ASME BPVC.VIII.2

PASS/NOZZLE-FEM 3.5. Program Manual

5.8.2. ASME BPVC.VIII.2-2021

The maximum distortion energy yield criterion shall be used to establish the equivalent stress. In this case, the equivalent stress is equal to the von Mises equivalent stress given by eq. (5.1) [4]:

$$ \displaystyle\sigma_e = \frac{\displaystyle 1}{\displaystyle \sqrt{2}} \sqrt{(\sigma_1-\sigma_2)^2+(\sigma_1-\sigma_3)^2+(\sigma_2-\sigma_3)^2}, $$

where σ₁, σ₂, σ₃ - the principal stress at the considered point.

5.8.2.1. Allowable membrane stress

The allowable stress is used for assessment general membrane stresses $P_m$ [fig. 5.1, 4]. It is defined by tables 5A and 5B as per [1]. Table 5A provides allowable stresses for ferrous materials for Section VIII, Division 2 construction. Table 5B provides allowable stresses for nonferrous materials for Section VIII, Division 2 construction. When tables 5A and 5B are provided value of allowable stress the program applies it:

$$ S = S_{tab}. $$

If user materials are not provided by tables 5A and 5B as per [1] then allowable membrane stress is assumed according to table 10-100 of Mandatory Appendix 10 [1] that shown in table 5.10 below.

Table 5.10. Criteria for Establishing Allowable Stress Values for Tables 5A and 5B
Product/Material	Below Room Temperature		Room Temperature and Above
Product/Material	Tensile Strength	Yield Strength	Tensile Strength	Yield Strength	Stress Rupture	Creep Rate
All wrought or cast ferrous and nonferrous product forms except bolting, and except for austenitic stainless steel, nickel alloy, copper alloy, and cobalt alloy product forms having an S_y/S_T ratio less than 0.625	$\frac{\displaystyle S_T}{\displaystyle 2.4}$	$\frac{\displaystyle S_y}{\displaystyle 1.5}$	$\frac{\displaystyle S_T}{\displaystyle 2.4}$	$\frac{\displaystyle R_y S_y}{\displaystyle 1.5}$	$\min\left(F_{avg}S_{R avg}, 0.8S_{R min}\right)$	$1.0 S_{C avg}$
All wrought or cast austenitic stainless steel, nickel alloy, copper alloy, and cobalt alloy product forms except bolting, having an S_y/S_T ratio less than 0.625	$\frac{\displaystyle S_T}{\displaystyle 2.4}$	$\frac{\displaystyle S_y}{\displaystyle 1.5}$	$\frac{\displaystyle S_T}{\displaystyle 2.4}$	$\min\left(\frac{\displaystyle S_y}{\displaystyle 1.5}, \frac{\displaystyle 0.9 R_y S_y}{\displaystyle 1.0}\right)$	$\min\left(F_{avg}S_{R avg}, 0.8S_{R min}\right)$	$1.0 S_{C avg}$

Nomenclature for this table 5.10 is as follows:

F_avg	=	multiplier applied to average stress for rupture in 100 000 h. At 815°C and below, F_avg=0.67. Above 815°C, it is determined from the slope of the log time-to-rupture versus log stress plot at 100 000 h such that log [F_avg]=1/n, but F_avg may not exceed 0.67.
n	=	a negative number equal to Δlog time-to-rupture divided by Δlog stress at 100 000 h
R_y	=	ratio of the average temperature dependent trend curve value of yield strength to the room temperature yield strength.
S_C avg	=	average stress to produce a creep rate of 0.01%/1 000 h.
S_R avg	=	average stress to cause rupture at the end of 100 000 h.
S_R min	=	minimum stress to cause rupture at the end of 100 000 h.
S_T	=	specified minimum tensile strength at room temperature.
S_y	=	specified minimum yield strength at room temperature.

5.8.2.2. Allowable local primary membrane plus bending stress

The allowable stress S_PL is used for assessment local primary stresses ($P_L$ or $P_L+P_b$). See fig. 5.1 [4]. This limit value is calculated as follows:

$$ S_{PL} = \left\{ \begin{array}{ll} 1.5S, & S_y/S_T \gt 0.7\quad or\quad T \ge T_{creep}, \\ \max\left(1.5S, S_y\right), & otherwise, \end{array} \right. $$

where T_creep - temperature above which, it is necessary to take into account time-dependent properties (creep etc).

