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 4.90 106 m2 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 24.0°C.

(a) 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 10.0°C, what is the tension in the wire? Take Young's modulus for steel to be 20.0 10^10 N/m2. (Assume the coefficient of thermal expansion of steel is 11 10^6 (°C)1.) N

(b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 10^8 N/m2. At what temperature would the wire reach its elastic limit? °C

(c) Explain how your answers to (a) and (b) would change if the Golden Gate Bridge were twice as long.

Explanation / Answer

(A) deltaL = L alpha delta(T)

= (1.28 x 10^3 m) (11 x 10^-6) ()(24 + 10)

= 0.479 m

T / A = Y ( deltaL / L )

T / (4.90 x 10^-6) = (20 x 10^10) (0.479 / 1280)

T = 591 N  

(b) 3 x 10^8 = (20 x 10^10) (deltaL / L )

(L alpha delta(T) / L ) = 1.5 x10^-3

(11 x 10^-6) delta(T) = 1.5 x 10^-3

delta(T) = 136.4 deg C  

T = 24 - 136.4 = - 112.4 deg C .......Ans

(c) both answers are independent of length.

hence there will no difference if wire is twice as long.

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