteristic strength of concrete fck= 35 MPa - density of the steel = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Configuration 8- Search for a symmetric sizing reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - **FERR_SYME = 'OUI '** - **SEUIL_SYME =** **1** cm2 - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of steel fyk= 500 MPa - Young's modulus of Eys steel = 210,000 MPa - type diagram (sant-901) for steel = 'B2' - characteristic strength of concrete fck= 35 MPa - density of the steel = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Configuration 9- Variation of the search threshold for a symmetric sizing reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - **FERR_SYME = 'OUI '** - **SEUIL_SYME =** **10** cm2 - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of steel fyk= 500 MPa - Young's modulus of Eys steel = 210,000 MPa - type diagram (sant-901) for steel = 'B2' - characteristic strength of concrete fck= 35 MPa - density of the steel = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Setup 10- Sizing at BAEL91: - calculation at BAEL91 - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of steel Fe= 500 MPa - Young's modulus of Eys steel = 210,000 MPa - diagram type (S-E) for steel = 'B2' - characteristic strength of concrete FCj= 35 MPa - density of the steel = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Configuration 11- Change of steel class (A): - calculation at EC2 - **FERR_COMP = 'OUI '** - **CLASSE_ACIER = 'A'** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of fyk steel = 500 MPa - Young's modulus of Eys steel = 210,000 MPa - diagram type (S-E) for steel = 'B2' - characteristic strength of concrete fck = 35 MPa - density of the steel [s] = 7800 kg/m3 - αcc = 1.0/γc = 1.5/γs = 1.15 * Configuration 12- Steel class change (C): - calculation at EC2 - **FERR_COMP = 'OUI '** - **CLASSE_ACIER = 'C'** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of fyk steel = 500 MPa - Young's modulus of Eys steel = 210,000 MPa - diagram type (S-E) for steel = 'B2' - characteristic strength of concrete fck = 35 MPa - density of the steel [s] = 7800 kg/m3 - αcc = 1.0/γc = 1.5/γs = 1.15 * Configuration 13- Calculation of reinforcement with the 'SANDWICH' method: - calculation at EC2 - **FERR_COMP = 'OUI '** - **METHODE_2D = 'Sandwich'** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of fyk steel = 500 MPa - Young's modulus of Eys steel = 210,000 MPa - diagram type (S-E) for steel = 'B2' - characteristic strength of concrete fck = 35 MPa - density of the steel [s] = 7800 kg/m3 - αcc = 1.0/γc = 1.5/γs = 1.15 * Configuration 14- Calculation of reinforcement with the method 'SANDWICH '+ Variation of precision criteria: - calculation at EC2 - **FERR_COMP = 'OUI '** - **METHODE_2D = 'Sandwich'** - **THETA_ITER = 1.0** - **EP_ITER = 0.02** - **ALPHA_ITER = 0.15** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of fyk steel = 500 MPa - Young's modulus of Eys steel = 210,000 MPa - diagram type (S-E) for steel = 'B2' - characteristic strength of concrete fck = 35 MPa - density of the steel [s] = 7800 kg/m3 - αcc = 1.0/γc = 1.5/γs = 1.15 * Configuration 15- Calculation of reinforcement with the method 'SANDWICH '+ Not taken into account §6.109 of EN-1992-2: - calculation at EC2 - **FERR_COMP = 'OUI '** - **METHODE_2D = 'Sandwich'** - **COND_109 = 'NON '** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - elastic limit of fyk steel = 500 MPa - Young's modulus of Eys steel = 210,000 MPa - diagram type (S-E) for steel = 'B2' - characteristic strength of concrete fck = 35 MPa - density of the steel [s] = 7800 kg/m3 - αcc = 1.0/γc = 1.5/γs = 1.15 Parameters with the ELS Feature ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In ELS Characteristic, we will consider 4 configurations on which we will start the calculation of the 10 load cases presented in §1.3.2: * Setup 1- Basic calculation: - calculation at EC2 - upper coating of csup = 4 cm - lower cinf coating = 4 cm - characteristic strength of concrete fck= 35 MPa - authorized limit stress in steel: μs, lim = 400 MPa - maximum compressive stress authorized at the level of the underside of concrete: ►c, inf, lim = 21 MPa - maximum compressive stress authorized at the level of the underside of concrete: ►c, sup, lim=21 MPa - steel-concrete equivalence coefficient: αE = 21 - density of the steel [s] = 7800 Kg/m3 * Configuration 2- Taking into account compression reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - characteristic strength of concrete fck= 35 MPa - authorized limit stress in steel: μs, lim = 400 MPa - maximum compressive stress authorized at the level of the underside of concrete: ►c, inf, lim = 21 MPa - maximum compressive stress authorized at the level of the underside of concrete: ►c, sup, lim=21 MPa - steel-concrete equivalence coefficient: αE = 21 - density of the steel [s] = 7800 Kg/m3 * Configuration 3- Search for a symmetric sizing reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - **FERR_SYME = 'OUI '** - **SEUIL_SYME =** **10** cm2 - upper coating of csup = 4 cm - lower cinf coating = 4 cm - characteristic