If the material is machine steel having a yield stress of σY=750 MPa, determine the factor of sa

If the material is machine steel having a yield stress of...

Key Concepts

Maximum Distortion Energy Theory

This theory, also known as the von Mises yield criterion, is used to predict the yielding of ductile materials under complex, multidirectional loading conditions. It is based on the concept that yielding occurs when the energy associated with distortional (shear) stresses reaches a critical threshold equal to that observed in a uniaxial tensile test.

Yield Stress

Yield stress is a material property that indicates the stress level at which a material begins to undergo plastic deformation. It is the point beyond which permanent deformation occurs, and it serves as a crucial parameter in determining the load-carrying capacity of a material.

Factor of Safety

The factor of safety is a design measure used to ensure that a structure or component operates within safe limits, even under uncertainty or overload. It is defined as the ratio of the material strength (such as yield stress) to the applied or anticipated stress, providing a buffer against failure.

Transcript

00:04 So in this question, we have a machine steel, right, and its real stress is equal to 750 megapascals.

00:15 Now, we need to determine its factor of safety, right? its factor of safety, considering the maximum distortion energy theory, right? so let's start with the solution or the solution is very easy.

00:46 So we are given by the figure of the problem that sigma sub x dash is equal to negative 500 megapascals, right? and sigma sub y dash is equal to 200 megapascals.

01:05 And sub x dash y dash is equal to zero now if we recall the movers circle or the equations 9 .1 to 9 .3 right so we can see that the principal stresses right the principle excuse me these principal dresses they are occurring or they occur at certain angles right and though they are those angles at which they share stress becomes zero right so if this is the case so it means that that it means that x subdash y subdash becomes equal to zero and this is our case therefore the normal stresses it we can say that the normal stresses are actual shear stresses right so it means that sigma that sigma sub one would be equal to sigma x and that would be equal to negative 500 megapascals and sigma sub 2 is equal to sigma sub y and that is equal to 200 megapascals and now as you can see that both of these principle stresses they are opposite in sign this one is a negative and this one is in positive right so it means that the correct form of the equation equation 10 to 0 .30 it would be sigma square sub y is equal to sigma one square negative the product of sigma sub 1 sub 2 plus the square of sigma sub 2 right so as you can see we have a square over here so it means that we need to take the square root of this whole equation so we would be left with sigma sub y on the left hand side and on the right hand side we would have the square root of um this whole side...

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