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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).

Respuesta :

Answer:

F = 1.58*10^{11} N

Explanation:

given data:

length of steel beam = 27 m

cross sectional area of rail = 35 cm

[tex]\Delta T = 39[/tex] Degree celcius

change in length of steel beam is given as

[tex]\Delta L = L_O \alpha \Delta T[/tex]

            [tex]= 20*1.1*10^{-5}*39[/tex]

           [tex] =8.58*10^{-3}[/tex] m

Young's modulus is

[tex]Y = \frac{FL}{A\Delta L}[/tex]

[tex]F = \frac{ YA\Delta L}{L}[/tex]

[tex]= \frac{2.0*10^{11}*25*10^{-4}8.58*10^{-3}}{27}[/tex]

F = 1.58*10^{11} N

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