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Problem 8.64

The properties of the cross section for a W 8 x 28 are taken from Appendix C:
 

d = 8.06 in tf = 0.465 in Ix = 98.0 in4
A = 8.25 in2 tw = 0.285 in bf = 6.535 in

The moment of the two forces about b is:

Also, P = 90 kips, and V = 20 kips.

Because point b is on the N.A., the normal stress does not include a bending moment term:

To obtain the shearing stress, I have to compute Q:
 

section Ai (in2) (in) (in3)
flange bftf = 3.039 d/2 - tf/2 = 3.7975 11.54
half web tw(d/2 - tf) = 1.016 1.811
totals 4.0548   13.35 = Q

Now I can compute the shearing stress:

To summarize, the element at b has these stresses:

Mohr's Circle can now be sketched:

From the circle, I have:

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