5.8.2.3. Allowable secondary stress

The allowable stress S_PS is used for assessment secondary stresses ($P_L+P_b+Q$). See fig. 5.1 [4]. This limit value is calculated as follows:

$$ S_{PS} = \left\{ \begin{array}{ll} 1.5\left[S(T_{min})+S(T_{max})\right], & S_y/S_T \gt 0.7\quad or\quad T \ge T_{creep}, \\ \max\left\{1.5\left[S(T_{min})+S(T_{max})\right], S_y(T_{min})+S_y(T_{max})\right\}, & otherwise, \end{array} \right. $$

where T_min - lowest temperature during the cycle, T_max - upper temperature during the cycle.

5.8.2.4. Allowable peak stress

The allowable peak stress S_a is assumed as per p. 5.5.3 [4] and based on fatigue curves as per Annex 3-F [4].

5.8.2.5. Allowable stress for testing conditions

The general membrane stress $P_m$ is assess as follows [p. 4.1.6.2, 4]:

$$ P_m \le \beta_{T} S_y. $$

The primary membrane stress plus bending stress $P_m+P_b$ is assess as follows [p. 4.1.6.2, 4]:

$$ P_m+P_b \le \left\{ \begin{array}{ll} \gamma_{min}S_y, & P_m \le S_y/1.5, \\ \left(\displaystyle\frac{1-\gamma_{min}}{\beta_T-1/1.5}\right)P_m- \left(\displaystyle\frac{1-\gamma_{min}}{\beta_T-1/1.5}\beta_T-1\right)S_y, & S_y/1.5 \lt P_m \le \beta_T S_y, \end{array} \right. $$

where $\beta_{T}$, $\gamma_{min}$ - test factors given in table 4.1.3 [4].

5.8.2.6. Assessments for design and operating loads

The PASS/NOZZLE-FEM performs stress analysis of all loadcases based on user loadcases. The table 5.11 summarizes the assessments that based on table 5.3 [4]. The occasinal load must be included in both the design and operating load combinations with specified factors according to table 5.3 [4].

Table 5.11. Assessment criteria
Loadcase	Assessment	Description
$WGT$	N/A	Only weight (dead) loads. For design and operating loads. It is only used to calculate range stress.
$T$	N/A	For operating loads. It is only used to calculate thermal stress for allowable loads.
$P+P_s$	$P_m \le S$	Only pressure and hydrostatic pressure. For design loads. It is only used to assess general membrane stressess. In nozzle junction is not considered in the case.
$P+P_s$	$P_L \le S_{PL}$	It is only used to assess local membrane stressess.
$P_d+P_s+WGT$	$P_L+P_b \le S_{PL}$	Pressure plus dead loads. For design and operating loads. It is only used to assess local primary stressess.
$P_d+P_s+WGT$	$\sigma_1+\sigma_2+\sigma_3 \le 4S$	For design loads. If suitable flag is enbaled then this checking is performed and for operating loads. It provides protection against local failure based on the results of an elastic analysis.
$P+P_s+DSG$	$P_L+P_b \le S_{PL}$	Design pressure plus design loads. It provides protection against plastic collapse.
$P+P_s+DSG$	$P_L+P_b+Q \le S_{PS}$	If suitable flag is enbaled then this checking is performed and for design loads.
$P+P_s+OPE$, $P+P_s+OPE+T$	$P_L+P_b+Q \le S_{PS}$	Operating pressure plus operating loads plus thermal strains. It provides protection against ratcheting.
$P+P_s+OPE-WGT$, $P+P_s+OPE-WGT+T$	$P_L+P_b+Q+F \le 2S_{a}(N)$, $N \le [N](S_{alt})$	Loadcase of stress range from operating pressure plus operating loads plus thermal strains. It provides fatigue assessment based on Smooth Bar Fatigue Curve and user defined fatigue strength reduction factor $K_f$. The assesment is provided by section 5.5.3 [4].
$P+P_s+OPE-WGT$, $P+P_s+OPE-WGT+T$	$\Delta S_{ess} \le [\Delta S]$, $N \le [N](\Delta S_{ess})$	It provides fatigue assessment based on Welded Joint Fatigue Curve and based on evaluating of equivalent structural stress range. This method is recommended for evaluation of welded joints that have not been machined to a smooth profile. The assesment is provided by section 5.5.5 [4].

PASS/NOZZLE-FEM 3.5. Program Manual