Answer to Question #155309 in Civil and Environmental Engineering for Ian

Question #155309

A line is recorded as 475.25 m long. It is measured with a 6.5 N tape which is 30.492 m long at 680F under a 10 lb. pull supported at end points. During measurement the temperature is 4.50C and the tape is suspended under a 71 N pull. The line is measured on 3% grade. What is the true horizontal distance? Modulus of elasticity of the tape is 1.93 X 108 KPa and cross-sectional area of tape is 0.0284 cm2. Coefficient of expansion of the tape material is 0.0000116 m/0C.


1
Expert's answer
2021-01-20T04:56:31-0500

Distance Measured on the ground, Dm=475.25 m

Grade on which line is measured = 3%

Modulus of Elasticity of tape, E= 200 GPa =2*1011 N/m2

Coefficient of Linear Expansion, = 0.0000116 m/oC

C/S Area of the tape, A= 0.0284 cm2 =2.84*10-6 m2

Standard Length, Lo=30.492 m

Standard Temperature, To=68oF=20oC

Standard Pull, Po= 10 lb = 44.5 N


During measurement

Weight of the Tape, W=6.5 N.

Temperature, Tm=4.5oC

Pull, Pm=71 N

Correction due to temperature is given by;


Correction due to Pull is given by;


Correction due to Sag is given by


Net Correction applied on the tape,


Hence, the Actual Length of the tape is given by:


Total Error to be corrected for inclined distance:

But

Grade =3% =


True Horizontal Distance:


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