X.D.1.5 “SGI_SR” criterion

This criterion is used to calculate with a single call three connection failure criteria: sliding, gapping and insert. The calculation is done by calculating strength ratios. The relation between strength ratio, reserve factor and margin of safety is as follows:

In this case, three strength ratios are calculated:

• For the sliding strength ratio, one calculates:

  $$S{R}_{\text{sliding}}=\frac{{\text{FoS}}_{\text{sliding}}\cdot \left(C_f\cdot \max <!--FUNCTION\; APPLICATION-->\left(F_{\text{axial}},0\right)+F_{\text{shear}}\right)}{C_f\cdot P_{\text{min}}},$$

  in which $C_f$ is the friction coefficient between assembled elements and $P_{\text{min}}$ is an estimate of the minimum possible pretension of the bolt.

• The gapping strength ratio is given by:

  $$S{R}_{\text{gapping}}=\frac{{\text{FoS}}_{\text{gapping}}\cdot \left(\max <!--FUNCTION\; APPLICATION-->\left(F_{\text{axial}},0\right)+M_{\text{bending}}∕R\right)}{P_{\text{min}}},$$

  in which $R$ is a parameter that allows to take into account the prying effect related to the bending moment in the connection and $P_{\text{min}}$ is an estimate of the minimum possible pretension of the bolt.

• The insert criterion is calculated as follows:

  $$S{R}_{\text{insert}}={\text{FoS}}_{\text{insert}}\cdot \sqrt{{\left(\frac{F_{\text{axial}}}{\text{PSS}}\right)}^2+{\left(\frac{F_{\text{shear}}}{\text{QSS}}\right)}^2},$$

  In which “PSS” is the axial allowable of the insert and “QSS” is its shear allowable.

In these expressions, various scalar values related to the connection force and moment vectors are calculated:

The arguments of the criterion are given in Table X.D.9:

• First argument is a DataBase.
• The second argument is a String that corresponds to extraction method. If this argument is “BSHFRC” or “BMFRC”, the forces and moments are assumed to be associated to elements. Otherwise they are associated to nodes. (This parameter influences the critical entity ID returned for each failure criterion.)
• Arguments 3 and 4 are Result objects that correspond to the connection forces and moments. Note that these Result objects can be modifed if the predefined criterion is calcualted. It is the case, for example, if the coordinate system wrt which force and moment components are expressed is changed.
• Arguments 5 to 8 define the direction vector that allows to convert vectorial forces and moments to the corresponding scalar derived components.
• Arguments 9 to 11 correspond to the safety factors of the different criteria. A negative safety factor means that the corresponding criterion must not be calculated. Then the corresponding output values are initalized to Boolean “FALSE”.
• Arguments 12 to 16 are clearly presented in Table X.D.9

The method returns an Array of 15 elements (5 elements for each criterion):

• Elements 1 to 5 correspond to the sliding criterion and are:
  • The maximum strength ratio;
  • The corresponding entity ID (element or node ID),
  • The corresponding connection axial force.
  • The corresponding connection shear force.
  • A Result object containing all the strength ratios.

  If the sliding safety factor is negative, the criterion is not calculated, and 5 “FALSE” Booleans are returned.

• Elements 6 to 10 correspond to the gapping criterion and are:
  • The maximum strength ratio;
  • The corresponding entity ID (element or node ID),
  • The corresponding connection axial force.
  • The corresponding connection bending moment.
  • A Result object containing all the strength ratios.

  If the gapping safety factor is negative, the criterion is not calculated, and 5 “FALSE” Booleans are returned.

• Elements 11 to 15 correspond to the insert criterion and are:
  • The maximum strength ratio;
  • The corresponding entity ID (element or node ID),
  • The corresponding connection axial force.
  • The corresponding connection shear force.
  • A Result object containing all the strength ratios.

  If the gapping safety factor is negative, the criterion is not calculated, and 5 “FALSE” Booleans are returned.