*Android phone, iPhone & iPad*

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## Load Cases

**At a glance:** Load cases on an Android phone, iPhone or iPad are described here. The General – Load Cases section gives an in-depth description of the processes mentioned here.

#### What is a load case

The main computation facilities are provided in an entity called a “load case”. Each cross-section can have several load cases associated with it. Each load case is intended to represent a particular situation in the life of the structural member that is of interest. Such matters of interest might be the ultimate strength, or the distortion under a known loading.

#### The main Load cases tab

The load cases are listed on the Load cases tab; one of the main tabs described in the *Android phone, iPhone & iPad – Introduction* under **Lists of Entities**.

The Load case edit facilities are **Entity edit facilities** as described in the *Android phone, iPhone & iPad* – **Introduction**. Here is an elaboration on that description.

**Button – “Zero all stage distortion” **on this Load Cases tab is described in **Chronological sequence**.

#### The input information

The kind of information to be input to a load case depends on the nature of the investigation. Nevertheless the information on the first panel that appears when the load case edit facility is invoked is the same for all load cases.

##### Reference axes

Associated with each load case is a set of reference axes that are part of the description of what is of interest. The orthogonal axes in the plane of the cross-section used to describe the cross-section are referred to as “the x, y axes”. The axis of interest in a particular analysis may be anywhere on the plane. To accommodate this a second set of orthogonal axes is used. The axis of interest is referred to as the “**reference axis**” and the axis at right angles to that axis as the “**other axis**“.

The x and y of the origin and the orientation angle of the references axis are input and edited on this first panel.

##### Switch – “Concrete displaced by bars”:

If this is on the computations take into account that part of the concrete is displace by the reinforcing. It is intended that this will normally be on. This can be set to off to obtain results for comparison with results from other computation facilities that do not account for the concrete displaced by the reinforcing.

##### Switch – “Restrained about other axis”:

This relates to the circumstances of the structural member. If this is on the member is restrained and the curvature about the other axis is zero. Otherwise the bending moment about the other axis is zero.

This can be important in computations involving trial and adjustment. Setting this to off adds a degree of freedom to the trial and adjustment process. Usually the expression “biaxial analysis” refers to an unrestrained case.

##### Maximum iterations

Maximum iterations: An integer number. Although this is on a specific load case it applies to all load-cases and all methods that use trail and adjustment. It is intended that this should normally not affect the computation. It is intended it should come into effect only when something is wrong. It is a limit on the total number of iterations as represented by the “It. Count” on the computation progress dialog. When this number is reached the computations stop and the buttons that change to another panel are enabled. ( next and back buttons on a phone or the ‘Next’ and ‘Load case home’ buttons on an iPad are enabled.)

There is a separate iteration count limit that applies only to the trial and adjustment on the curvature. This is in the inner most loop of the nested trial and adjustment routines used for two and three degrees of freedom. The count is reset to one each time that inner-most loop is invoked. The limit is set at 150 and cannot be changed by the user. Experience so far is that whenever this limit is reached something is wrong.

A suggested value for the overall maximum iterations is 2000. However this may not be appropriate in all situations.

##### Iteration wait

Iteration wait: An integer number. Although this is on a specific load case it applies to all load-cases and all methods that use trail and adjustment. However, it applies only when the “Show progress display” switch is On. The iteration wait controls the speed of the computation. It is approximately the wait between iterations in milli seconds. To slow down the progress increase this wait time. To speed up the progress decrease this wait time. However, if the wait time is too short the Stop, Step and Escape buttons will not work. In this regard the minimum wait time varies from device to device. The default value, 150 is intended to be above that minimum on most devices.

##### Method = :

Method = : A selection box; the alternative offered being the names of methods. Several different computation facilities are provided each of which is called a “method” and each method has a name.

Only one method can be current in a load case. However the current method can be changed at any time so that a combination of the methods can be used.

The various methods are:

**Ultimate bending moments.** The input is the axial load and the main output is the ultimate strength bending moment about the reference axis. In the result:

- At least one corner of a concrete component is at the ultimate compressive strain nominated for the material of that component.
- No corner of a concrete component is at a strain more compressive than its ultimate compressive strain.

