prismatic bars

[logistic_guy]

Two prismatic bars of \(\displaystyle a\) by \(\displaystyle b\) rectangular cross section are glued as shown in the figure. The allowable normal and shearing stresses for the glued joint are \(\displaystyle 700\) and \(\displaystyle 560 \ \text{kPa}\), respectively. Assuming that the strength of the joint controls the design, what is the largest axial load \(\displaystyle P\) that may be applied? Use \(\displaystyle \varphi = 40^{\circ}\), \(\displaystyle a = 50 \ \text{mm}\), and \(\displaystyle b = 75 \ \text{mm}\).

 

[logistic_guy]

The idea of this exercise is to calculate the axial load \(\displaystyle P\) using two different equations. They will yield different results. The largest axial load \(\displaystyle P\) is the samller value of the two.

A little knowledge in tensor transformation and geometry/trigonometry will be very useful to understand the formulas that we will be using.