Results Interpretation: Max and Min Beam Stresses in Envelopes
Description
The The LISTINGS Tab provides a table of Max and Min beam stress results. Each Max or Min value is a single result over the cross section, not a distribution. For non-envelope cases, Min Fibre Stress (for example) is simply the most-negative value of fibre stress that occurs over the cross section; similarly Max Fibre Stress (for example) is simply the most-positive value of fibre stress that occurs over the same cross section.
For envelope cases, each quantity in the columns list is firstly enveloped according to the Envelope Type (Minimum, Maximum, Absolute and Magnitude, see CASES: Envelope Cases) for every sampling point on the cross section, and then the Max or Min values are reported as the maximum or minimum values of the envelope over that cross section. Therefore, the listed stress values are not always of practical significance: for example, extracting Min Fibre Stress for a Max Envelope type. Note that for result quantities that are considered to be unsigned, such as shear stress, von Mises stress, yield area ratio, etc., the magnitudes are used when applying the enveloping type.
As an example, the following describes how Min Fibre Stress and Max Fibre Stress results are produced by each of the four envelope types. The logic also applies to other Max and Min beam stress types.
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MIN Envelope
The minimum fibre stress for all included result cases is calculated at each sampling point on the cross section. This produces a list of one minimum fibre stress value for each sampling point (i.e., the minimum from the included result cases). The minimum of these sampling point values is reported as Min Fibre Stress while the maximum is reported as Max Fibre Stress. For this type of envelope, Min Fibre Stress is of practical significance as it is the minimum value over the cross section for all the included result cases. Max Fibre Stress is not of practical significance as it is simply the maximum of the minimum enveloped values over the cross section.
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MAX Envelope
The maximum fibre stress for all included result cases is calculated at each sampling point on the cross section. This produces a list of one maximum fibre stress value for each sampling point (i.e., the maximum from the included result cases). The maximum of these sampling values is reported as Max Fibre Stress while the minimum is reported as Min Fibre Stress. For this type of envelope, Max Fibre Stress is of practical significance as it is the maximum value over the cross section for all the included result cases. Min Fibre Stress is not of practical significance as it is simply the minimum of the maximum enveloped values over the cross section.
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ABS Envelope
The fibre stress with the largest magnitude for all included result cases is calculated at each sampling point on the cross section. This produces a list of one magnitude fibre stress value for each sampling point (i.e., the maximum magnitude from the included result cases). The largest of these absolute values is reported as Max Fibre Stress while the smallest is reported as Min Fibre Stress. For this type of envelope, Max Fibre Stress is of practical significance as it is the value with the largest magnitude over the cross section for all the included result cases. Min Fibre Stress is not of practical significance as it is simply the smallest magnitude of the maximum enveloped magnitudes over the cross section.
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MAG Envelope
This is identical to the ABS Envelope except that the reported value is signed. The sign comes from the result case that produces the enveloped value.
Based on the above description, the terms Max and Min beam stresses as used in the LISTINGS refer to the already enveloped values over the cross section, and not to the enveloping over the included result cases.
A few specific values:
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The most positive fibre stress result will turn up as the Max Fibre result in the MAX Envelope.
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The most negative fibre stress result will turn up as the Min Fibre result in the MIN Envelope.
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If the most positive result has a magnitude greater than the magnitude of the most negative result, the most positive result will turn up as the Max Fibre result in the ABS Envelope.
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If the most negative result has a magnitude greater than the magnitude of the most positive result, the magnitude of the most negative result will turn up as the Max Fibre result in the ABS Envelope.
The following table summarises what Min and Max mean for the various envelope and stress types. The grey text cells identify results that are generally not meaningful when extracted from the respective envelope.
