Optimisation: Cross Section and Composite Action

If Calculation Approach is set to "Design" in the composite setup or member data, the program will attempt to find and propose an optimum cross-section for each cross-section group, and composite action for each member in the group. The optimisation procedure is executed based on the Design Approach which is also found in the setup. A maximum height restriction may be implemented as well.

If Calculation Approach is set to "Check" in the composite setup or member data, there will be no optimisation, however, if the composite action used in the checks is different from that assigned to the member, the composite action may be updated.

Except for the section "Updating the project" below, the information on this page is relevant only for Calculation Approach = "Design".

Updating the project

The proposed design parameters (for Calculation Approach = "Design") or the corrected composite action (for Calculation Approach = "Check") can be used to update the project by selecting Apply design proposals to model in the Composite Properties.

When using Calculation Approach = "Design", each cross-section group (i.e. assignment of "Cross-section" on the member), will receive a single cross-section proposal (as needed). The individual members in the group, however, will receive a composite action proposal corresponding to the proposed cross-section as needed.

Grouping of cross-section assignments for optimisation

It is recommended some consideration be given to the cross-section assignment of each member prior to running the optimisation. Cross-sections should be grouped so that all members that have a particular cross-section assignment have a similar length, effective width, support conditions, orientation to sheeting, and loading. This allows the program to optimally design the cross-section.

Do not assign the same cross-section to primary and secondary members (i.e. parallel and perpendicular to profiled sheeting)

Do not assign the same cross-section to members which are to be designed and to members which are to be checked. In this case, the cross-section of the "checked" members may get updated along with the "designed" members.

For members with a wide variation in loading or length, or with different support conditions, the same cross-section assignment may be used, however, this may result in some members (e.g. those with smaller loading) being over-designed. Although inefficient from a design perspective, this may be desired to reduce the overall number of different cross-sections needed.

Optimisation Procedure

The procedure used to select the member's optimum parameters is as follows:

Note: the term "current member" refers to the member with the cross-section and degree of connection that exists in the project at the time the design is run.

Preliminary checks and calculations

Checks are initially performed for every section along the length of the current member using every load combination associated with the stage (construction or final) and type (ULS or SLS) of each check. For each check, a maximum unity check value is found and stored together with the location and load combination with which it is associated. This information (i.e. the location and internal forces and deflections resulting from the controlling load combination) will be used in subsequent checks used to determine the optimum parameters. Since, unlike internal forces, deflections will vary depending on the design parameters, deflection values used in serviceability checks must be approximated during the optimisation using deflection constants. The deflection constants are calculated as follows:

• For construction stage deflection: Deflection Constant = (Deflection at construction stage) / (Moment of Inertia of Cross-Section)

• For final stage deflections: Deflection Constant = (Deflection at final stage) / (Composite Moment of Inertia of Cross-Section)

Qualification for optimisation

Once all checks are run initially, if the maximum UC (unity check) is between 0.9 and 1.0, the optimisation routine will not run since the current parameters are considered optimal or close to optimal. If, however, the maximum UC is greater than 1.0 or less than 0.9, the optimisation will run. Additionally, if the maximum UC is less than 1.0 and the composite action used is different from that which is defined on the member (by 5% or more) then the optimisation will not run, but instead only the composite action will be updated. This typically occurs for secondary members for which the studs are designed based on the spacing of ribs of the profiled sheeting. It may also occur for primary member when the number of studs is rounded up to the nearest whole number resulting in a differing degree of composite action.

Optimisation routine

The following is a summary of what occurs in the optimisation routine if the member meets the requirements for optimisation:

1. A table of cross-sections of the same type as the current member (e.g. UKB) is created and sorted by weight. If a height restriction is imposed, only cross-sections with a height less than the maximum (according to setting in the setup or member data) are included in this table.

