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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Normal stress in x-direction, σx
Normal stress in y-direction, σy
Shear stress in xy-plane, τxy

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OUTPUT   VARIABLES   &   GRAPHS

VARIABLES	Values
♦ Max normal stress, σ1		Graphs:  2D Mohr's circle
♦ Min normal stress, σ2
♦ Max shear stress, τmax
♦ Angle of rotation, θ  °

Principal Stresses And The Mohr's Circle

Consider a plane stress problem, with three known stress components: normal stresses σ_x and σ_y, and shear stress τ_xy. The resultant maximum normal stress called the principal stress σ₁, and minimum stress (principal stress σ₂) are given by the equations below. The principal axes are the 2 mutually perpendicular axes where the state of stress in each surface normal to the axes contains a tensile or compressive stress and zero shear stress. Also given below is the equation for the special angle for the rotated element on which these principal stresses act.

where
     σ_x = normal stress in x direction
     σ_y = normal stress in y direction
     τ_xy = shear stress in xy-plane
     σ₁ = maximum principal stress
     σ₂ = minimum principal stress
     θ = angle of rotation to the principal stress axes
     τ_max = maximum shear stress

All stress values are given here in the same units.

The Mohr's circle is a graphical representation of the analytical equations above. From it, the characteristics and extremas of the stresses on the element can be determined. In the implementation here, the shear stress is positive upwards, and rotation is clockwise positive.

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.
• Mohr's Circle for 2-D & 3-D stress analysis, www.engapplets.vt.edu/Mohr/java/nsfapplets/MohrCircles2-3D/Applets/applet.htm; Virginia Tech Department of Aerospace and Ocean Engineering, Blacksburg VA, USA.