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Calculation stiffness of the rib

The calculation stiffness of the rib depends on check box Rib in command for calculation Code dependent deflection, see "Command for Code dependent deflection".

Check box Rib is OFF:

• stiffness 1D is calculated only for cross-section which is defined in rib properties and for internal forces without taking into account check box RIB, see "Calculation stiffness of 1D element"
• stiffness 2D for 2D elements are calculated by standard way, see "Calculation stiffness of 2D element"
• the 1D reinforcement which is designed (Type of reinforcement = Required or Provided) or input (Type of reinforcement = User) in part of the slab of final cross-section is not taken into account for calculation stiffness of 2D elements

Check box Rib is ON:

• Equilibrium (strain, stresses, height of compression zone ...)for final cross-section (rib cross-section + part of the slab) is calculated for each dangerous combination and each type of stiffness (short-term immediate stiffness, short-term creep stiffness, long-term creep stiffness, short-term total stiffness).The equilibrium is calculated for internal forces with effect of the rib ( forces from 1D member and 2D elements inside effective width are recalculated to centre of gravity of final cross-section
• Stiffness of the rib (1D member ) only for rib cross-section is calculated with taking into account height of compression zone from equilibrium on whole (final) section. Stiffness’s are calculated to centre of gravity of transformed final cross-section , see "Calculation stiffness of 1D element"

• Calculation stiffness of 2D member depends on it,if 2D element is inside or outside of effective width of the rib. Stiffness of 2D elements outside of the effective width is calculated by standard way, see "Calculation stiffness of 2D element", it follows stiffness are calculated in direction of principal stresses. Stiffness of 2D elements inside effective width is calculated in two directions: direction of the rib (a_rib)and direction perpendicular to the rib. (a_rib+90)
•   The stiffness perpendicular to the rib is calculated by standard way according to procedure as for 1D element, see "Calculation stiffness of 1D element"

  • for rectangular cross-section (b =1m, h = thickness of 2D element in centre of gravity)

  • for internal forces perpendicular to the rib N = n(a_rib+90) , M_y= m(a_rib+90) and M_z=0 according procedure as for 1D element
•   The stiffness in direction of the rib is calculated according to following procedure:
  • the 1D reinforcement which is designed (Type of reinforcement = Required or Provided) or input (Type of reinforcement = User) in part of the slab of final cross-section is taken into account for calculation stiffness of 2D elements and this reinforcement is transformed to 2D reinforcement and it is added to standard 2D reinforcement

  • uncracked stiffness (EA_I, EIy_,I, EIz,_I) will be calculated for whole thickness of 2D element with standard 2D reinforcement (required/provided/user) and with transformed reinforcement from 1D member. The stiffness is calculated to transformed centre of gravity of uncracked section

  • cracked stiffness is calculated in case that (sct <= scr). The stiffness (EA_II, EIy,_II, EIz,_II) will be calculated with taking into account parameters from calculation 1D element which is nearest to centre of gravity of 2D element. The height of compression zone is calculated according to formula

    x_s = (A_cc – A_cc,RIB)/b_eff

    where

    A_cc –compressive area of whole cross-section for cracked CSS

    A_cc,RIB – compressive area of part of cross-section (rib cross-section) for cracked CSS

    b_eff – effective width of the slab for check

    sct - is maximum tensile strength calculated for final cross-section (rib cross-section + part of the slab) and for characteristic combination

    The stiffness is calculated to transformed centre of gravity cracked section

  • average stiffness will be calculated from cracked and uncracked stiffness with taking into account distribution coefficient , which is calculated from the stresses calculated for whole cross-section of 1D element which is nearest to centre of gravity of 2D element.

    bending stiffness around y-axis (EIy) = 1/[z/(EIy)_II + (1-z)/ (EIy)_I]

    bending stiffness around z-axis (EIz) = 1/[z/(EIz)_II + (1-z)/ (EIz)_I]

    axial stiffness (EA) = 1/[(z/(EA)_II + (1-z)/( EA)_I],

  • if 2D mesh elements belong to more ribs (centre of gravity of the 2D mesh elements is inside more effective widths) , the average stiffness are calculated in directions of the each ribs (D11_1, D11_2....) and perpendicular to the each rib (D22_1, D22_2). Average values of stiffnesses will be calculated from values in direction of the all ribs D11 = D11_1+ D11_2….. and from values perpendicularly on direction of the all ribs t D22 = D22_1+ D22_2…..The other component of stiffness matrix will be calculated from these averages values. The averages value of angle of the rib is used for calculation deflection too.
  • the other component for the stiffness matrix is calculated according to "Calculation stiffness of 1D element"

Eccentricity of stiiffness (distance between centre of gravity of concrete cross-section and centre of gravity of cracked transformed cross-section) is not taken into account in current version

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