VM132

VM132
Stress Relaxation of a Tightened Bolt Due to Creep

Overview

Reference:	S. Timoshenko, Strength of Material, Part II, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg. 531, article 93.
Analysis Type(s):	Static Analysis (ANTYPE = 0) (with creep properties and initial strain)
Element Type(s):	3D Spar (or Truss) Elements ( LINK180)
Input Listing:	vm132.dat

Test Case

A bolt of length and cross-sectional area A is tightened to an initial stress σ_o. The bolt is held for a long period of time t₁ at an elevated temperature T_o. The bolt material has a creep strain rate given by dε/dt = kσⁿ. Determine the stress σ in the bolt at various times during creep relaxation.

Figure 185: Tightened Bolt Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

n = 7

k = 4.8 x 10^-30/hr

= 10 in

A = 1 in²

σ_o = 1000 psi

T_o = 900°F

t₁ = 1000 hr

Analysis Assumptions and Modeling Notes

An integration time step of 10 hours over the 1000 hour time range (that is, 100 iterations) is used. The initial strain is calculated by σ_o/E = (1000 psi)/(30 x 10⁶ psi) = 1/30000.

Results Comparison

	Target	Mechanical APDL (1)	Ratio
Stress, psi @ t = 190 hr	975.	975.	1.00
Stress, psi @ t = 420 hr	950.	950.	1.00
Stress, psi @ t = 690 hr	925.	925.	1.00
Stress, psi @ t = 880 hr	910.	910.	1.00
Stress, psi @ t = 950 hr	905.	905.	1.00

Stress (σ) corresponds to the quantity SIG in POST26 listing.