Reference problem ===================== Geometry --------- We consider a beam with a rectangular cross section, with dimensions :math:`h={H}_{Z}=\mathrm{0,3}m` and :math:`{b}_{w}={H}_{Y}=\mathrm{0,5}m`. .. image:: images/100002010000023E0000027F5875E08F68834DD3.png :width: 2.839in :height: 3.1602in .. _RefImage_100002010000023E0000027F5875E08F68834DD3.png: Material properties ---------------------- Not applicable to mechanical resolution (see § :ref:`1.3 `). See paragraph :ref:`1.3.2 ` for the parameters for determining the limit state for the material. .. _RefNumPara__20284_980306414: Boundary conditions and loads ------------------------------------- There is no mechanical resolution operator called in this test. A generalized analytical field of effort is applied as input to the operator CALC_FERRAILLAGE, corresponding to one of the following configurations: Case of loading at ELU ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1. compression force of :math:`1000000\text{N}`, and a shear force of :math:`100000\text{N}` along the axis :math:`\text{Z}` 2. traction force of :math:`1000000\text{N}`, and a shear force of :math:`-100000\text{N}` along the axis :math:`\text{Z}` 3. tensile force of :math:`1000000\text{N}`, a shear force of :math:`-100000\text{N}` along the axis :math:`\text{Z}` and a torsional moment of :math:`10000\text{Nm}` 4. bending moment of :math:`100000\text{Nm}` around the :math:`\text{Z}` axis. 5. Bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Y}` axis. 6. bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Z}` axis and pull force of :math:`100000\text{N}` 7. bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Y}` axis and pull force of :math:`100000\text{N}` 8. bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Z}` axis and pull force of :math:`2000000\text{N}` 9. bending moment of :math:`100000\text{Nm}` around the :math:`\text{Z}` axis and :math:`-150000\text{Nm}` bending moment around the :math:`\text{Y}` axis 10. bending moment of :math:`100000\text{Nm}` around axis :math:`\text{Z}`, moment of bending of :math:`-150000\text{Nm}` around axis :math:`\text{Y}`, and compression force of :math:`3000000\text{N}` 11. bending moment of :math:`-150000\text{Nm}` around the :math:`\text{Z}` axis 12. bending moment of :math:`-260000\text{Nm}` around the :math:`\text{Z}` axis 13. bending moment of :math:`-380000\text{Nm}` around the :math:`\text{Z}` axis 14. compression force of :math:`4500000\text{N}`, bending moment of :math:`380000\text{Nm}` around the axis :math:`\text{Z}` and a shear force of :math:`100000\text{N}` following :math:`\text{Z}` .. _RefNumPara__20286_980306414: Load cases with the ELS Feature ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1. compression force of :math:`1000000\text{N}`, and a shear force of :math:`100000\text{N}` along the axis :math:`\text{Z}` 2. traction force of :math:`1000000\text{N}`, and a shear force of :math:`-100000\text{N}` along the axis :math:`\text{Z}` 3. tensile force of :math:`1000000\text{N}`, a shear force of :math:`-100000\text{N}` along the axis :math:`\text{Z}` and a torsional moment of :math:`10000\text{Nm}` 4. bending moment of :math:`100000\text{Nm}` around the :math:`\text{Z}` axis. 5. Bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Y}` axis. 6. bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Z}` axis and pull force of :math:`100000\text{N}` 7. bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Y}` axis and pull force of :math:`100000\text{N}` 8. bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Z}` axis and pull force of :math:`2000000\text{N}` 9. bending moment of :math:`100000\text{Nm}` around the :math:`\text{Z}` axis and :math:`-150000\text{Nm}` bending moment around the :math:`\text{Y}` axis 10. bending moment of :math:`100000\text{Nm}` around axis :math:`\text{Z}`, moment of bending of :math:`-150000\text{Nm}` around axis :math:`\text{Y}`, and compression force of :math:`3000000\text{N}` 11. bending moment of :math:`-150000\text{Nm}` around the :math:`\text{Z}` axis 12. bending moment of :math:`-260000\text{Nm}` around the :math:`\text{Z}` axis 13. bending moment of :math:`-380000\text{Nm}` around the :math:`\text{Z}` axis 14. compression force of :math:`4500000\text{N}`, bending moment of :math:`380000\text{Nm}` around the axis :math:`\text{Z}` and a shear force of :math:`100000\text{N}` following :math:`\text{Z}` Case of loading at the ELS Quasi-Permanent ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1. compression force of :math:`1000000\text{N}`, and a shear force of :math:`100000\text{N}` along the axis :math:`\text{Z}` 2. traction force of :math:`1000000\text{N}`, and a shear force of :math:`-100000\text{N}` along the axis :math:`\text{Z}` 3. tensile force of :math:`1000000\text{N}`, a shear force of :math:`-100000\text{N}` along the axis :math:`\text{Z}` and a torsional moment of :math:`10000\text{Nm}` 4. bending moment of :math:`100000\text{Nm}` around the :math:`\text{Z}` axis. 5. Bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Y}` axis. 6. bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Z}` axis and pull force of :math:`100000\text{N}` 7. bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Y}` axis and pull force of :math:`100000\text{N}` 8. bending moment of :math:`-100000\text{Nm}` around the :math:`\text{Z}` axis and pull force of :math:`2000000\text{N}` 9. bending moment of :math:`100000\text{Nm}` around the :math:`\text{Z}` axis and :math:`-150000\text{Nm}` bending moment around the :math:`\text{Y}` axis 10. bending moment of :math:`100000\text{Nm}` around axis :math:`\text{Z}`, moment of bending of :math:`-150000\text{Nm}` around axis :math:`\text{Y}`, and compression force of :math:`3000000\text{N}` 11. bending moment of :math:`-150000\text{Nm}` around the :math:`\text{Z}` axis 12. bending moment of :math:`-260000\text{Nm}` around the :math:`\text{Z}` axis 13. bending moment of :math:`-380000\text{Nm}` around the :math:`\text{Z}` axis 14. compression force of :math:`4500000\text{N}`, bending moment of :math:`380000\text{Nm}` around the axis :math:`\text{Z}` and a shear force of :math:`100000\text{N}` following :math:`\text{Z}` 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 csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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 [s] = 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 csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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 [s] = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Configuration 3- Taking into account the impact of compression on the shear force resistance and the impact of shear force and torsion on the longitudinal reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - **UTIL_COMPR = 'OUI '** - **EPURE_CISA = 'OUI '** - upper csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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 [s] = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Configuration 4- Search for a symmetric sizing reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - **FERR_SYME = 'OUI '** - **SEUIL_SYME =** **1** cm2 - upper csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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 [s] = 7800 Kg/m3 - αcc= 1.0/γc= 1.5/γs= 1.15 * Configuration 5- Sizing at BAEL91: - calculation at BAEL91 - **FERR_COMP = 'OUI '** - upper csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 4 cm - elastic limit of steel Fe= 500 MPa - Young's modulus of Eys steel = 210,000 MPa - type diagram (sant-901) for steel = 'B2' - characteristic strength of concrete fcj= 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 csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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 = 15 - density of the steel [s] = 7800 Kg/m3 * Configuration 2- Taking into account compression reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - upper csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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 = 15 - 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 =** **5** cm2 - upper csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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 = 15 - density of the steel [s] = 7800 Kg/m3 * Setup 4- Calculation at BAEL91 - calculation at BAEL91 - **FERR_COMP = 'OUI '** - upper csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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 = 15 - 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 csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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= 0.4 - maximum compressive stress allowed in concrete for the control of non-linear creep: μc, 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 = 15 - density of the steel [s] = 7800 Kg/m3 * Configuration 2- Taking into account compression reinforcement: - calculation at EC2 - **FERR_COMP = 'OUI '** - upper csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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= 0.4 - maximum compressive stress allowed in concrete for the control of non-linear creep: μc, 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 = 15 - 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 =** **5** cm2 - upper csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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= 0.4 - maximum compressive stress allowed in concrete for the control of non-linear creep: μc, 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 = 15 - density of the steel [s] = 7800 Kg/m3 * Setup 4- Calculation at BAEL91 - calculation at BAEL91 - **FERR_COMP = 'OUI '** - upper csup coating, Y = csup, Z =4 cm - lower cinf coating, Y = cinf, Z = 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= 0.4 - maximum compressive stress allowed in concrete for the control of non-linear creep: μc, 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 = 15 - density of the steel [s] = 7800 Kg/m3