Two long wooden beams of square cross section / x = 0.1 m are butt-jointed using...

Transcribed Image Text:

Two long wooden beams of square cross section / x = 0.1 m are butt-jointed using an epoxy adhesive. The adhesive was stirred before application, trapping air bubbles which, under pressure in forming the joint, deform to flat, penny-shaped cracks of diameter 2 mm (see figure). For these cracks assume a geometry factor Y= 1 in the expression for stress intensity factor. The fracture toughness of the epoxy Kic 1.3 MPa.m = (a) If the beams are loaded in axial tension, what is the load F, that leads to fast fracture? (b) The beams are now loaded in 3 point bending, with a central load F, and a total span L = 2 m. Show that the maximum tensile stress at the surface of the beam is given by = 3FbL/2t. Assuming that there is a bubble close to the beam surface, find the maximum load that the beam can support without fast fracture. Tension Bending 0 0 0 0 0 0 Fi Fb/2 L = 2m Ob Fb/2 Fb Two long wooden beams of square cross section / x = 0.1 m are butt-jointed using an epoxy adhesive. The adhesive was stirred before application, trapping air bubbles which, under pressure in forming the joint, deform to flat, penny-shaped cracks of diameter 2 mm (see figure). For these cracks assume a geometry factor Y= 1 in the expression for stress intensity factor. The fracture toughness of the epoxy Kic 1.3 MPa.m = (a) If the beams are loaded in axial tension, what is the load F, that leads to fast fracture? (b) The beams are now loaded in 3 point bending, with a central load F, and a total span L = 2 m. Show that the maximum tensile stress at the surface of the beam is given by = 3FbL/2t. Assuming that there is a bubble close to the beam surface, find the maximum load that the beam can support without fast fracture. Tension Bending 0 0 0 0 0 0 Fi Fb/2 L = 2m Ob Fb/2 Fb