Problem # p032 |

The cross-section of beam shown in the figure is a symmetric triangle with "a" as the baseline and "h" as its height. The shearstress distribution in this beam due to bending is described by the quantity Q(y)/b(y) with the coordinate "y" as indicated in the figure. |

- Derive the equation for Q(y)/b(y). For b(y) as indicated in the above
figure you may use the following equation :
b(y) = a*(2/3-y/h)

Also, for a symmetric triangle the centroid is located at 1/3 of its height away from its baseline. - Using the equation you developed under 1) find the expression for
Q(y)/b(y) at y=-h/3 (top of cross-section).
- Using the equation you developed under 1) find the expression for
Q(y)/b(y) at y=0 (neutral axis of cross-section).
- Using the equation you developed under 1) find the expression for
Q(y)/b(y) at y=h/6.
- Using the equation you developed under 1) find the expression for
Q(y)/b(y) at y=2h/3 (bottom of cross-section).
- At which of the investigated values of y is Q(y)/b(y) the largest ?
( You need to use differentiation to prove your assertion ).