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This graphical representation of the 2-D stress transformation equations provides a quick, accurate and visual protrayal of the 2-D state of stress. The definition of the three circle diagram is sketched below. Draw the circle and determine two of the principal stresses. Then plot the first coordinate pair sx, txy at point A.

This enlarges the outermost circle which means that the overall state of stress has increased. This convention is useful for determining isostatiacs proper orientation of principal stresses and other components relative to the x,y coordinates.

It finds the principal stresses and a maximum shear stress although this maximum shear stress may be quite misleading in 3-D stress. The same is true in 3-D stress. In this case, there is no effect on the overall stress state. Look at the modified examples below.

These two points form the diameter of the circle with its center at point C. This shows all potential non-zero 2-D stress components.


First sketch the normal stress axis along the horizontal and the shear stress axis along the vertical. Note that the principal stress values are always ordered by convention so the s1 is the largest value in the tensile direction libri s3 is the largest value in the compressive direction.

Be forewarned the principal stresses and this peak shear stress are isostaticaz to play a strong role in determining the factor of safety in mechanical design. Principios basicos de farmacologia Principios isostaticaz de farmacologia.

The triangle C, sx, and txy form a 30, 40, 50 triangle, so the circle radius is In example 1, the second principal stress, s2, becomes zero and the third principal stress, s3, is negative, but the overall range is the same. Carrying this attitude through the mechanical design process is a recipe for failure.

What about the two 2-D examples? Since there are no non-zero z component shear stresses, sz is the third principal stress with a value of —25 C.

This tutorial is designed to introduce and place strong emphasis on the role of 3-D stress in the process of. Plot the next coordinate pair sy, tyx at B. How do they become 3-D representations?

Sketch the normal stress, s, and shear stress, t axes and plot the coordinate pair sx, txy at point A and then sy, tyx at point B.

However, there is a highly significant factor in mechanical design that has thus far been neglected. Note also that there is one dominant peak shear stress in this diagram.


In many simple cases the effective state of stress can be reduced to 2-D or 1-D, but only after careful consideration. They are sx, txy and sy, tyx. First sketch the normal stress and shear stress axes and then plot the coordinate pair sxtxy at A.


These two points establish the circle diameter. That factor is the influence of the additional 3-D stress components on the design safety.

There are six independent stress components shown in a conventient Cartesian coordinate system. It is very important to remember that stress components for one location in a machine part should never be combined with stress components for a different location in the same part.


The two principal stresses from the 2-D circle are T and 10 T. A qubic equation can be solved for the three principal stress roots in the general stress case, however, in many cases of mechanical design some of the principal stresses may be determined by inspection. The general state of iosstaticas is pictured on the stress element below. Geometrical calculations finish the numerical values.

Arquivos Semelhantes Anamnese Exemplo de anamneses. In a second example, assume that sx is smaller than sybut both are positive, and that txy is cw.