Question

Suppose the ends of a 27-m-long steel beam are rigidly clamped at 0°C to prevent expansion. The rail has a cross-sectional area of 35 cm^2. What force does the beam exert when it is heated to 39°C? (αsteel = 1.1 × 10^−5/C°, Ysteel = 2.0 × 10^11 N/m^2).

Answer 1

F = 1.58*10^{11} N

Step-by-step explanation:

given data:

length of steel beam = 27 m

cross sectional area of rail = 35 cm

`\Delta T = 39` Degree celcius

change in length of steel beam is given as

`\Delta L = L_O \alpha \Delta T`

`= 20*1.1*10^(-5)*39`

`=8.58*10^(-3)` m

Young's modulus is

`Y = (FL)/(A\Delta L)`

`F = ( YA\Delta L)/(L)`

`= (2.0*10^(11)*25*10^(-4)8.58*10^(-3))/(27)`

F = 1.58*10^{11} N