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

Answer:

F = 1.58*10^{11} N

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

$Y = \frac{FL}{A\Delta L}$

$F = \frac{ YA\Delta L}{L}$

$= \frac{2.0*10^{11}*25*10^{-4}8.58*10^{-3}}{27}$

F = 1.58*10^{11} N