a 250m long bridge is imporoperly designed so that it cannot expand with tempera

Question

a 250m long bridge is imporoperly designed so that it cannot expand with temperature it is made of concrete with a = 12*10^6 c^-1 and y = 2.0*10^10pa.

a. if the maximum change in temperature at the site is 20c find the change in length of the bridge if it were free to expand

b. find the stress on concrete. if the maxium stress that the bridge can withstand before crumbling is 2.0*10^7 pa will it crubmleÂ

c. what temperature change would have to take place in order for the bridge to crumbleÂ

d. what would the change be in the length of the bridge for the temperature change found in c

Explanation / Answer

A)we know that change in length Δl = lαΔt ------1 Δt = maximum change in temperature = 20 C α = coefficient of linear expansion= 12x10-6 C-1 l = length of the bridge = 250-m then Δl = 250*12x10-6*20 m = 0.06 m . B) we know that young's modulus Y = stress/strain strain = Δl/l from equation 1 Δl/l =αΔT THEN Y = stress/ Δl/l = stress/αΔT then stress = YαΔT C) given that maximum stress the bridge can withstand with outcrumbling is 2.0 x 107 Pa Y= 2.0x1010 Pa We know that stress = YαΔT as α = 12x10-6C-1. stress = 2.0x1010 Pa *12x10-6C-1*20 = 4.8*10-6Pa with increase in temperature then stress is less thanmaximum stress . thus bridge will not crumble

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