## Function

- Use optimization techniques or combine equations to determine the optimal load factors that satisfy the specific constraints of a structure.
- This function optimizes tensions of cables at the initial equilibrium position of a cable structure. The program can calculate the initial cable force by inputting the restrictions such as displacement, moment, etc. and satisfying the constraints.

## Call

From the main menu, select **[Results] tab > [Type : Bridge Specialization] > ****[Cable Bridge] group > [Cable Control] > [unknown Load Factor]**

## Input

Fig. Unknown Load Factor dialog box

To calculate unknown load factors using optimization techniques, load combinations, load cases pertaining to the unknown load factors, specific constraints, and object functions are required. All these data are collected in a unique and unknown load factor group for analysis. Several groups can be formulated where they can be saved, modified, or deleted.

The unknown load factors obtained by using the Unknown Load Factor feature for the final stage model do not include the change in stiffness of the cable due to the change in pretension and hence the user must perform iterations to determine the pretension in the cables to satisfy constraints. The following procedure can be adopted:

1. Define the constraints and obtain the Unknown Load Factors for the Cable Pretension Forces.

2. Determine the Cable Pretension Force by multiplying those factors with the assigned Cable Forces

3. Change the Cable Pretension Forces with the new ones ( obtained in step 2)

4. Perform the Analysis.

5. Check whether the constraints are satisfied with modified pretensions

6. If not then determine the Unknown load factors again and keep repeating steps 2 to 5 till you get the constraints satisfied after static analysis ( step 5)

**Add New**: Click Add New to create a new Unknown Load Factor Group by specifying the conditions to obtain the unknown load factor.

**Modify**: Modify a previously created Unknown Load Factor Group.

**Delete**: Delete a previously created Unknown Load Factor Group.

When a new Unknown Load Factor Group is created by clicking **Add New **or when a group is modified by clicking **Modify**, enter or modify the data in the Unknown Load Factor Detail shown below.

Fig. Unknown Load Factor Detail dialog box

### Item Name

Enter the name of the Unknown Load Factor Group.

### Load Comb

Select a load combination from the previously entered load combinations in "Results>Combinations" to calculate the unknown load factors. The load combination used to calculate the unknown load factors must include the load cases that form the basis of the load factors.

In the latest version of midas Civil, the numbers of loads are limited to 150 in each load combination. Therefore, if the load conditions to determine the Unknown Load Factors exceed 150, then the conditions should be divided into two or more combinations, each less than 150 load cases, and each combination should be defined. The load combinations should then be grouped, and the group should be selected as another load combination.

### Object function type

Select the method of forming an object function consisting of unknown load factors.

**Linear**: The sum of the absolute values of Load factor x scale factor

**Square**: The linear sum of the squares of Load factor x scale factor

**Max Abs**: The maximum of the absolute values of Load factor x scale factor

### Sign of unknowns

Assign the sign of the unknown load factors to be calculated.

**Negative**: Limit the range of the calculated values to the negative (-) field.

**Both**: Do not limit the range of the calculated values.

**Positive**: Limit the range of the calculated values to the positive (+) field.

### Unknown

Check in the load case for which the unknown load factor is to be obtained. When load cases are activated as unknown load factors, the character "Unknown" appears in the Factor field of the relevant load case.

### LCase

The name of the load case to be used as an unknown load factor.

### Factor

The load factors for each load condition that constitute the load combination criteria are displayed. If the load condition is an unknown load, it is indicated as "Unknown."

### Weighted Factor

Weighted Factors are scale factors that control the relative importance of the unknown load factors in the object functions.

### Constraints

Enter the constraints to be satisfied by the load combination results that include the unknown load factors. When specifying the constraints, a list of constraints is created. The constraints may be selectively applied. The constraint types are displacement, reaction, and member force for the truss or beam element.

**Add**: Select to create a new constraint.

**Modify**: Select to modify a previously entered constraint.

**Delete**: Select to delete a previously entered constraint.

**Table**: Enter and modify the constraint data easily and quickly using the table. Copy and paste constraint data from an Excel file is also available.

