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# Rods $A B$ and $B C$have diameters of$4$ mm and $6$ mm, respectively. If the $3$ kN force is applied to the ring at $B$ , determine the angle $\theta$ so that the average normal stress in each rod is equivalent. What is this stress?

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We have to determine the angle of the 3 kN force and the normal stress of each rod, if it has to be equal in both rods. The arrangement is given in Prob. 1-56.

Given data:

\begin{aligned} &\text{Diameter of rod AB: }&&d_{AB} = 4\text{ mm}\\ &\text{Diameter of rod BC: }&&d_{BC} = 6\text{ mm}\\ \end{aligned}

We will begin by calculating the angle of the rod $BC$ with the tangent definition.

\begin{aligned} \tan{\alpha}&=\dfrac{3}{4}\\ \alpha&=\arctan{\left( \dfrac{3}{4} \right)}\\ &=36.87^{\circ} \end{aligned}

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