**Yield bending moments.** The input is the axial load and the choice of a reinforcing bar of steel that yields. The main output is the bending moment about the reference axis when that bar starts to yield. In the result the chosen reinforcing bar is at the strain nominated as the yield strain in the material description.:

**Utility:-Curvatures and one strain.** The input is the curvature about the reference axis, the curvature about the other axis and the strain at the reference point. The output is the bending moment about the reference axis, the bending moment about the other axis and the axial load at the reference point.

**Utility:-Strain at three points.** The input is the choice of three locations on the cross-section and the strain at each of those locations. The output is the bending moment about the reference axis, the bending moment about the other axis and the axial load at the reference point.

**Given bending moment**. The input is the axial load at the reference point and the bending moment about the reference axis. The output is the curvature about the reference axis, the curvature about the other axis and the strain at the reference point. This has been implemented for the unrestrained case but not yet for the restrained case. Thus in the result the bending moment about the other axis is zero.

**Utility:-Curvatures and Axial load.** The input is the axial load at the reference point, the curvature about the reference axis and the curvature about the other axis. The output is the strain at the reference point, the bending moment about the reference axis and the bending moment about the other axis.

##### Buttons on this first panel

On this first panel of the load case edit facility are various buttons.

**Button – Next: **This changes to a panel specific to the selection method.

**Button – “Adopt this load case as at a stage”:** This is intended for use after the computations. It sets the stage distortion of all the components to the total distortion of this load case. It requires that the current result is valid but it makes all the results invalid. The use of this is explained further under Chronological Sequence.

**Button – “Write result to a text file”:** In response to this a description of the load case is written to a text file. Such text files are explained in the Android phone & iPhone – Files, TXT Files.

**Button – “Display result”** on an **iPad onl**y: This changes to the general result panel. If the result is not valid this is dimmed and not enabled.

**Button – “Close load case” **on an iPad and the Back button on a phone: This closes the load case changing the panel back to the entity list panel with the main tab buttons.

#### Methods that do not provide automatic trial and adjustment.

The “Utility:-Curvatures and one strain” and “Utility:-Strain at three points” methods simply invoke the explicit algorithm.

With these methods the **next** button on the **first panel** leads to a panel that has provision for the input variables, a “Compute loading” button and below that provision for the resulting three loading variables.

The **nex**t button on this panel leads to the general result panel described under **General Result Panel**.

##### Utility: Curvatures and axial strain method

Utility: Curvatures and axial strain: input is values for the three distortion variables and the output is the three loading variables.

**Button – “Set input to current case”** has a purpose when other methods are used in combination. The methods that provide automatic trial and adjustment have some of the loading variables in the input and some of the distortion variables are in the output. To accommodate this there are two sets of memory locations for the six variables; one set of six for the input and another set of six for the output. This button copies the three distortion variables from the output set to the input set.

##### Utility: Strain at three points method

Utility: Strain at three points: input is the location of three points and values for the strain at those three points.

It is required that the three points are not in a straight line. The application automatically checks for this and can give an error message. An example of three points that are not in a straight line are the two concrete corners on the top of a rectangular beam and the centre of a reinforcing bar near the bottom.

It is not necessary each point is a corner of the concrete or the centre of a bar. Nevertheless there is a facility for choosing a point if it is to be a corner of the concrete or the centre of a bar.

**Button – “Choose a point or corner”** A graphic edit panel that has a component selection box appears. Any point or corner can be selected.

When the back button on a phone or the “Choose” button on an iPad is tapped the graphic edit panel disappears and the X, Y and load case strain displayed appear on the main input panel.

If the strain at a particular point is to be related to the stress/strain relationship of the material then the “other” distortions and the “stage” distortion need to be taken into account. Examples to illustrate this requirement are:

- where the concrete is to be at the ultimate strain
- where a steel bar is to be at the first yield strain.

There are facilities for this computation. If the material is of kind “concrete” or of kind “steel that yields” then the recorded ultimate strain or yield strain can be used.

**Switch – “Use current strain values”**. When this is on the current strain values are used. Note it is the load case strain that will be used. This has a purpose when the result from another method is to be investigated further.

When this switch is off the stress-strain can be manipulated although it will be the corresponding load case strain that is used. If the material of the selected component is “concrete” or “steel that yields” a second switch appears; “Use specified strain”.

