A simply supported beam of length 18 ft. is subjected to a trapezoidally distributed load that has a value of 3 kip/ft at x = 0 ft. and 6 kip/ft at x = 18 ft.. The beam is made of a low carbon steel that has a yield strength of 48 ksi. Select the lightest W-beam that will support the distributed load. Furthermore, the maximum deflection cannot be more than 0.8 in.

Please use the following steps in choosing the beam:

1. Determine the reactions at the supports due to the applied load.

2. Draw SF and BM diagrams

3. Determine the maximum moment, shear force

4. Use the equations for normal stress to determine the section modulus.

5. Use tables to determine the W-beam that has the lowest section modulus that is bigger than the above.

6. Calculate the I for the beam by using the allowable deflection. See if the beam from step 5 has this I. If not, choose a different W-beam.

7.Now, take into account the weight of the beam and check to make sure that the beam can support the applied load as well as the self-weight. In addition, check to make sure that the shear strength of the beam is not exceeded.

8. A plot of the deflection curve of the beam

9. A plot of the slope of the deflection curve of the beam

10. Draw Mohrs Circle for a point on top of the cross-section of the beam where the maximum bending moment occurs. Determine the principal stresses and draw an element showing the principal planes.