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)
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
S7 x 20 7 3.86 42.4 3.17
S7 x 15.3 7 3.662 36.7 2.64

For the beam designations indicated below, determine the maximum normal stress $\sigma_x$ assuming that the maximum moment is equal to $M_{max} = 2 \times 10^5 \rm\ lb \cdot in$.

Designation $\sigma_x$
S8 x 18.4
S7 x 20
S12 x 35
S10 x 35

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Compute the normal stress

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Started at:
2026-08-04 22:42:37 (CDT)
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{
  "sigma1": 13.88888888888889,
  "sigma2": 16.509433962264154,
  "sigma3": 5.240174672489083,
  "sigma4": 6.802721088435375
}
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