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Required information

Two cover plates, each $7\mathrm{.}5$ mm thick, are welded to a W$46074$ beam as shown. The allowable normal stress for both the beam and the plates is ${}_{\text{a}\text{l}\text{l}}=150$MPa.

Given: $w=40k\frac{N}{m}$

$S=1460{10}^{3}m{m}^3$ for $W46074$

Moment of inertia of the beam $=333{10}^{6}m{m}^3$

Determine the required value of the length of the plates. $($Round the final answer to two decimal places.$)$

The required value of the length of the plates is m$.$