If the material is not “concrete” and not “steel that yields” or this second switch is off then the number for the stress- strain has a blue glow indicating it can be edited.

**Switch – “Use specified strain”**. When this switch is on the stress-strain is set to the ultimate strain or yield strain of the material and the corresponding load case strain is used.

When this switch is off the the number for the stress- strain has a blue glow indicating it can be edited.

**Note:** At this stage in the development the application does not record the details of this computation in the XSF file. Only the resulting location and load case strain at that location are recorded.

#### Methods that provide automatic trial and adjustment.

With methods that provide automatic trial and adjustment the next button on the first panel leads to a sequence of panels specific to the selected method. There is one or more panels that present the data input facilities, a panel that presents a computation progress dialog and the last, a panel that presents the computation result. A button on that result panel leads to the general result panel described under ‘General Result Panel’.

A button on the last data input panel starts the computations and changes the panel to the computation progress panel. On a phone this is the next button and on an iPad there is a ‘Compute’ button.

That last data input panel also has a **‘Show progress display**’ switch. When this is off the progress panel is blank and there is an automatic change to the result panel when the computations finish . Also the computation are faster; so fast that often it appears that the progress panel is not shown at all.

**Axial load** and a tolerance on that axial load is a required input for all these methods.

**Curvature deviation first estimate** and a curvature deviation increment is also required for the unrestrained case. A first estimate of zero usually works. Other values can reduce the computation time. An increment of five degrees is suggested.

**Subject Location:** Each method has a subject location. This is usually a corner of a shape component, or at a point in a point component although it may be anywhere on the cross section. The computation progress panel displays the subject location.

The ‘Ultimate bending moments’ method determines it automatically. The ‘Given bending moment’ method with the ‘Ignore first estimate’ switch on also determines it automatically.

In other circumstances it is determined by the user.

Several of the methods have input facilities for a strain value ‘at’ and an X and a Y value. That X, Y is a subject location. Where all this is under a heading ‘**First estimate**’ it is only the strain value that is variable in the automatic trial and adjustment: the subject location is constant.

There is further discussion of ‘subject location’ in the General volume.

**The other input requirements** for each method are:

##### Ultimate bending moments method

**Ultimate bending moments** method requires no other input.

##### Yield bending moments method

**Yield bending moments** method requires the load case strain at the yielding reinforcing and the location of that reinforcing. There is a facility to choose a bar.

When the back button on a phone or the “Choose” button on an iPad is tapped the graphic edit panel disappears and the X, Y and load case strain displayed appear on the main input panel.

The yield strain nominated in the material description is a stress-strain so the “other” strain and the “stage” strain need to be taken into account. This can be automatic.

**Switch – “Use specified strain”** If this is on the strain stipulated in the material description is used. If this switch is off the stress-strain has a blue glow indicating it can be edited.

In either case it is the corresponding load case strain that appears in the main input panel.

**Note:** At this stage in the development the application does not record the details of this computation in the XSF file. Only the resulting point location and load case strain at that point are recorded.

##### Given bending moment method

**Given bending moment** method requires a bending moment and a tolerance on that bending moment. The first estimate facilities include a strain at a subject location. Also there is a switch to ignore the first estimates and a button to automatically determine first estimates.

**Switch – “Ignore first estimates”:** When this switch is on the ultimate bending moment method is invoked at the start to determine a subject location and the strain at that location. Then, that strain is adjusted with the objective of the computed bending moment being of the stipulated value.

At a successful result the first estimates are automatically set to the values in the result. Those first estimates might be good for a subsequent computation with different but similar input information. Thus setting this switch off might save computation time.

**Button – “Set first estimates to current case”: **Another reason for setting the “Ignore first estimates” switch off is when the ultimate bending moment method will not work. Other methods can be used to determine starting values for the strain adjustments with the bending moment objective.

This button leads to facilities where any corner or point of any component can be chosen as the subject location and the strain at that corner or point is set as the first estimate. It is envisaged computations with another method were done before the method was changed to Given bending moment and this facility used.

##### Utility:- Curvatures and axial load method

**Utility:- Curvatures and axial load** requires a value for the curvature about the reference axis and the curvature about the other axis. This does not have facilities for a curvature deviation first estimate: curvature deviation is irrelevant. It does have facilities for a first estimate strain at a subject location and also an “Ignore first estimate” switch. When this is on the first estimate strain is zero.

