Compute the normal stress

Consider the I-beam cross-section:

The table below has the geometric properties for different specifications for a steel beam:

Designation h (in) w (in) Ix (in^4) Iy (in^4)
S15 x 50 15 5.64 486 15.7
S15 x 42.9 15 5.501 447 14.4
S12 x 50 12 5.477 305 15.7
S12 x 40.8 12 5.252 272 13.6
S12 x 35 12 5.078 229 9.87
S12 x 31.8 12 5 218 9.36
S10 x 35 10 4.944 147 8.36
S10 x 25.4 10 4.661 124 6.79
S8 x 23 8 4.171 64.09 4.31
S8 x 18.4 8 4.001 57.6 3.73

For the beam designations indicated below, determine the maximum normal stress $\sigma_x$ assuming that the maximum moment is equal to $M_{max} = 3 \times 10^5 \rm\ lb \cdot in$.

Designation $\sigma_x$
S12 x 31.8
S12 x 50
S15 x 42.9
S10 x 25.4

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Title:
Compute the normal stress

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Started at:
2026-08-04 22:47:28 (CDT)
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{
  "sigma1": 8.256880733944955,
  "sigma2": 5.901639344262295,
  "sigma3": 5.033557046979865,
  "sigma4": 12.096774193548388
}
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