The Golden Gate Bridge in San Francisco has a main span of length 1.28 km, one o

Question

The Golden Gate Bridge in San Francisco has a main span of length 1.28 km, one of the longest in the world. Imagine that a steel wire with this length and a cross-sectional area of 4.00 times 10^-6 m^2 is laid on the bridge deck with its ends attached to the towers of the bridge, on a summer day when the temperature of the wire is 35.0 degree C. (a) When winter arrives, the towers stay the same distance and the bridge deck keeps the same shape as its expansion joints open. When the temperature drops to -10.0 degree C, what is the tension in the wire? Take Young's modulus for steel to be 20.0 times 1010 N/m^2. (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 times 108 N/m^2. At what temperature would the wire reach its elastic limit? (c) Explain how your answers to (a) and (b) would change if the Golden Gate Bridge were twice as long.

Explanation / Answer

a)

delta L/L = (1.1 x 10^-5)*(35)
= 38.5 x 10^-5

that delta L/L is strain
delta L/L = sigma/E which is stress/young's

stress = 38.5 x 10^-5 x 20 x 10^10
= 7.7 x 10^7 N/m^2

tension = stress * area
= 7.7 x 10^7 x 4 x 10^-6 = 308 N

b)

well we got 7.7 x 10^7 N/m^2 for a 35 degree drop
so, to get 3 x 10^8 N/m^2
we need 35*30/7.7 = 136.36 degree drop
that is 25 - 136.36 = -111.36 deg C

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