Question

Question 7 options: A steel tape that has a length of 100.00 at 68 degrees F is to be used to lay off a building with the dimensions 450.00 ft by 515.00 ft. What should the tape readings be if the tape temperature is 104 degrees F at the time of measurement

Answer 1

Answer:

The tape readings at 104°F will be 449.88 ft by 514.86 ft

Explanation:

Co-efficient of linear expansivity of Steel = α = 7.3 × 10⁻⁶ ft/ft.°F (from literature)

α = ΔL/(L₀(ΔT)

ΔL = change in length = ?

L₀ = original length = 100.0 ft

ΔT = change in temperature = 104 - 68 = 36°F

ΔL = α × (L₀(ΔT))

ΔL = 7.3 × 10⁻⁶ × 100 × 36 = 0.02628 ft = 0.0263 ft

ΔL = Lf - L₀

Lf = L₀ + ΔL = 100 + 0.0263 = 100.0263 ft

This tape is used to measure a dimension of 450 ft × 515 ft,

Meaning, the 450 ft will give a reading of 450 × 100/100.0263 = 449.88 ft

And the 515 ft gives a reading of 515 × 100/100.0263 = 514.86 ft.

The tape readings at 104°F will be 449.88 ft by 514.86 ft