αs = 11.7 × 10-6/°C) and section BC is make of brass (Eb = 105 GPa and also αb = 20.9 × 10-6/°C). Discovering that the pole is at first unstressed, recognize the compressive pressure induced in ABC as soon as there is a temperature rise of 55°C.

You are watching: A rod consisting of two cylindrical portions



Complete question:

A stick consisting of two cylindrical portions ab and BC is restrained at both ends. Section AB is make of steel (Es = 200 GPa and αs = 11.7 × 10-6/°C) and part BC is made of brass (Eb = 105 GPa and also αb = 20.9 × 10-6/°C). (diameter of ab is 30mm, size of abdominal is 250 mm) and (diameter of BC is 50mm, length of BC is 300 mm).

Knowing the the pole is originally unstressed, determine the compressive pressure induced in ABC as soon as there is a temperature climb of 55°C

juniorg8.com:

The compressive pressure induced in abc is 156.902 kN

Explanation:

Area of section AB:

*
= 7.0695 X 10⁻⁴ m²

Area of section BC:

*
= 1.96373 X 10⁻³ m²

Free heat expansion:

*
= (0.25)(11.7 X 10⁻⁶)(55) + (0.3)(20.9 X 10⁻⁶)(55)

= 505.725 X 10⁻⁶m

Shortening due to induced compressive force P:

*

*

= 1.7682 X 10⁻⁹P + 1.455 10⁻⁹P

= 3.2232 X 10⁻⁹P

For zero network deflection,

*

∴ 3.2232 X 10⁻⁹P = 505.725 X 10⁻⁶

*

P = 156.902 X 10³ N = 156.902 kN

Therefore, the compressive force induced in abc is 156.902 kN


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