##### The last input panel with all these methods

This last input panel has a switch

**Switch – “Show progress display”:** If this is on data indicating the computation progress will be displayed on the progress panel. The progress panel has buttons that control the progress. If this switch is off the progress panel will be blank, the computations will be faster and the trial and adjustment result panel will appear automatically.

If the “Show progress display” switch is on a second switch is visible:

**Switch – “Auto start computations”:** If this switch is off the Step or Go buttons on the progress panel will be required to start the computations.

On a phone the next button on the last input panel invokes the computations and on an iPad there is a ‘Compute’ button on the last input panel..

#### Nested one-dimensional routines

The application uses one-dimensional trial and adjustment routines nested one within another to achieve two and three dimensional trial and adjustment.

**Inner-most loop:** The Ultimate bending moment method, Yield bending moment method and Given bending moment methods do adjustments of the reference axis curvature magnitude with the objective of the axial load having a stipulated value. This is the inner most loop. It is an adaptation of a well established computation procedure described in most standards texts. Trial and adjustment on the depth of the neutral axis described in the texts is tantamount to adjustments of the curvature magnitude with the objective of the axial load having a particular value.

**Middle loop:** In the unrestrained case this inner most loop is within a routine that adjusts the curvature deviation angle with the objective of there being zero bending moment about the other axis.

**Outer-most loop:** For the Given Bending Moment method this middle loop is within a routine that adjusts the strain at the subject location with the objective of the bending moment having a stipulated value.

#### The computation progress panel

##### Process control

While a computation involving trial and adjustment is in progress a progress panel is visible and the next, back and ‘Load case home’ buttons are disabled.

If the “Show progress display” switch is On information indicating the progress is displayed and there are buttons labeled ‘Stop’, ‘Step’, ‘Go’ and ‘Escape’:

**Escape:** The escape button will cause the computations to be abandoned and the next, back and ‘Load case home’ buttons to be enabled.

**Stop:** The stop button will interrupt the computation so the various numbers displayed can be inspected.

**Step:** Step will cause one cycle of the computations.

**Go:** Go will cause the automatic trial and adjustment to resume.

If a solution is found, a problem is encountered or the Escape button is tapped: the computations stop, a note appears above these buttons indicating why, these buttons are disabled and on an phone the next and back buttons are enabled and on an iPad the ‘Next’ and ‘Load case home’ buttons are enabled.

The next button leads to a panel that displays the trial and adjustments result.

##### Progress display

The top four lines of the progress display identify a subject. The meaning of this depends on the method that invoked the display. Generally a particular location on the cross-section is identified that is the subject location.

Under that is the heading ‘It. Count=’ where the number of cycles of the computations is displayed.

Below that are three parts separated by spaces that correspond to the three degrees of freedom in the trial and adjustment. These are not all visible all the time: they don’t have meaning all the time.

The inner-most loop is represented by lines labeled “**Curvature=”** and **“Ax. load error=”**. These show a curvature value and the corresponding error in the computed axial load. Immediately above those lines there may be lines labeled “Cur. Dev.=” and “Subject strain=” that show the curvature deviation and the strain at the subject location used in the computation of that axial load error.

The middle loop is represented on lines labeled **“Cur. dev.=” **and “**Mom. Other Ax=”** that display a curvature deviation and an other axis bending moment result. These result from the last cycle of the inner-most loop in which the axial load error was within tolerance.

The outer-most loop is represented on two lines labeled **“Subject strain=’** and “**Mom. Error=**” that display a strain at the subject location and the resulting error in the reference axis bending moment. These result from the last cycle of the middle loop in which the other axis bending moment was within tolerance. (The other axis bending moment tolerance is one thousandth of the reference axis bending moment magnitude.)

#### Trial and adjustment result panel

The trial and adjustment result panel sets out the values for the six variable in terms of the reference axes and also possibly a comment on the trail and adjustment process. The distortion represents only the Load-case distortion.

Sometimes two set of values for the six variables are displayed. This can occur only when the automatic trial and adjustment process fails. It is envisaged that possibly one of these result sets is useful in that the loading variables are close to known values that are of interest.

A segmented control allows the user to choose between the two and the chosen result is displayed on the General result panel and result detail facilities.

