An old warehouse is to be rehabilitated for commercial usage. The existing Douglas fir timber beams in the warehouse are 8-in. wide and 18-in. deep.
To increase the load-carrying capacity, a 6-in. wide by ΒΌ-in. thick carbon fiber reinforced plastic (CFRP) plate will be bonded to the bottom surface of the beams.
The moduli of elasticity for the timber and the CFRP are 1,700 ksi and 23,800 ksi, respectively. The allowable normal stresses of the timber and the CFRP are 1,200 psi and 175,000 psi, respectively.
a) Determine the allowable moment capacity of the existing 8-in. by 18-in. timber beams.
b) Determine the allowable moment capacity of the timber beam reinforced with the CFRP plate.