# Calculating modulus of elasticity?

1. Mar 29, 2011

### tobyrzepka

I'm trying to figure out how to calculate the modulus of elasticity for a board clamped to a surface plate at one end and free-floating on the other. I've measured the deflection with a 1k weight at the free end of the board. So I've got that data as well as the dimensions of the free-hanging portion of the board.

I've done this test with numerous boards of different thicknesses and dimensions and want to compare them in terms of stiffness.

2. Mar 29, 2011

### Mapes

Hi tobyrzepka, welcome to PF. Try a search for "beam bending equations" to find the deflection vs. Young's modulus for a number of different boundary conditions. For the case of a cantilevered beam (clamped at one end, transverse load on the other), the deflection is $\delta=PL^3/3EI$, where $I=wt^3/12$ is the second moment of area. Does this answer your question?

3. Apr 3, 2011

### polymerou

Like Mapes stated correctly, δ=F*L^3 / 3E*I

Since you measured deflection you can solve as E (elasticity modulus) and you'll have it.

E=I*F*L^3 / 3δ

F = Force applied (1kg as you mentioned)
L = Length (Length of each board)
E = Elasticity modulus (You will do the math)
I = Inertia moment (b*h^3)/12 where h=width of board and h=height (thickness)
δ= Deflection (As you measured)

I hope that helped

4. Jul 6, 2011

### dawg78s

So you said :
I = Inertia moment (b*h^3)/12 where h=width of board and h=height (thickness)

I assume you meant b = width of the board, and h = height... is that right?

5. Jul 26, 2011

### the_red_jeste

b=width, h=depth/height

for a rectangular section I =(b.h^3)/12