Given a W12X50 that is 15 ft long. The beam is simply supported and supports its self-weight and a motorized piece of equipment in the center. The equipment weighs 80,000 lbs. During operation the equipment generates a net upward and downward force of 9,000 lbs. The beam has an endurance limit of 20 ksi and a tensile strength of 80 ksi.

a) Using Goodman Criteria is the beam at risk of fatigue failure? If so, given the equipment generates 200 cycles a day, how many days until the beam reaches its fatigue limit?
b) Using the Ellipse fatigue failure criteria does the beam fail?