User:Egm3520.s13.team5.carrasquilla

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$$\int_{a}^{b}f{x}dx $$

1.1

1.1 Two solid cylindrical rods AB and BC are welded together at B and loaded. Determine the smallest allowable values of $$ d_{1} $$ and $$ d_{2} $$.

Given: $$ \sigma_{AB}$$ = 175 MPa $$ \sigma_{BC}$$ = 150 MPa Load at AB = 40 kN             Load at BC = 30 kN

Equations/Derivations:

The average normal stress under axial loading is given by: $$\sigma = \frac{P}{A}=\frac{P}{\frac{\pi }{4}d^{2}}= \frac{4P}{\pi d^2}$$

where $$P$$ is the magnitude of the applied force and $$ A$$the area of the cross-section of the subjected member. Rearranging the equation (....) in order to isolate $$d$$, the diameter of the member, yields: $$d= \sqrt{\frac{4P}{\sigma \pi }} $$

Member AB

$$P$$ = 40+30= 70 kN = 70 ×103 N $$d_{1}= \sqrt{\frac{4P}{\sigma \pi }} = \sqrt{\frac{4(70\times10^3)}{(175\times10^6)\pi }} = 0.02256 \ m $$

$$solution: 22.56 mm $$

Member BC

$$P$$= 30 kN= 30 × 103 N $$ d_{2}= \sqrt{\frac{4P}{\sigma \pi }} = \sqrt{\frac{4(30\times10^3)}{(150\times10^6)\pi }} = 0.01596 \ m  $$

$$solution: 15.96 mm $$