Applies To
Product(s):	AutoPIPE
Version(s):	ALL;
Area:	Calculations
Date Logged & Current Version	April. 2014 09.06.00.15

Problem:

Original issue description: strength check on a pipe (ex. 18 inch) riser under operating condition using AutoPIPE.

Results show that the Maximum Utilization Ratio for a single load case – bursting (ex. P5) was some value (ex. 0.62). However the Maximum Utilization Ratio for combined load case (Gravity +Temperature +Pressure) was a much smaller value (ex. 0.03).

Why is the max combined UR value less than the max UR of a single load case?

Solution:

The interaction ratio or the utilization ratio can be loosely described as sum of squares of the ratio of applied stress to allowable plastic limits. As these stress ratios are lower than 1, squaring them would give you an even smaller number.

Example:

Following are the detailed calculations for the GRTP5_U{1} combination at point A03 (English Units) from an example model:

General

D outer wall diameter = 18.00 in

t wall thickness = 0.9842 in

fy Characteristic material strength = 55416.02 psi

fu Characteristic ultimate strength = 69896.59 psi

f_cb = Min[f_y ; f_u/1.15]

= Min[55416.02 ; 60779.64]

= 55,416.02

Moment Term

γ_m (Gamma m) = 1.15

γ_SC (Gamma SC) = 1.26

M_Sd (Design moment) = 131549.9 lb/in

α_c = 1.12

M_p(t2) = f_y x (D-t)² x t

= 55416.02 x (18.00-0.9842)² x 0.9842

= 15,792,236

Mterm (Moment term) = γ_m x γ_SC x [M_Sd / (α_c x M_p(t2))]

= 1.15 x 1.26 x [131549.9 / (1.12 x 15,792,236)]

= 0.0107

Axial Force Term

S_Sd (Design effective axial force) = 13930.13 lb

S_p(t2) = f_y x π x (D-t) x t

= 55416.02 x 3.14 x (18.00-0.9842) x 0.9842

= 2,915,698

Fterm (Force term) = γ_m x γ_SC x [S_Sd / (α_c x S_p(t2))]

= 1.15 x 1.26 x [13930.13 / (1.12 x 2,915,698)]

= 0.00467

Pressure Term

α_p = 1-β

= 1 – 0.4635

= 0.5365

p_i = 2538.16 psi

p_e = 0.0 psi

p_b(t2) = [2 x t / (D – t)] x f_cb x (2/3^0.5)

= [2 x 0.9842 / (18.00 – 0.9842)] x 55,416.02 x 1.155

= 7,404.2

Pterm (Pressure term) = α_p x [(p_i – p_e) / (α_c x p_b(t2))]

= 0.5365 x [(2,538.16 – 0.0) / (1.12 x 7,404.2)]

= 0.1642

Interaction ratio = [Mterm + Fterm²]² + Pterm²

= [0.0107 + 0.00467²]² + 0.1642²

= 0.02707 (Result displayed by AutoPIPE)