Yield Stress Criterion - CAESAR II - Help

CAESAR II Users Guide (2019 Service Pack 1)

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CAESAR II
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CAESAR II Version
11.0 (2019)

Specifies the method the software uses to calculate maximum stress. Select VonMises or Max3DShear.

CAESAR II calculates the maximum stress (which is not a code stress) according to either the von Mises Theory or the Maximum Shear Theory.

Code stress refers to a stress calculated by an equation provided by the code. For more information on code-defined stresses, see the CAESAR II Quick Reference Guide.

The Stresses Extended output report produced by CAESAR II contains a value representative of the maximum stress state through the cross section, calculated according to the indicated yield criteria theory.

Configuration Setting

Failure Theory

Calculated Stress

Max3D Shear

Maximum Shear Stress

Maximum Stress Intensity

von Mises

Maximum Energy of Distortion

Octahedral Shearing Stress

The software computes the selected stress at four points along the axis normal to the plane of bending (outside top, inside top, inside bottom, outside bottom), and includes the maximum value in the stresses report. The equations used for each of these yield criteria are listed below. If von Mises Theory is used, the software computes the octahedral shearing stress, which differs from the von Mises stress by a constant factor.

For codes B31.4, B31.4 Chapter IX, B31.4 Chapter XI, B31.8, B31.8 Chapter VIII, and DNV, this setting controls which equation the software uses to compute the equivalent stress. For these codes, the software uses the equations shown in the piping code to determine the yield stress criterion in the Stresses Extended output report.

Stress Formulation

CAESAR II reports the largest stress using four calculation points through the pipe cross section, as show in the following figure.

Yield Stress Criterion -

The four points are established by a line perpendicular to the bending moment acting on the pipe (shown in red). Points 1 and 4 are on the outside surface of the pipe, where radial stress is zero. Point 1 is in bending tension and Point 4 is in bending compression. Points 2 and 3 are on the inside surface of the pipe where radial stress is compressive (negative) pressure.

Longitudinal stress (Sl), hoop stress (Sh), radial stress (Sr) and shear stress (St) are calculated at each position using the appropriate formulas.


Position


Longitudinal Stress (Sl)


Hoop Stress (Sh)

Shear
Stress (St)

Radial
Stress (Sr)

1

2

3

4

The table formulas assume that this is a B31.3-style stress equation with Lamé hoop stress.

These stresses are translated into the principal stresses S1, S2, and S3. The following shows a graphical representation of a typical calculation of the four position points.

Yield Stress - Calculation Point 1 Yield Stress - Calclulation Point 2

Yield Stress - Calculation Point 3Yield Stress - Calculation Point 4

Determine the principal stress using the longitudinal stress (Sl), the hoop stress (Sh), and the shear stress (St)—which sets the red line. The principal stress refers to the points where the red circle crosses the normal stress axis (shear stress equals zero). Place the radial stress (Sr) (which has a shear stress of zero) on the same axis. The largest intersection point is S1 and the smallest is S3.

Equivalent Stress, Octahedral Shearing Stress, von Mises Stress:

Yield Stress - Principal Stress Equation

Use the S1, S2, and S3 values in the equation above to determine the octahedral shearing stress at each position. CAESAR II reports the largest of these four values.

3D Maximum Shear Stress Intensity (S.I.):

S.I. = S1-S3

When you configure the software to report 3D maximum shear stress intensity, it reports the largest intensity (S1-S3).