On a phone the next button leads to the general result display. On an iPad there is a ‘Display result’ button.

#### General result panel

The general result panel is available for all the computation facilities whether or not trial and adjustment is involved.

##### The overall result

The first panel sets out the overall result in various forms.

In this the distortion values represent only the Load-case distortion.

The first two lines describe the reference axes and the next six lines display the six variable in terms of those reference axes.

This is followed by the bending moment expressed in polar co-ordinates. This is the bending moment with the axial load at the origin of the references axes although the orientation angle is in terms of the global X, Y axes.

Then, if there is an axial load the cartesian co-ordinates of the axial load in terms of the global X, Y axes.

At the bottom is an account for the axial force in the various kinds of materials. Here the expression “mild steel” means “steel that yields”.

On a phone the next button leads to panels that give details of each corner and each point. On an iPad there is a ‘Inspect result details’ button.

##### Result details at each corner and point

Each panel for the result details gives information pertaining to one object; corner or point. They are graphic edit panels with a component selection box as described in *Android phone, iPhone & iPad – Introduction*, G**raphical information, Graphic edit panels**.

Each panel sets out the X and Y values of the object location. Then, details of the strain at that location in the selected component. This includes:

- The Load case strain computed from the Load case distortion,
- The Stage strain computed from the Stage distortion of the component,
- The total strain which is the sum of the Load case strain and the Stage strain,
- The Other strain computed from the Other distortion of the component,
- The Stress-strain which is the total strain minus the Other strain.

Below this is a line displaying the stress computed from this Stress-strain and the Stress/Strain relationship of the material.

Note that if the Stress-strain is at a discontinuity in the Stress/Strain relationship of the material the stress displayed may be either side of that discontinuity; the choice being more-or-less random. This can occur when the rectangular stress block is used in an ultimate strength computation. At least one corner of the concrete has a strain that coincides with the discontinuity at the side of the stress block. Thus the stress displayed might be zero rather than the maximum stress. In the model the stress very close to such a corner is the maximum stress. Such a displayed zero stress does not indicate an error in the overall computation.

#### Load case graphics on an iPad

On an iPad the background to the various load case data panels is an image of the cross-section.

As with the graphics on a phone the reference point is indicated by a little blue circle and the reference axis is also shown in blue.

Also as with a phone there is a little red circle that acts as a cursor indicating a corner or point that is the subject.

With the load case facilities on an iPad there are also circles of a dark cyan color that indicate what is of interest. These circles are slightly larger than the red cursor circle.

Two concentric circles indicate the subject of a yield computation.

Two concentric circles also indicate the point with the focus in the three point method, while the other two points are indicated by single circles.

With a computation result three concentric circles indicate the location of the axial load (if there is an axial load). If this is outside the area that displays the cross-section the scale of the image is reduced so that it is accommodated. The axial load can possibly be some distance from the cross section so that the reduction is scale affects the readability of the cross section image. There is a button to hide the axial load location that overcomes this problem.

#### A note on steel that has a strain limit

It has been common to assume that reinforcing steel sustains a load regardless of how large the strain. Many standard codes of practice included this assumption. Examples are ACI318:14 clause 20.2.2.1 and Eurocode 2: (BS EN 1992-1-1:2004) clause 3.2.7 (2) b).

A steel stress/strain relationship that has a strain limit and stipulates that beyond that limit there is no stress reflects reality. However, this can cause a problem with the **Ultimate Bending Moment** method particularly if that breaking strain limits the strength of the cross-section. Eurocode 2: (BS EN 1992-1-1:2004) clause 3.2.7 (2) a) describes such as stress/strain relationship.

The existence of such a strain limit should be apparent on the graphic image of a material. Zero stress at the strain extremity of the graph indicates such a limit.

In such cases the **Yield bending moments** “method” might help.

Use the Yield bending moments “method” and increased the strain in the critical bar from the yield strain to a strain slightly less than the strain limit. This can be done on the “choose a bar” panel. Set the “Use specified yield strain” switch to off then change the stress-strain.

The result would be the bending moment at a tension failure. This result could be used as the first estimate for the **Given bending moment **method. Change the selected method to Given bending moment and then tap the “Set first estimate to current case” button and select that critical bar. Also set the “Ignore first estimates” switch to off.