Question

The state of stress (in MPa ) at a point is shown in the figure. It is known that Iy=-7.275\times 10^(5) MPa^(3),\sigma _(\mu )=147.7127MPa and \tau _(mar )=126.2246MPa at this point. a.- Find \sigma and r and write down all the stress components at the point with the correct signs and subscripts. b.- If the direction corresponding to \sigma _(p1) is 0.1955i=0.9496j-0.2449k and the direction corresponding to \sigma _(p) is 0.8222i 0.0226j 0.5688k, find the normal to the maximum shear stress plane. I,j and k are unit vectors parallel to the x,y and z directions.

          The state of stress (in MPa ) at a point is shown in the figure. It is known that Iy=-7.275\times 10^(5) MPa^(3),\sigma _(\mu )=147.7127MPa and \tau _(mar )=126.2246MPa at this point.
a.- Find \sigma  and r and write down all the stress components at the point with the correct signs and subscripts.
b.- If the direction corresponding to \sigma _(p1) is 0.1955i=0.9496j-0.2449k and the direction corresponding to \sigma _(p) is 0.8222i 0.0226j 0.5688k, find the normal to the maximum shear stress plane. I,j and k are unit vectors parallel to the x,y and z directions.

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the state of stress in mpa at a point is shown in the figure it is known that iy 7275times 105 mpa3sigma mu 1477127mpa and tau mar 1262246mpa at this point a find sigma and r and write dow 21367

Added by Ronald B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Elias Robbins

05/17/2022

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The state of stress (in MPa) at a point is shown in the figure. It is known that $I_3 = -7.275 \times 10^5$ MPa$^3$, $\sigma_{p1} = 147.7127$ MPa and $\tau_{max} = 126.2246$ MPa at this point. a.- Find $\sigma$ and $\tau$ and write down all the stress components Show more…

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The state of stress (in MPa ) at a point is shown in the figure. It is known that Iy=-7.275\times 10^(5) MPa^(3),\sigma _(\mu )=147.7127MPa and \tau _(mar )=126.2246MPa at this point. a.- Find \sigma and r and write down all the stress components at the point with the correct signs and subscripts. b.- If the direction corresponding to \sigma _(p1) is 0.1955i=0.9496j-0.2449k and the direction corresponding to \sigma _(p) is 0.8222i 0.0226j 0.5688k, find the normal to the maximum shear stress plane. I,j and k are unit vectors parallel to the x,y and z directions.

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Transcript

00:01 Hey guys, this problem, we are given stresses in these planes.

00:08 It is plain stress.

00:09 So this is what your element should look like drawn right here.

00:13 I've already gone ahead and drawn the more circle for what it should look like for the sake of time, as well as the equations we're going to be using in this problem.

00:20 So using these equations, we can just fill them in.

00:23 29 .5 minus 29 divided by 2 plus square root of squared plus 27 squared.

00:53 Now as you can see this turns into zero because the top is zero.

00:59 Same thing's going to happen down in sigma 2.

01:02 These are your principal stresses by the way, sigma 1 and sigma 2.

01:05 This comes out to be plus 39 .99 megapascals, which you can just round to 40 megapascals positive.

01:16 Now for this one, as you can see, this also is going to turn into zero.

01:20 And the only difference is this sign right here.

01:24 So we already know this and it's just going to be 40, negative 40 megapascals.

01:28 Now, to find the maximum shear stress, which is denoted by tau -max, you just do the 40 megapascals minus negative 40 megapascals.

01:41 And this is 80, but you just divide by 2.

01:44 So it ends up just being 40 megapascals as well...

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