The wooden beam will be made of Douglas fir, which is estimated to have a yield stress of 6 ksi. A larger Factor of Safety of 2 will be applied to account for uncertainties associated with the properties of wood. The yield shear stress, Ty, for the wood will be assumed to be 10% of the normal yield stress, oy. The allowable shear stress, Tallow, will also be calculated using the same Factor of Safety. The wooden beam will have a rectangular cross-section that is solid, with a width of b and a height (or depth) of h. The relationship between the height and width is given as h=2b. These are the tasks that need to be performed.

The yield stress of the A992 structural steel used for the steel beam is 50 ksi. The allowable stress, represented by allow, will be determined by applying a Factor of Safety of 1.5 to the yield stress. The yield shear stress, Ty, is typically taken as 10% of the normal yield stress, oy. To determine the allowable shear stress, Tallow, the same Factor of Safety as the allowable stress will be applied.

- Produce a graphical depiction of the forces exerted on the beam using a Free Body Diagram.

- Compute the reactions at the two supports of the beam.

- Create a graph illustrating how the Shear Force varies along the length of the beam, and indicate the highest value achieved.

- Create a graph illustrating how the Bending Moment varies along the length of the beam, and indicate the highest value achieved.

- Determine the absolute maximum values of the Shear Force and Bending Moment from the diagrams.

- Opt for the most economical W steel beam that fulfills the criterion that the maximum Bending Moment is less than or equal to the allowable Bending Moment.

- Verify that for the selected W section, the maximum Shear Stress is less than or equal to the allowable Shear Stress.

- Pick a wooden beam with cross-sectional dimensions b and h that meet the required strength standards for maximum allowable bending stress.

- Verify that for the chosen b x h section, the maximum Shear Stress satisfies the allowable Shear Stress criteria.

w=0.5 kip/ft

a = 5 ft A

L=20 ft