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 4.70 times 10^-6 m^2 is laid in a straight line on the bridge deck with its ends attached to the towers of the bridge. On a summer day the temperature of the wire is 40.0degreesC. When winter arrives, the towers stay the same distance apart and the bridge deck keeps the same shape as its expansion joints open. When the temperature drops to -10degreesC, what is the tension in the wire? (Take Young's modulus for steel to be 2.00 times 10^11 N/m^2, and the average linear expansion coefficient for steel to be 1.1 times 10^-5 degrees C^-1.) ___ N Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 times 10^8 N/m^2. At what temperature would the wire reach its elastic limit? _____ degrees C Explain how your answers to parts (a) and (b) would change if the Golden Gate Bridge were twice as long.

Explanation / Answer

(a) Thermal contraction = L * tension / Y * area

Since the wire does not actually contract or stretch, stress expansion = thermal contraction and

L a deltaT = L * tension / Y * area

or

Tension = Y * area * a * deltaT = 2x10^11 * 4.70x10^-6 * 1.1x10^-5 * (40 - (-10)) = 517 N

(b) stress = tension / area = Y a deltaT

3 x 10^8 = 2 x 10^11 * 1.1 x 10^-5 * deltaT

=> delta T = 136.4 deg C

Therefore, the new temp would have to be 40 + 136.4 = 176.4 deg Celsius

(c) Since the above expression does not include length of the bridge (L). So, there will not be any effect on the results obtained in (a) and (b) when the bridge's length becomes twice.

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