General
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Load Cases
At a glance: Descriptions of load cases processes and definitions of load cases terms here are applicable to all versions of the application. For specific instructions on the use see the volumes specific to the Mac, PC or Android phone, iPhone & iPad versions
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 points of interest might be the ultimate strength, or the distortion under a known loading
The explicit algorithm
All the various methods use the same explicit algorithm. This works with six variables;
three representing the loading; being:
- The axial load at the origin of the reference axes.
- The bending moment about the reference axis
- The bending moment about the other axis
and three representing the distortion; being:
- The axial strain at the origin of the reference axes.
- The curvature about the reference axis
- The curvature about the other axis.
This explicit algorithm takes as input the three distortion variables and outputs the three loading variables. For a description of this algorithm see Thompson, P. J. Discussion of “Ultimate Strength Domain of Reinforced Concrete Sections under Biaxial Bending and Axial Load”, ACI Structural Journal, Nov-Dec 2013 pp 1109-1112.
Only Load Case distortions displayed
The distortion variables that appear on the Load Case edit facilities represent only the “load case” distortions. The “stage” distortion and “other” distortions of each component are automatically taken into account so that the explicit algorithm works with the Stress Distortions.
In contrast the loading values output by the explicit algorithm and as displayed represent the total loading on the cross-section.
Note that the load case distortion obeys plane-sections-remain-plane over the whole cross-section.
The need for intervention in the automatic process
Generally the explicit algorithm will always work and generally the output is correct in that in accordance with the cross-section and material descriptions and the model they represent the output loading would cause the input distortion. An exception to this is the limiting strain problem. (See limiting strain problem.)
However, there is no automatic trial and adjustment procedure to assess the affect of a given loading that is guaranteed to work in every case. The methods provided should work in most usual cases and facilities are provided to make the procedures useful even when they do not work perfectly.
The Ultimate Bending Moment method 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 the trial and adjustment on the curvature about the reference axis.
Curvature deviation
The facilities that cope with the unrestrained case have a further degree of freedom in the trail and adjustment being the orientation of the curvature: the neutral axis is not always parallel with the reference axis. Expressed in rectangular co-ordinates in terms of the reference axes the curvature about the “other” axis is not always zero.
The trial and adjustment that deals with this works with the variables expressed in polar co-ordinates. The six variables in polar co-ordinates are:
three representing the loading; being:
- The axial load at the origin of the reference axes.
- The magnitude of the bending moment
- The orientation of the bending moment expressed as the angle from the reference axis.
and three representing the distortion; being:
- The axial strain at the origin of the reference axes.
- The magnitude of the curvature
- The orientation of the curvature expressed as the angle from the reference axis.
These distortion variables represent the “load case” distortions as distinct from the “stage” distortion and “other” distortions of each component.
A variable called “curvature deviation” is defined as the angle between the orientation of the bending moment and the orientation of the curvature.
Curvature deviation is made the subject of trial and adjustment. Generally it is between minus 90 degrees and plus 90 degrees and usually zero is a satisfactory first estimate.
In the unrestrained case the orientation of the objective bending moment is aligned with the reference axis so that the final value of the deviation angle is the orientation of the curvature relative to the reference axis. The curvature deviation angle is seen as a distortion variable.
This trial and adjustment process is not suitable where the bending moment is small. It has proved satisfactory for ultimate strength, first yield strength and most service load situations where there is a bending moment. Where the bending moment is very small the method “Utility: curvatures and axial load” is suggested with manual trial and adjustment on the curvatures.
Limiting strain problem
A computation problem occurs in the explicit algorithm rather than the trial and adjustment process. It can occur where there is a discontinuity in the stress-strain relationship of the concrete. There are such discontinuities with the rectangular stress block at the strains corresponding to the sides of the block.
It occurs when the stress distortion of a shape component has no curvature and the strain corresponds to a discontinuity in the stress-strain relationship.
The application includes an automatic check for this condition. If it occurs during automatic trail and adjustment automatically the result of the particular cycle is ignored, a distortion variable is changed slightly and the automatic trial and adjustment is continued. This usually works and the final result is not affected.
If, however, the computation is for a final output result no result is displayed and the error message “Limiting strain problem” is displayed.
In this situation it is suggested the user make a small, possibly trivial change in the objective variables and repeat the computations.