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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Principal stress, σ1
Principal stress, σ2
Yield strength, Sy

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OUTPUT   VARIABLES   &   GRAPHS

FACTOR-OF-SAFETY	n
♦ Maximum-normal-stress theory		Graphs:  Static design diagram
♦ Maximum-shear-stress theory
♦ Distortion-energy theory

Safety Factors In Static Design

A ductile material is one which exhibit a true strain ( > 5%) at fracture, and the yield point in tension and in compression are practically the same. Consider a material subjected to known biaxial principal stresses and it is required to estimate the Safety factors. There are 3 static design theories for determining the applicable safety factors: the maximum-normal-stress theory, the maximum-shear-stress theory and the distortion-energy theory. The relevant equations are given below:

where
     n = factor of safety
     σ₁ = maximum principal stress
     σ₂ = minimum principal stress
     S_y = yield strength of material

All stress and yield values are given here in the same units.

The Static design diagram is a graphical representation of the failure locus for the stress state, essentially demarcating the regions where the each design theory apply.

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point
    ◊ If the required Java plug-in not installed on your computer, an auto-download of this plug-in will be initiated before the plot is displayed.

BIBLIOGRAPHY

• Brown TH; Marks' Calculations for Machine Design; McGraw Hill, New York, 2005, Chapter 5.
• Young WC & Budynas RG; Roark's Formulas for Stress and Strain; 7th Edition, McGraw Hill, New York, 2002.