Question

QUESTION 1:

A steel beam is 5.0 m long at a temperature of 20C. The temperature rises to 40C. (a) What is the change in beam’s length

due to thermal expansion? (b) Suppose that the ends of the beam are initially in contact with rigid vertical supports. How

much force will the expanded beam exert on the supports if the beam has a cross sectional area of 60 cm^2 ?

Ans: a =1.2 mm,b = 2.9 x 10^5N

Answer 1

a)
given
L = 5 m

T1 = 20 degrees celsius
T2 = 40 degrees celsius

we know,
coefficient linear expansion of steel, alfa = 12*10^-6 /C

so, delta_L = L*alfa*(T2 - T1)

= 5*12*10^-6*(40 - 20)

= 0.0012 m

= 1.2 mm <<<<<<<<<<<-----------------Answer

b) we know, Youngs modulus of steeel Y = 200*10^9 pa

we know, Y = stress/strain

= (F/A)/(delta_L/L)

Y*delta_L/L = F/A

==> F = Y*delta_L*A/L

= 200*10^9*1.2*10^-3*60*10^-4/5

= 288000 N

= 2.9*10^5 N <<<<<<<<<<<-----------------Answer