|
Stress Type |
MIN Envelope - produces a signed result |
MAX Envelope - produces a signed result |
ABS Envelope - produces an unsigned result |
MAG Envelope - produces a signed result |
|
|
1 |
Min Axial Stress |
Minimum signed axial stress | Minimum of the maximum signed axial stress values | Minimum of the maximum absolute axial stress values | Same as ABS Envelope but signed |
|
2 |
Max Axial Stress |
Maximum of the minimum signed axial stress values | Maximum signed axial stress | Maximum absolute axial stress | Same as ABS Envelope but signed |
|
3 |
Min Bending Stress Plane 1 |
Minimum signed bending stress | Minimum of the maximum signed bending stress values | Minimum of the maximum absolute bending stress values | Minimum of the largest signed bending stress magnitudes |
|
4 |
Max Bending Stress Plane 1 |
Maximum of the minimum signed bending stress values | Maximum signed bending stress | Maximum absolute bending stress | Maximum of the largest signed bending stress magnitudes |
|
5 |
Min Bending Stress Plane 2 |
Minimum signed bending stress | Minimum of the maximum signed bending stress values | Minimum of the maximum absolute bending stress values | Minimum of the largest signed bending stress magnitudes |
|
6 |
Max Bending Stress Plane 2 |
Maximum of the minimum signed bending stress values | Maximum signed bending stress | Maximum absolute bending stress | Maximum of the largest signed bending stress magnitudes |
|
7 |
Min Fibre Stress |
Minimum signed fibre stress | Minimum of the maximum signed fibre stress values | Minimum of the maximum absolute fibre stress values | Minimum of the largest signed fibre stress magnitudes |
|
8 |
Max Fibre Stress |
Maximum of the minimum signed fibre stress values | Maximum signed fibre stress | Maximum absolute fibre stress | Maximum of the largest signed fibre stress magnitudes |
|
9 |
Max Shear Stress due to Shear Force 1 |
Minimum signed shear stress values | Maximum signed shear stress values | Maximum absolute shear stress values | Same as ABS Envelope but signed |
|
10 |
Max Shear Stress due to Shear Force 2 |
Minimum signed shear stress values | Maximum signed shear stress values | Maximum absolute shear stress values | Same as ABS Envelope but signed |
|
11 |
Max Shear Stress due to Torque |
Minimum signed shear stress values | Maximum signed shear stress values | Maximum absolute shear stress values | Same as ABS Envelope but signed |
|
12 |
Max Shear Stress Plane 1 |
Minimum signed shear stress values | Maximum signed shear stress values | Maximum absolute shear stress values | Same as ABS Envelope but signed |
|
13 |
Max Shear Stress Plane 2 |
Minimum signed shear stress values | Maximum signed shear stress values | Maximum absolute shear stress values | Same as ABS Envelope but signed |
|
14 |
Max Shear Stress Plane 1-2 |
Minimum signed shear stress values | Maximum signed shear stress values | Maximum absolute shear stress values | Same as ABS Envelope but signed |
|
15 |
Mean Shear Stress due to Shear Force 1 |
Minimum signed mean shear stress values | Maximum signed mean shear values | Maximum absolute mean shear values | Same as ABS Envelope but signed |
|
16 |
Mean Shear Stress due to Shear Force 2 |
Minimum signed mean shear stress values | Maximum signed mean shear values | Maximum absolute mean shear values | Same as ABS Envelope but signed |
|
17 |
Min Principal Stress |
Minimum signed principal stress | Maximum of the minimum signed principal stress values | Maximum absolute minimum principal stress | Same as ABS Envelope but signed |
|
18 |
Max Principal Stress |
Minimum of the maximum signed principal stress values | Maximum signed principal stress | Maximum absolute maximum principal stress | Same as ABS Envelope but signed |
|
19 |
Min Pipe Hoop Stress |
Minimum signed hoop stress | Minimum of the maximum signed hoop stress values | Minimum of the maximum absolute hoop stress values | Same as ABS Envelope but signed |
|
20 |
Max Pipe Hoop Stress |
Maximum of the minimum signed hoop stress values | Maximum signed hoop stress | Maximum absolute hoop stress | Same as ABS Envelope but signed |
|
21 |
Max von Mises Stress |
Minimum of the maximum von Mises stress values | Maximum von Mises stress | Maximum von Mises stress | Same as ABS Envelope but signed |
|
22 |
Max Tresca Stress |
Minimum of the maximum Tresca stress values | Maximum Tresca stress | Maximum Tresca stress | Same as ABS Envelope but signed |
|
23 |
Yield Area Ratio |
Minimum of the maximum yield area ratios | Maximum yield area ratio | Maximum yield area ratio | Same as ABS Envelope but signed |
See Also