Question

13 3. (15 points) Two steel plates are to be held by means of 14-mm diameter high-strength steel bolts fitting snugly inside cylindrical brass spacers. Knowing that the average normal stress must not exceed 250 MPa in the bolts and 100 MPa in the spacers, determine the outer diameter of the spacers that yields the most economical and safe design. $\sigma = \frac{P}{A}$ $P = \sigma A$ $604300 \times 10^6 Pa \cdot \frac{\pi}{4} (0.012^2 m^2) = 83929.2 N$ Space - P = $\sigma A \implies 83929.2 N$ $= 120 \times 10^6 Pa \cdot \frac{\pi}{4} (d_{out}^2 - d_{in}^2) ?$ $\sqrt{\frac{83929.2 A}{120 \times 10^6 Pa}} \cdot (\frac{\pi}{4})^{0.5} l^2$ $= \sqrt{d_{out}^2 - 0.012^2 m + 0.012^2}$ outer diameter = 22.45mm

          13
3. (15 points) Two steel plates are to be held by means of 14-mm diameter
high-strength steel bolts fitting snugly inside cylindrical brass spacers.
Knowing that the average normal stress must not exceed 250 MPa in the
bolts and 100 MPa in the spacers, determine the outer diameter of the
spacers that yields the most economical and safe design.
$\sigma = \frac{P}{A}$
$P = \sigma A$
$604300 \times 10^6 Pa \cdot \frac{\pi}{4} (0.012^2 m^2) = 83929.2 N$
Space - P = $\sigma A \implies 83929.2 N$
$= 120 \times 10^6 Pa \cdot \frac{\pi}{4} (d_{out}^2 - d_{in}^2) ?$
$\sqrt{\frac{83929.2 A}{120 \times 10^6 Pa}} \cdot (\frac{\pi}{4})^{0.5} l^2$
$= \sqrt{d_{out}^2 - 0.012^2 m + 0.012^2}$
outer diameter = 22.45mm

13
3. (15 points) Two steel plates are to be held by means of 14-mm diameter
high-strength steel bolts fitting snugly inside cylindrical brass spacers.
Knowing that the average normal stress must not exceed 250 MPa in the
bolts and 100 MPa in the spacers, determine the outer diameter of the
spacers that yields the most economical and safe design.
σ = (P)/(A)
P = σ A
604300 × 10^6 Pa ·(π)/(4) (0.012^2 m^2) = 83929.2 N
Space - P = σ A 83929.2 N
= 120 × 10^6 Pa ·(π)/(4) (dout^2 - din^2) ?
√((83929.2 A)/(120 × 10^6 Pa))· ((π)/(4))^0.5 l^2
= √(dout^2 - 0.012^2 m + 0.012^2)
outer diameter = 22.45mm

Added by Jennifer B.

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