Welcome to module 41 of Mechanics of Materials Part One. Today's learning outcome is to design an engineering structural member or members to meet a specified factor of safety. And so, this is a review from last time, we said that design was creating a new component or structure that will meet specifications or performance criteria. We define factor of safety as being strength of material over the computed stress that we have or the actual stress. And we wanted a factor of safety greater than 1 to avoid failure. And so, let's go ahead, and do an example. This is a wooden truss bridge, rather old. However, similar newer structures have the same basic concepts. And so, we have truss members. In this bridge that hold the loads, and so let's say, we want to go ahead and design one of those truss members. And the wooden truss member is required to support 100,000 pounds load in tension. We want to design for a factor of safety that's greater than or equal to two with respect to yielding of the wood. We're given that the yield stress for the wood being used is 4,000 lbs per square inch, and so, what cross-sectional area of beam should we design for? And so, let's go ahead and start by writing the factor of safety. Factor of safety is going to be equal to the strength of the material for yielding. And that's going to be divided by the max computed stress, and for the max computed stress, we have over here, the max computed. Stress is going to be equal to sigma. Equals P over A. P is given as being 100,000 pounds and we want to design for the area. And so, our factor of safety is going to be again, the strength of the material for yielding. The strength of the material we're given as being 4000 psi for the wood that we are using. The max computed stress is going to be 100,000 lbs divided by the area in inches squared. And, we want that to be greater than or equal to two, for our design. And, so the area then, has got to be greater than two times 100,000, or 200,000 divided by 4,000. And, this is going to be inches squared, cuz the pounds and the pounds cancel from the numerator and the denominator and that ends up being 50 inches squared. And so, the cross sectional area then that's required. Is got to be 50 inches, or 50 inches squared or greater. So, A has to be greater than or equal to 50 inches squared. And so, if I'm choosing these truss members 50 inches squared. 7 times 7 would be 49. So, to be safe, let's go a little larger than that. Maybe, we could use a eight by eight. Eight inch by eight inch. Or eight by eight. Wooden truss member. And so, that's a simple example of how to use a factor of safety. Building in factor of safety into your design. And I've got a worksheet for you to do. This is our campus recreational center on Georgia Tech's campus. Let's say, that we have an i-beam that's made of A36 steel, and it's subjected to 130,000 lb tensile load. It has a cross-sectional area of 8.79 square inches. We're given that the yield stress for the A 36 steel that's being used is 36,000 PSI. And the design calls for a 2.5 factor of safety with respect to yielding. And so, is this design of this I beam adequate for the load that's being subjected to. And so, you can do that worksheet on your own, and I've got the solution in the module materials. [MUSIC]