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 Shear Stress Theory

The maximum shear stress theory, also known as the Tresca criterion, is an approach used in failure analysis to predict yielding of ductile materials. It states that yielding begins when the maximum shear stress in a material reaches a critical value that is related to the material’s yield strength in simple tension. This theory is particularly useful because many materials fail due to shear stresses rather than normal stresses.

Factor of Safety

The factor of safety is a design parameter that provides a safety margin in engineering calculations to account for uncertainties in material properties, loading conditions, and future usage scenarios. It is defined as the ratio of the material's yield stress or ultimate strength to the maximum applied stress, ensuring that structures and components perform reliably under anticipated loads without failure.

Yield Stress

Yield stress is the material property that designates the stress level at which a material begins to undergo plastic deformation. Beyond this stress, the material will not return to its original shape once the load is removed, and permanent deformations occur. It is a crucial parameter in material selection and design to ensure that structures and components operate safely under loading conditions.

Transcript

00:02 So determine the factor of safety, right? and we need to determine it considering the maximum share stress theory, right? so we have a material that is machine steel and its real stress in 750 megapascals.

00:35 We need to determine the factor of safety considering the maximum share of stress theory.

00:40 Now this question is very simple, right? so now what we are going to do over here is that you need to refresh your knowledge on the equation 9 .1 through 9 .3, right? because we would be needing it.

01:02 Now we are given by the figure of the problem that sigma sub x is equal to 150 megapa.

01:12 And sigma sub y is equal to negative 450 megapascals right now the sub x y is equal to 0 right so if we recall the moher's circle or the equations so we would see that the principle multiple stresses occur at certain angles, right? occur at certain angles where they share stress becomes equal to share stress, excuse me, share stress becomes equal to.

02:28 Right so it states that according to these moher's a circle or these equations that are 9 .1 to 9 .3 that principal stress occur at certain angles right and these are those angles where the sheer stress becomes equal to zero right so if that is the case it means that our sub x dash pi dash is equal to 0, right? and this is a case, therefore, we can say that the normal stresses are actual share stresses, right? it would mean this.

03:23 Now, if that is the case, so it means that the sigma sub 1 stress, right? it would be equal to sigma sub -x, and that would be equal.

03:34 To 150 megapaxels and sigma sub 2 would be equal to sigma sub y and would be equal to negative 4 50 megapascals right now as you can see that these typical strutters right they are opposite in signs right as you can see that this one is positive and this one is negative so it means that they are opposite sides and this means that the correct form of the correct form of equation 10 .27 it would be sigma of y is equal to the absolute value of the difference of sigma sub one negative sigma sub two so that is equal to and negative negative is positive so when you get sigma sub y is equal to 600 megapascals right as you can see that of this new found value right there's excuse me so this new found value that is 600 megaspers it is less than given value that is 700 megapascals so it means that the material does not fail according to the maximum shares with theory...

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