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Note also that there isostatocas one dominant peak shear stress in this diagram. How do they become 3-D representations? Then plot the first coordinate pair sx, estruturas at point A.

Arquivos Semelhantes Anamnese Exemplo de anamneses. In this case, there is no effect on the overall stress state. Principios basicos de farmacologia Principios basicos de farmacologia.

These two points establish the circle diameter. Once all the stress components at a given location are determined, they may then be combined to find principal stresses, maximum shear stress or other measures that are useful for predicting design success or failure. It finds the principal stresses and a maximum shear stress although this maximum shear stress may be quite misleading in 3-D stress. Geometrical calculations finish the numerical values.

This tutorial is designed to introduce and place strong emphasis on the role of 3-D stress in the process of. The two principal stresses from the 2-D circle are T and 10 T.

This convention is useful for determining the proper orientation of principal stresses and other components relative to the x,y coordinates. Simple geometric triangles can then determine the circle radius and all principal stress and peak shear stress values. Connecting these points locates the circle center at point C.

The same is true in 3-D stress. 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.


However, the second example has the same first two principal stresses s1 and s2, but s3 is 0. 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. Note that the principal stress values are always ordered by convention so the s1 is the largest value in the tensile direction and s3 is the largest value in the compressive direction.


The triangle C, sx, and txy form a 30, 40, 50 triangle, so the circle radius is These two points form the diameter of the circle with its center at point C.

In the real world of applications all objects are 3-D. This enlarges the outermost circle which means that the overall state of stress has increased. This graphical representation of the 2-D stress transformation equations provides a quick, accurate and visual protrayal of the 2-D state of stress.

What about the two 2-D examples? 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. In a second example, assume that sx is smaller than sybut both are positive, and that txy is cw. That factor is the influence of the additional 3-D stress components on the design safety. The center C is located at a stress value of First sketch the normal stress and shear stress axes and then plot the coordinate pair sxtxy at A.

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

They are sx, txy and sy, tyx. In many simple cases the effective state of stress can be reduced to 2-D or 1-D, but only after careful consideration. However, there is a highly significant factor in mechanical design that has thus far been neglected. Everything in the mechanical design realm has solid 3-D characteristics. The same is true for the state of stress in the solid.


In this case, there isostatkcas an appreciable contribution by the 3-D effect that must not be ignored in accounting for design safety. In the early stages of mechanical design, the locations of most likely stress failure and the corresponding stress components acting at those locations must be identified.

Then plot the second pair 0, tyx at point B. It is very important to remember that stress estducturas for one location in a machine part should never be combined with stress components for a different location in the same part.

First sketch the normal stress axis along the horizontal and the shear stress axis along the vertical. Plot the next coordinate pair sy, tyx at B. The definition of the three circle diagram is sketched below.

Since there are no non-zero z component shear stresses, sz is the third principal stress with a value of —25 C. There are six independent stress components shown in a conventient Cartesian coordinate system. Draw the circle and determine two of the principal stresses. Carrying this attitude through the mechanical design process is a recipe for failure.

The general state of stress is pictured on the stress element below.


The maximum shear stress is at the peak of the largest circle and is equal to half the difference between s1 and s3. As an example, assume that sx is positive and txy is positive cw with sy equal zero. Look at the modified examples below.