Fig. Constraint Table

**When Add or Modify is selected.**

**When Add or Modify is selected.****Constraint Name**: Specify the constraint name

**Constraint Type**: Specify the constraint type

** **

**1. When the Constraint Type is Reaction**

Fig. Unknown Load Factor Constraint - Reaction

**Node ID**: Enter the constrained node number.

**Component**: Select a reaction component from the 6 degrees of freedom.

**Equality/Inequality Condition**

**Equality**: Condition where the value of the displacement in the load combination that includes the unknown load factors (or the displacement value of the relevant component of another node) is equal to the entered value.

**Value**: Enter the displacement component value that must be satisfied by the load combination that includes the unknown load factors.

**Other Node**: The nodal displacement of another node for the specified component, entered in the load combination, is imposed on the Node ID.

**Inequality**: Where the value of the displacement in the load combination that includes the unknown load factors is between the Upper Bound and the Lower Bound, you may enter both the Upper Bound and Lower Bound or either of them.

**Upper Bound**: Upper limit of the condition

**Lower Bound**: Lower limit of the condition

**Simultaneous Equation Method**: If all the selected constraints are Equality Type, and the number of constraints and unknown loads are also equal, then this option can be selected. In this case, the program will determine the unknowns by combining the equations without using the optimization technique.

**2. When the Constraint Type is Displacement**

Fig. Unknown Load Factor Constraint - Displacement

**Node ID**: Enter the constrained node number.

**Component**: Select a displacement component from the 6 degrees of freedom.

**Equality/Inequality Condition**

**Equality**: Condition where the value of the reaction in the load combination that includes the unknown load factors (or the reaction value of the relevant component of another node) is equal to the entered value.

**Value**: Enter the reaction component value that must be satisfied by the load combination that includes the unknown load factors.

**Other Node**: The reaction of another node for the specified component, entered in the load combination, is imposed on the Node ID.

**Inequality**: Where the value of the reaction in the load combination that includes the unknown load factors is between the Upper Bound and the Lower Bound, you may enter both the Upper Bound and Lower Bound or either of them.

**Upper Bound**: Upper limit of the condition

**Lower Bound**: Lower limit of the condition

**3. When the Constraint Type is Truss Force**

Fig. Unknown Load Factor Constraint - Truss Force

**Element ID**: Enter the constrained truss element number.

**Point**: Select one end of the member for force constraint.

**Equality/Inequality Condition**

**Equality**: Condition where the value of the truss element's member force in the load combination that includes the unknown load factors (or the member force value of another truss element) is equal to the entered value.

**Value**: Enter the truss element's member force value that must be satisfied by the load combination that includes the unknown load factors.

**Other Truss**: The member force of another truss, entered in the load combination, is imposed on the Element ID.

**Inequality**: Where the value of the truss element member force in the load combination that includes the unknown load factors is between the Upper Bound and the Lower Bound, you may enter both the Upper Bound and Lower Bound or either of them.

**Upper Bound**: Upper limit of the condition

**Lower Bound**: Lower limit of the condition

**4. When the Constraint Type is Beam Force**

Fig. Unknown Load Factor Constraint - Beam Force

**Element ID**: Enter the constrained beam element number.

**Point**: Select a point along the length of the member for force constraint.

**Component**: Select a component of the member forces.

**Equality/Inequality Condition**

**Equality**: Condition where the value of the beam element's member force in the load combination that includes the unknown load factors (or the member force value of another beam element) is equal to the entered value.

**Value**: Enter the beam element's member force value that must be satisfied by the load combination that includes the unknown load factors.

**Other Beam**: The member force of another beam, entered in the load combination, is imposed on the Element ID.

**Inequality**: Where the value of the beam element member force in the load combination that includes the unknown load factors is between the Upper Bound and the Lower Bound, you may enter both the Upper Bound and Lower Bound or either of them.

