I'm building a shelf out of an Oriented Strand Board (OSB-3), reinforced with steel strip attached to it's bottom side. Please check my calculations for deflection.
The OSB thickness is $h_{OSB}=18 \text{ mm}$, it's width $b_{OSB}=500 \text{ mm}$, I googled OSB's modulus of elasticity to be $E_{OSB}=3.5 \text{ GPa}$. For steel strip it's $h_{st}=4 \text{ mm}$, $b_{st}=60 \text{ mm}$, $E_{st}=200 \text{ GPa}$. The shelf span $L=2000 \text{ mm}$. Load is uniformly distributed $q=500 \text{ N/m}$.
I approach the task with utmost utilitarianism, using online tools and off-the shelf formulas:
I transform area of OSB into steel: $$b_{eq}=\dfrac{E_{OSB}}{E_{st}} \cdot b_{OSB}=\dfrac{3.5}{200}\cdot 500=8.75 \text{ mm}$$
I find moment of inertia of uniform inverted T-beam from step 1, using an on-line calculator: $$I=16079 \text{ mm}^4$$
I obtain max deflection at center $$d=\dfrac{5qL^4}{384E_{st}I}=\dfrac{5\cdot500\text{ N/m}\cdot(2000\text{ mm})^4}{384\cdot200\text{ GPa}\cdot16079\text{ mm}^4}=32 \text{ mm}$$
My questions:
- Does OSB modulus of elasticity look legit?
- Did I miss something, are the calculators and formulas appropriate here?