Problem 4. The beam has a rectangular cross section and is...

Problem 4. The beam has a rectangular cross section and is subjected to the loading shown. Determine the state of stress at point B. (1) Show the results in a differential element for point B; (2) develop a Mohr's circle that represents the stress state at B; (3) calculate the principal stresses and the maximum shear stress at B.

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00:01 So, let us understand the concept with the help of a diagram.

00:04 So, diagram will be like this.

00:06 So, we have rectangular box and here we have y axis and here we have x axis and this is the z axis and here we have the point b.

00:16 So, here it is sigma x in this direction and that is stress is applying in direction and another stress that is sigma of x is applying in this direction.

00:33 So, now we will find sorry we have load that is p1 is equal to 500 pound and axial stress that is sigma of a will be equal to p1 by a.

00:57 So, on putting the values we will get 500 upon 4 multiplied by 3.

01:02 So, this is equal to 500 upon 12.

01:07 So, on solving this will give 41 .67 per square inch.

01:15 Now load p2 is equal to 400 pound and bending moment that is m will be equal to 400 multiplied by 10 which is equal to 4000 pound inch.

01:45 Now bending stress will be equal to that is bending stress that is sigma b will be equal to m upon i.

01:58 So, we have m y upon i.

02:03 So, here y is minus 1 inch and i is 3 multiplied by 4 cube by 12.

02:13 So, this is equal to 16 inch to the power 4.

02:17 So, therefore we can say that on putting the values we will have sigma of b will be equal to 4000 multiplied by minus 1 upon 16.

02:27 So, we know that 2 8 times is 16 and 2 2s are 4...

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