strength of concrete fck= 35 MPa - authorized limit stress in steel: μs, lim = 400 MPa - maximum compressive stress authorized at the level of the underside of concrete: S-C, INF, LIM = 21 MPa - maximum compressive stress authorized at the level of the underside of concrete: S-C, SUP, LIM = 21 MPa - steel-concrete equivalence coefficient: αE = 21 - density of the steel [s] = 7800 Kg/m3 * Setup 4- Calculation at BAEL91 - calculation at BAEL91 - **FERR_COMP = 'OUI '** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - characteristic strength of concrete FCj= 35 MPa - authorized limit stress in steel: μs, lim = 400 MPa - maximum compressive stress authorized at the level of the underside of concrete: S-C, INF, LIM = 21 MPa - maximum compressive stress authorized at the level of the underside of concrete: S-C, SUP, LIM = 21 MPa - steel-concrete equivalence coefficient: N = 21 - density of the steel [s] = 7800 Kg/m3 Settings at the ELS Quasi-Permanent ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ At ELS Permanent4 configurations will be considered on which we will start the calculation of the 10 load cases presented in §1.3.3: * Setup 1- Basic calculation: - calculation at EC2 - upper coating of csup = 4 cm - lower cinf coating = 4 cm - characteristic strength of concrete fck= 35 MPa - elastic limit of steel: fyk = 500 MPa - Young's modulus of steel: Eys = 210,000 MPa - maximum crack opening allowed on the underside: wmax, inf = 0.15 mm - maximum crack opening allowed on the upper side: wmax, sup = 0.15 mm - loading time coefficient: kt= 0.6 - maximum compressive stress allowed in concrete for the control of non-linear creep: bsc, lim, NL= 15.75 MPa - estimated diameter of the bars on the lower face along the X axis: Φ INF, X = 25 mm - estimated diameter of the bars on the upper face along the X axis: Φ SUP, X= 25 mm - estimated diameter of the bars on the lower face along the Y axis: Φ INF, Y= 25 mm - estimated diameter of the bars on the upper face along the Y axis: Φ SUP, Y= 25 mm - steel-concrete equivalence coefficient: αE = 21 - density of the steel [s] = 7800 Kg/m3 * Configuration 2- Taking into account compression reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - characteristic strength of concrete fck= 35 MPa - elastic limit of steel: fyk = 500 MPa - Young's modulus of steel: Eys = 210,000 MPa - maximum crack opening allowed on the underside: wmax, inf = 0.15 mm - maximum crack opening allowed on the upper side: wmax, sup = 0.15 mm - loading time coefficient: kt= 0.6 - maximum compressive stress allowed in concrete for the control of non-linear creep: bsc, lim, NL= 15.75 MPa - estimated diameter of the bars on the lower face along the X axis: Φ INF, X = 25 mm - estimated diameter of the bars on the upper face along the X axis: Φ SUP, X= 25 mm - estimated diameter of the bars on the lower face along the Y axis: Φ INF, Y= 25 mm - estimated diameter of the bars on the upper face along the Y axis: Φ SUP, Y= 25 mm - steel-concrete equivalence coefficient: αE = 21 - density of the steel [s] = 7800 Kg/m3 * Configuration 3- Search for a symmetric sizing reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - **FERR_SYME = 'OUI '** - **SEUIL_SYME =** **10** cm2 - upper coating of csup = 4 cm - lower cinf coating = 4 cm - characteristic strength of concrete fck= 35 MPa - elastic limit of steel: fyk = 500 MPa - Young's modulus of steel: Eys = 210,000 MPa - maximum crack opening allowed on the underside: wmax, inf = 0.15 mm - maximum crack opening allowed on the upper side: wmax, sup = 0.15 mm - loading time coefficient: kt= 0.6 - maximum compressive stress allowed in concrete for the control of non-linear creep: bsc, lim, NL= 15.75 MPa - estimated diameter of the bars on the lower face along the X axis: Φ INF, X = 25 mm - estimated diameter of the bars on the upper face along the X axis: Φ SUP, X= 25 mm - estimated diameter of the bars on the lower face along the Y axis: Φ INF, Y= 25 mm - estimated diameter of the bars on the upper face along the Y axis: Φ SUP, Y= 25 mm - steel-concrete equivalence coefficient: αE = 21 - density of the steel [s] = 7800 Kg/m3 * Setup 4- Calculation at BAEL91 - calculation at BAEL91 - **FERR_COMP = 'OUI '** - upper coating of csup = 4 cm - lower cinf coating = 4 cm - characteristic strength of concrete fck= 35 MPa - elastic limit of steel: fyk = 500 MPa - Young's modulus of steel: Eys = 210,000 MPa - maximum crack opening allowed on the underside: wmax, inf = 0.15 mm - maximum crack opening allowed on the upper side: wmax, sup = 0.15 mm - loading time coefficient: kt= 0.6 - maximum compressive stress allowed in concrete for the control of non-linear creep: bsc, lim, NL= 15.75 MPa - estimated diameter of the bars on the lower face along the X axis: Φ INF, X = 25 mm - estimated diameter of the bars on the upper face along the X axis: Φ SUP, X= 25 mm - estimated diameter of the bars on the lower face along the Y axis: Φ INF, Y= 25 mm - estimated diameter of the bars on the upper face along the Y axis: Φ SUP, Y= 25 mm - steel-concrete equivalence coefficient: αE = 21 - density of the steel [s] = 7800 Kg/m3