Question

8.5 and 8.6 (a) Knowing that $\sigma_{all} = 160$ MPa and $\tau_{all} = 100$ MPa, select the most economical metric wide-flange shape that should be used to support the loading shown. (b) Determine the values to be expected for $\sigma_m$, $\tau_m$, and the principal stress $\sigma_{max}$ at the junction of a flange and the web of the selected beam.

          8.5 and 8.6 (a) Knowing that $\sigma_{all} = 160$ MPa and $\tau_{all} = 100$ MPa, select the most economical metric wide-flange shape that should be used to support the loading shown. (b) Determine the values to be expected for $\sigma_m$, $\tau_m$, and the principal stress $\sigma_{max}$ at the junction of a flange and the web of the selected beam.
        
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8.5 and 8.6 (a) Knowing that σall = 160 MPa and τall = 100 MPa, select the most economical metric wide-flange shape that should be used to support the loading shown. (b) Determine the values to be expected for , , and the principal stress σmax at the junction of a flange and the web of the selected beam.

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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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8.5 and 8.6a Knowing that oal = 160 MPa and a = 100 MPa, select the most economical metric wide-flange shape that should be used to support the loading shown. (b) Determine the values to be expected for σm, τm, and the principal stress σmax at the junction of a flange and the web of the selected beam. 8.5 and 8.6 (a) Knowing that all = A 275 kN B 0000 1.5 m Fig. P8.6 3.6 m C 1.5 m D 275 KN 8.5 and 8.6a Knowing that σal = 160 MPa and σa = 100 MPa, select the most economical metric wide-flange shape that should be used to support the loading shown. (b) Determine the values to be expected for σm, τm, and the principal stress σmax at the junction of a flange and the web of the selected beam. 1275 kN B A 275 kN 3.6 m 1.5 m Fig. P8.6 1.5 m
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Transcript

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00:01 The first thing that we need to appreciate when answering this question is the calculation of the principal stress.
00:08 By definition, the principal stress is going to be equal to the stress in the x direction divided by 2 plus the square root of the x direction stress divided by 2 raised to the power of 2 plus tau in the x and y blink.
00:26 So based on this, what would need to do is to move on to determining the values of his stress in the x direction and that of a tau in the x -y plane.
00:41 And to do that, we need to first of all appreciate that the stress in the y direction is equal to zero.
00:48 And the stress in the x direction is going to be equal to negative md multiplied by y divided by the value of i.
00:57 And this expression right here, this md, this md is as good as negative 7 over 8 pl.
01:09 And for this would have an i value that is equal to bh cubed divided by 12.
01:19 And if we make the substitutions, we are looking at an i value that is equal to 0 .437.
01:28 By 10 to the power 7.
01:31 Then moving on to determining this y value, this y value is equal to h divided by two minus the value of...
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