Please provide final answer in at least 3 decimals Knowing t

Please provide final answer in at least 3 decimals

Knowing that or sigma_all = 24 ksi and tau_all = 14.1 ksi, (a) select the most economical 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. Select the most economical wide-flange shape that should be used to support the loading shown from the following table: W8 Times 21 Y12 Times 16 W12 Times 22 W10 Times 19

Solution

GIVEN:- all = 24kpsi = 3456 kpft2, all = 14.1kpsi = 2030.4 kpft2,

SOLUTION:-

(a) By Shear force diagram (not shown) and Bending moment diagram (not shown), we obtain the maximum bending moment that the beam is subjected to and it is given by BMmax = 33.975 kp.ft

By formula Max bending stress  bmax = BMmax / Z, yields following stress results respectively for the section moduli Z mentioned in the table - 3235, 3146, 2265 and 3775.

And the most economical shape would be W12 x 22 since it produces bending stress of 2265 which is the least and is within the limits of all = 24kpsi = 3456 kpft2 (ANSWER)

(b) m = all + all and   m = all

  So, m = 24 + 14.1 = 38.1 kpsi and m = 14.1 kpsi (ANSWER)

Now, max =  bmax for selected beam = BMmax / Z = 33.975 / 0.015 = 2265 kp/ft2

  That is max = 15.73 kpsi (ANSWER)