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Determine the length of the cantilevered beam so that the maximum bending stress in the beam is equivalent to the maximum shear stress.

Respuesta :

The shear stress at any given point y1 along the height of the cross section is calculated by: where Ic = b·h3/12 is the centroidal moment of inertia of the cross section. The maximum shear stress occurs at the neutral axis of the beam and is calculated by: where A = b·h is the area of the cross section.
lhmarianateixeira

In this exercise we have to calculate the formula that will be able to determine the length of the cantilevered, like this:

[tex]\sigma_{max}C=\frac{M_{max}C}{I}[/tex]

So to determinated the maximum tensile and compreensive stress due to bending we can describe the formula as:

[tex]\sigma_b = \frac{MC}{I}[/tex]

Where,

  • [tex]\sigma_b[/tex] is the compressive stress or tensile stress
  • [tex]M[/tex] is the B.M
  • [tex]C[/tex] is the N.A distance
  • [tex]I[/tex] is the moment of interior

So making this formula for the max, we have:

[tex]\sigma_c=\frac{MC}{I} \\\sigma_T=-\sigma_c=-\frac{MC}{I}\\\sigma_{max}=M_{max}\\[/tex]

With all this information we can put the formula as:

[tex]\sigma_{max}C=\frac{M_{max}C}{I}[/tex]

See more about stress in the beam at brainly.com/question/23637191

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