Problem 1 Given: WT 8 x 50 \"T\" shaped cross-section. Required: Using the appro
ID: 1713707 • Letter: P
Question
Problem 1 Given: WT 8 x 50 "T" shaped cross-section. Required: Using the approximate geometry of the cross-section given in the steel manual, a) the location of the plastic neutral axis (PNA) for bending about the X-X axis, as reported and the principles of mechanics of materials, verify in Table 1-8, pg. 1-61 b) the plastic section modulus, Z, reported in this same table about the X-X axis (Z c) Note that your results may not exactly agree with the tabled values. generally is calculated as Mp divided by Fy). verify that this section is "compact" for flexure.Explanation / Answer
Depth of section = 8.48 in
width of flange = 10.4 in
thickness of flange = 0.985 in
thickness of web = 0.585 in
height of web = 8.48-0.985=7.495 in
i) location of deoth of plastic neutral axis
Area of web = 7.495*0.585=4.3845 in2
Aea of flange=10.4*0.985=10.244 in2
Since the area of flange is less than arrea of web, the plastic neutral axis will be within flange
Let the depth of plastic neutral axis be d as measured from topmost surface of the section
10.4*d =10.4*(0.985-d) +7.495*0.585
d = 0.703 in
Therefore, depth of plastic neutral axis from topmost face of section = 0.703 in
b) Plastic section modulus = (10.4*0.703*0.703/2)+(10.4*0.2817*0.2817/2) + (7.495*0.585*4.029) = 20.648 in3
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