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A theodolite is set on a Benchmark A in order to measure the relative elevation AAB of a point B. The theodolite delivers an angle Z = 70° and the measured slope is S = 150m. The instrument elevation hi = 1.60 m and the observed value on the road set at the point B is r = 1.25m.

A theodolite is set on a Benchmark A in order to measure the relative elevation AAB of a point B. The theodolite delivers an angle Z = 70° and the measured slope is S = 150m. The instrument elevation hi = 1.60 m and the observed value on the road set at the point B is r = 1.25m.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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A theodolite is set on a Benchmark A in order to measure the relative elevation AAB of a point B. The theodolite delivers an angle Z = 70° and the measured slope is S = 150m.

The instrument elevation hi = 1.60 m and the observed value on the road set at the point B is r = 1.25m.

A theodolite is set on a Benchmark A in order to measure the relative elevation AAB of a point B. The theodolite delivers an angle Z = 70° and the measured slope is S = 150m. The instrument elevation hi = 1.60 m and the observed value on the road set at the point B is r = 1.25m. Rod (r) B AÁB Horizontal E -H- Figure 1: Trigonometric leveling 1) Establish the relative elevation AAB of the point B as a function of S, Z, hi and r? 2) Calculate numerically AAB? 3) Suppose that the error on the theodolite elevation is eni = 5mm, the error on S is es = 1cm, the error on Z is ez = 15", and the error on the rod reading is e, = 3mm. Estimate analytically the error eAB on AAB ? Calculate eaAB numerically?
Transcribed Image Text:A theodolite is set on a Benchmark A in order to measure the relative elevation AAB of a point B. The theodolite delivers an angle Z = 70° and the measured slope is S = 150m. The instrument elevation hi = 1.60 m and the observed value on the road set at the point B is r = 1.25m. Rod (r) B AÁB Horizontal E -H- Figure 1: Trigonometric leveling 1) Establish the relative elevation AAB of the point B as a function of S, Z, hi and r? 2) Calculate numerically AAB? 3) Suppose that the error on the theodolite elevation is eni = 5mm, the error on S is es = 1cm, the error on Z is ez = 15", and the error on the rod reading is e, = 3mm. Estimate analytically the error eAB on AAB ? Calculate eaAB numerically?
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