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A bridge to be fabricated of steel girders is designed to be 500 m long and 12 m wide at ambient temperature (assumed 20°C). Expansion joints will be provided to compensate for the change in length in the girders as the temperature varies. Each expansion joint can compensate for a maximum of 20 mm of change in length. From historical records it is estimated that the minimum and maximum temperatures in the region will be -35°C and 40°C, respectively. Determine (a) the minimum number of expansion joints required and (b) the length that each bridge section should be fabricated.

Respuesta :

Answer:

a) 22.5number

b) 22.22 m length

Explanation:

Given data:

Bridge length = 500 m

width of bridge = 12 m

Maximum temperature = 40 degree C

minimum temperature  = - 35 degree C

Maximum expansion can be determined as

[tex]\Delta L = L \alpha (T_{max} - T_{min})[/tex]

where , \alpha is expansion coefficient [tex]= 12\times 10^{-6}[/tex] degree C

SO, [tex]\Delta L = 500\times 12\times 10^{-6}\times ( 40 - (-35)) [/tex]

[tex]\Delta L = 0.45 m = 450 mm[/tex]

number of minimum expansion joints is calculated as

[tex]n = \frac{450}{20} = 22.5[/tex]

b) length of each bridge

[tex]Length = \frac{500}{22.5} = 22.22 m[/tex]