# Solution to Problem 520 | Flexure Formula

**Problem 520**

A beam with an S310 × 74 section (see Appendix B of textbook) is used as a simply supported beam 6 m long. Find the maximum uniformly distributed load that can be applied over the entire length of the beam, in addition to the weight of the beam, if the flexural stress is not to exceed 120 MPa.

**Solution 520**

Relevant data from Appendix B, Table B-4 Properties of I-Beam Sections (S-Shapes): SI Units, of text book.

Designation | S310 × 74 |

S | 833 × 10^{3} mm^{3} |

From the shear diagram:

$M_{max} = \frac{1}{2}(3)(3w)$

$M_{max} = 4.5w \, \text{N}\cdot\text{m}$

$(\,f_b\,)_{max} = \dfrac{M}{S}$

$120 = \dfrac{4.5w (1000)}{833 \times 10^3}$

$w = 22,213.33 \, \text{N/m}$

$w = 2,264.36 \, \text{kg/m}$

$w = DL + LL$

$2\,264.36 = 74 + LL$

$LL = 2,190.36 \, \text{kg/m}$

$LL = 21.5 \, \text{ kN/m}$ *answer*

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