Question

he bronze bar 3 m long with a cross-sectional area of 320 mm2

is placed

between two rigid walls. At a temperature of -200C, there is a gap Δ = 2.5 mm.

Find the temperature at which the compressive stress in the bar will be 35 MPa.

Use α = 18.0 × 10-6

/

0C and E = 80 GP​

Answer 1

Question : A bronze bar 3 m long with a cross sectional area of 320 mm2 is placed between two rigid walls as shown in Fig. P-265. At a temperature of -20°C, the gap Δ = 2.5 mm. Find the temperature at which the compressive stress in the bar will be 35 MPa. Use α = 18.0 × 10-6 m/(m·°C) and E = 80 GPa.

Solution : at temperature -20°C,

gap , ∆ = 2.5 × 10¯³ m

coefficient of temperature, α = 1.8 × 10¯⁵/°C,

Elasticity, E = 80GPa = 8 × 10¹⁰ Pa

Let temperature is T at which compressive stress in the bar will be 35 MPa

Here change in temperature = change in Young's modulus + gap

⇒αL∆T = PL/E + ∆

⇒1.8 × 10¯⁵ × 3 × (T + 20) = (35 × 10⁶)(3)/(8 × 10¹⁰) + 2.5 × 10¯³

⇒5.4 × 10¯² (T + 20) = 35 × 3/8 × 10¯¹ + 2.5

⇒T + 20 = 70.6°C

⇒T = 50.6°C

Therefore the temperature at which compressive stress in the bar will be 35Mpa, is 50.6°C