**Upper Bound**: Upper limit of the condition

**Lower Bound**: Lower limit of the condition

**Simultaneous Equation Method**

If all the selected boundary conditions are of the Equality Type, and the number of unknown loads matches the number of boundary conditions, you can check this option. In this case, the simultaneous equations method, instead of optimization techniques, is used to determine the load factors.

Even if the user does not select the Simultaneous Equations Method, if the given loads and boundary conditions can be directly solved using simultaneous equations, the software internally utilizes the simultaneous equations method. In MIDAS, the Gauss-Jordan method is employed for solving simultaneous equations.

If the conditions cannot be solved by simultaneous equations, the following dialog box message will be displayed:

Fig. Warning message when the simultaneous equations method used

**Get UnknownLoad Factors**

This tab calculates the selected Unknown Load Factors by using the constraints. It calculates the unknown load factors that minimize the restricted functions and shows the result as follows.

Fig. Unknown Load Factor Result

**Factor** : Calculated unknown load factors

**Value** : Resulting values of the constraints

**Upper Bound** : Upper bound of each constraint

**Lower Bound** : Lower bound of each constraint

**Influence Matrix** : The calculated results of Unknown Load Factors are produced including Influence Matrix.

Fig. Unknown Load Factor Result which contains influence matrix

**Make Load Combination**: Load combinations are automatically generated by using the calculated Unknown Load Factors.

**Generate Excel File**: The calculated results of Unknown Load Factors including Influence Matrix are produced in an Excel file.

Fig. Results of Unknown Load Factors converted into an Excel file

In the converted Excel file, we can find unknown load factors satisfying desired constraints by changing the unknown load factors, which change the constraints.

### Functionality of Unknown Load Factor considering construction stage

**Functionality of Unknown Load Factor considering construction stage**

Fig. Unknown Load Factor Detail dialog box - When analysing the construction stage

**Item Name**

Specify a group name representing the unknown load factors.

**Stage Name**

Select a Construction Stage for which unknown load factors will be calculated.

When using this feature to estimate the cable tension during construction stages of a cable-stayed bridge, if the cable tension is activated in a Stage/Step simultaneously with other loads (such as crane loads or segment self-weight), applying the unknown load factors only to the cable tension will not yield accurate results for other loads.

Additionally, when the cable element is activated along with its self-weight, the unknown load factors applied to the cable tension will also affect the cable self-weight, leading to incorrect results.

To avoid this issue, it is recommended to activate the load group containing the cable tension and the load group containing other loads in separate Steps or Stages. Furthermore, since the element self-weight is always activated in the first Step of each Stage, it is preferable to activate the load group for cable tension in a User Step or the Last Step.

The functionality of Unknown Load Factor considering Construction Stage Analysis can be used in PostCS. Preparing input is identical to that for general static loads.

### Optimization technique for linear boundary conditions

**Optimization technique for linear boundary conditions**

The mathematical expression for the optimization technique used for linear boundary conditions in Midas Civil can be represented as follows:

Subject to

: Matrices

: Vectors

**Get Unknown Load Factors**

Print out the values of unknown load factors that minimize the objective function using the provided set of constraints.

Fig. Unknown Load Factor Result

**Iterative Analysis**

This tab performs an iterative analysis to calculate the Unknown Load Factor for each construction stage.

For a case considering the creep when calculating the cable forces of a Cable-Stayed Bridge during construction, since creep occurs due to the cable force, the most optimum cable force during construction cannot be calculated in one analysis. In this case, there should be an iterative process to optimize the cable force. By clicking with the number of times to iterate and the condition to converge inputted the iterative analysis will be performed. The following process will repeat and perform the most optimum cable force during construction.

Fig. Unknown Load Factor iterative analysis conditions dialog box

Fig. The flow chart to analyze cable forces for each construction stage

When using this function to perform automatic iterative analysis the following should be known. Whenever a new Pretension of the cables is inputted a new model file (*.mcb file) will be produced, and the program will provide as many analyses as the number of iterate the program is requested. The analysis may stop when the Unload Load Factor reaches 1. Then all the cable forces inputted to the final model file will be the optimized cable force during construction.