Question

You are given the job of designing a bridge that is to be made of concrete slabs that rest on a steel support frame. The total length of the bridge is 304 m, and you want to be sure that the expansion joints are sufficiently large. If the temperature increases by 28°C, what is the difference in the new lengths of the concrete and steel components of the bridge?

concrete _______m

steel ______m

Which of these components will have the largest increase in length? (The two components are considered expanded by the same amount if their expansions are within 5% of each other. a)concrete b)steel c)they both expand by the same amount

Answer 1

change in length are perposational to the coefficient of terminal expention alpha with

deltaL/L₀ = alpha*deltaT ........1

given that

L_o = 304 m

coefficient of thermal expantion of steel alpha = 12*10^-6 k^-1

coefficient of thermal expantion of concrete alpha_c = 12*10^-6 k^-1

change in the temperature delta T = 28 K

consider the length of the bridge and neglet the expention of the total joints in the bridge

expantion of steel support frame is caculated by using equ. 1

delta L = L₀ *alpha*deltaT

= 304*12*10^-6*28

= 10.2144*10^-2 m

expansion of concrete slabes is calculated by using equ. 1

deltaL = L₀*alpha_c*deltaT

= 304*12*10^-6*28

= 10.2144*10^-2 m

from the calculation that the steel and concrete expance equally bcs of the same coefficient of the linear expantion the difference in the length of the steel and concrete expantion is zero.as both expand equally.