A simply supported basswood beam shown below Click on the image to enlarge is 28

Question

A simply supported basswood beam shown below

Click on the image to enlarge

is 28 inches long and carries a load of 210 pounds. It has a hollow box cross-section as shown

Click on the image to enlarge

where b = 4 inches, h = 8 inches, and t = 0.75 inches. Basswood has the following material properties: Modulus of Elasticity = 1.46x106lbm/in2 and Density = 28lbm/ft3. Determine the moment of inertia, deflection, volume, and weight of the beam.

I =  in4.

Deflection =  inches.

Volume =  in3.

Weight =  lbs.

Explanation / Answer

area
A=4*8 - 4.5*8.5=6.25 in^2
volume = 6.25*28=175 in^3
I=1/12*(4*8^3 - 4.5*8.5^3)=59.63 in^4
weight per unit length
28/12^3*6.25=0.101 lbm/in
weight of beam
0.101*28=2.83 lbm
deflection for simply supported beam under it's own weight (uniformly distributed load)
delta(middle)=5*w*l^3/(384*E*I)=
5*2.83*28^3/(384*1.46*10^6*59.63)=
0.00000929 in

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