A vehicle roof crossbeam of rectangular cross section is to be made of unidirectional continuous carbon fiber reinforced epoxy in the skins and a polyurethane foam in the core. The fiber volume fraction in the composite skins is 0.55. The beam is 300 mm in length and 50 mm in width. Assume that for design purposes, the beam is simply supported at its ends and it is loaded at its mid-length with a vertical load of 10 kN. If the core thickness is equal to the total skin thickness, determine the thickness of the beam so that the deflection at its mid-length does not exceed 1/100th of its length. Calculate the weight of the beam and compare it with the weight of a steel beam of solid rectangular cross section of the same width as the composite beam. Properties of the carbon fiber, epoxy and foam are as follows.
Material Density (g/cm3) Modulus (GPa) Strength (MPa)
Carbon Fiber 1.8 248 4,070
Epoxy 1.1 1.5 75
Plastic Foam 0.2 0.16