A laminated wood beam of square cross section is built up by

A laminated wood beam of square cross section is built up by gluing together three strips, each 20 mm tall times 60 mm wide in cross section. The beam has a total weight of 5 kg and is simply supported with span length L = 3m. Determine the maximum moment M that may be applied, as seen in the figure at right, if the maximum shear stress in the glue is 0.3 MPa.

Solution

the weigth makes a moment is the direction of M

moment of the weigth=5*9.81*(3/2)= 73.575 Nm

know the equation of max strees is given by

S=Mc/J

S=0.3MPa= 300000 Pa

c=30 mm = 0.03 m

J=0.06^2 x 0.06^2 / 6 = 0.000002 m^4

M=m + 73.575

so we evaluate:

300000=(73.575+m)(0.03)/(0.000002)

m=52.15 N m in the opositive direction