2. The optimisation begins to cycle through the cross-section table, starting with the lightest member.

3. The composite action is set to the maximum allowed composite action (determined by stud spacing requirements).

4. All strength and serviceability checks are performed:

4a. If one or more strength or serviceability checks fails (i.e. maximum UC is greater than or equal to 1.0), the next strongest cross-section in the table is selected and steps 3 and 4 are repeated. The 'next strongest' is considered as the next cross-section in the table (sorted by weight) which has a plastic section modulus greater than the current cross-section.

4b. If all strength and serviceability checks pass (i.e. maximum UC is less 1.0) for the cross-section using the maximum allowed composite action, the composite action is then reduced as low as possible until a minimum value is found which still allows all strength and serviceability checks to pass. For secondary members (i.e. perpendicular to profiled sheeting), only degrees of composite action associated with working stud placement scenarios (see Stud Design for additional information) are evaluated in this process.

5. The working cross-section and it's associated composite action determined in step 4b are added to a list of working design parameters.

6. If the goal of the optimisation is to minimize the beam (i.e. design approach is set to 'Minimize beam size'), the first working design is chosen (since it is the lightest) and the optimisation routine ends. Otherwise, the optimisation routine will continue to iterate through the cross-section table and steps 3-5 are repeated. In this case, for step 5, the working design parameters are only added to the list if the number of studs is fewer than the last added working design (this is done to prevent larger cross-sections which have no advantage over smaller cross-sections from being considered).

7. Once the list of working designs is attained, a final set of design parameters (i.e. cross-section and its associated composite action) is selected from the list based on the design approach. If design approach is set to 'Minimize beam size' the cross-section with the smallest area is chosen. If design approach is set to 'Minimize number of studs' the design which results in the fewest studs is chosen. If design approach is set to 'Balanced' the design which has a composite action closes to 50% is chosen. If design approach is set to 'User-defined' the design which has a composite action closes to that input for 'Target degree of composite action' in the setup or member data is chosen.

Controlling cross-section design proposal for updating project

It is recommended that cross-sections are grouped so that all members have a particular cross-section assignment have a similar length, effective width, support conditions, orientation to sheeting, and loading. This allows the program to optimally design the cross-section. Although grouping of cross-sections should be done by the user, if not grouped properly, variations in these physical and/or loading conditions may lead to members in the cross-section which have varying results and therefore varying design proposals. When this is the case, the program will take the cross-section of the member which has the highest initial maximum unity check for strength and serviceability checks. In other words, the member that has the highest maximum ULS or SLS unity check controls the design.

Notes

Detailing checks

In the optimisation routine, if the strength and serviceability checks pass (step 4) but the detailing checks do not pass, the design parameters are still added to the list of working designs (step 5). However, once the optimisation routine finishes, if one or more of the working designs have passing detailing conditions, the designs with failing detailing conditions are removed from consideration prior to step 7. If none of the working designs have passing detailing conditions, all working designs remain for consideration in step 7 (despite failing detailing conditions) and a warning message will be displayed.

Deflection checks and camber

The deflections used in the serviceability checks are predicted by multiplying the deflection constants (See 'Preliminary Checks and Calculations' above) by the moment of inertia and composite moment of inertia for the construction and final stages, respectively.

For deflection checks, if camber is set to an absolute or relative value, the value of camber specified by the user is included in the check. If camber is set to "design", then the program checks that the camber needed is not greater than the maximum allowed camber. The final camber value will be designed after the optimisation according to the procedure described in "Camber Design" section.

Sorting of cross-section table

The plastic section modulus is used to determine stronger cross-section since the bending check generally governs the strength checks.

No design proposals found

If no working design proposals are found, a warning message is displayed . A common reason a working design proposal may not be found is if the height restriction is turned on restricting the number of cross-sections that can be considered in the design. Additionally, working parameters may not be found due to minimum spacing requirements (most often with primary members). In this case, consider allowing 2 rows of studs on the member (see "Composite Setup").

If design proposals are found which allow strength and serviceability checks to pass, but do not allow detailing checks to pass, the model can still be updated, but the warning message will be displayed.