Answer to Question #231191 in Civil and Environmental Engineering for Alan Enrico V Tuib

Question

A line is recorded as 472.90 m. long. It is measured with a 0.65 kg. tape which is 30.005 m. long at 20

Answer 1

Here is your complete and exact question: 

A line is recorded as 472.90 m long. It is measured with a 0.65 kg tape which is 30.005m long at 20°C under a 50 N pull supported at both ends. During measurement the temperature is 5°C and the tape is suspended under a 75 N pull. The line is measured of 3% grade. What is the true horizontal distance? E = 200 GPa, cross-sectional are of tape is 3 mm² and coefficient of linear expansion is 0.0000116 m/°C.

Solution:

 given data

Length of measurement (L) = 472.90 m

Designated length of tape (l) = 30.005 m

Weight of tape (W) = 0.65 kg

Temperature at the time of Standardization (T_o)= 20°C

Pull at the time of Standardization (P_o) = 50 N

Temperature at the time of measurement (T_M)= 5°C

Pull at the time of measurement (P_m)=75N

Gradient at which line is measured = 3%

Coefficient of linear expansion () 0.0000116 m/°C

Cross sectional area of tape (A) = 3 mm2

E = 200 GPa

To determine:

True horizontal distance of line.

To find the True horizontal distance of line, corrections are needed to be applied as follows:

1. Correction due to standardization (or correction due to absolute length)

(b)Total error to be corrected for inclined distance: