The Golden Gate Bridge has a main span length (between the two towers) of 1.28 k

Question

The Golden Gate Bridge has a main span length (between the two towers) of 1.28 km. Imagine that a steel wire with cross-sectional area 4.00 times 10^-6 m^2 extends linearly across the bridge deck between the towers. On the summer day that the wire is laid out the temperature reaches 35 degreeC. (a) In the winter, when the temperature is -10.0 degreeC, what is the tensile force, F, exerted on the wire? Assume the Young's modulus, Y, for steel is 20.0 times 10^10 N/m^2. F/A = YDeltaL/L_o (b) Permanent deformation occurs if the stress, S, on the steel exceeds its elastic limit of S_max - 3.00 times 10^8 N/m^2.

Explanation / Answer

ANSWER

Part a)

From theory we know that,

Thermal contraction = L a deltaT and stress expansion = 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 =

tension = 2x10^11 * 4x10^-6 * 1.1x10^-5 * (35 - (-10)) =

tension = 396 Newtons

Part b)

Then,

stress = tension / area = Y a deltaT

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

delta T = 136.36 deg C

So the new temp would have to be

35 + 136.36 = 171.36 deg Celsius

Regards!!!

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