Example 44
Example 44
Problem: Two vertical forces are applied to a beam of the cross section shown. Determine the maximum tensile and compressive stresses in portion BC.
Solution: From a free body of the
entire beam, and using 
Taking a cut through the beam between B and C, and calling the point K...
Next, I use 
recognizing
that the beam is in compression on the top edge and tension on the bottom.
Both c and I are dependent on the centroidal position, so I'll find the
centroid next.
The x-coordinate of the centroid is obvious from symmetry; it is zero. I have shown the centroids of each rectangular section (1 & 2) with a red dot. The overall centroid is shown with a blue dot. The calculation of the centroid is easier with a table:
| section | Ai (in2) |  |
 |
| 1 | 1.5 | 1.5 | 2.25 |
| 2 | 2.0 | 3.25 | 6.50 |
| sums | 3.5 | 8.75 |
.
This is, of course, measured from the origin, which is why I showed the
axes I chose. Now I need to compute I and so I use the parallel axis theorem:
Now I have the information needed to compute the stresses:
4 This is Problem 4.10 in Beer & Johnston's Mechanics of Materials, 2nd Edition, McGraw-Hill.