6.16 A cantilever beam is subjected to an inclined load....

6.16 A cantilever beam is subjected to an inclined load. Find (a) the maximum tensile stress, (b) the maximum compressive stress. The angle $\theta$=30°. \newline 200 N \newline $\theta$ \newline 2m \newline 20 cm \newline beam's cross-section \newline 30 cm \newline Ans: (a) $\sigma_{max}(+)=+6.955\times10^4$ Pa at bottom of the base section, (b) $\sigma_{max}(-)=-6.378\times10^4$ Pa at top of the base section.

Transcript

00:09 So the question, the maximum bending movement of the cantilever beam at point a will be given by mx m max will be equals to 250 multiplied by 5 plus 22 .5 multiplied by 8 multiplied by 8 by 8 by 8 by 2.

00:29 Okay, so after solving we get m max equals to 1970 lb feet or m max equals to 23640 lb inch okay so now to determine the maximum tensile stress we have sigma max equals to m max divided by i multiplied by c2 okay so, substituting the values, we get sigma max equals to m -max is 23640 and c -2 is 0 .617 and i is 3 .36.

01:20 Okay? so from here we get sigma -max equals to 4341 .03ps or sigma -ex equals to 4 .3ps or sigma -max equals to 4 .34 .03ps or sigma -ex equals to 4 .34 k s i so this is the answer for the part a of the problem okay now moving to the part b to calculate the maximum compress in this part this is the tensile stress okay so now we will determine the maximum compressive stress and maximum compress this is our tensile stress okay so we can write it as t okay so the maximum compressive stress sigma max compressive will be given by m max divided by i multiplied by c1.

02:17 Okay, so substituting the values, we get sigma max compressive equals to mx is 23640 and c1 is 2 .269 divided by i is 3 .36.

02:33 So from here we get sigma max compressive.

02:37 Compressive equals to 15964 psi or sigma max compressive is equal to 15 .96 ks.

02:53 So this is the maximum compressive stress in the cantilevel p.

02:59 Okay.

03:00 So now moving to the part b of the problem.

03:04 So first of all, calculating the maximum bending movement of the cantilever beam, which will occur at point a.

03:13 So we can write m max equals to p multiplied by 5 into 12 plus 22 .5 multiplied by 8, multiplied by 8 by 2, multiplied by 12.

03:31 Okay, so from here we get m max equals to 60p plus 8 640 lb inch.

03:45 So now the maximum compressive stress will be sigma maximum compressive, it will be equals to m max divided by i multiplied by c1.

03:59 So, substituting the values, we get sigma max compressive equals to mx is 60p plus 8640, multiplied by c1 is 2 .269, divide by i is 3 .36...

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