Answered: An existing tunnel needs to be…

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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Transcribed Image Text:An existing tunnel needs to be connected to a newly constructed bridge with sag and crest vertical curves and a constant-grade section located between the two curves. The profile view of the tunnel and bridge is shown below, wherein Gcon denotes the grade of the constant-grade section, and subseripts "s" and "c" refer to the sag and crest curves, respectively. Suppose a design speed of 35 miles/hour is needed. Determine the lengths of curves required to connect the bridge and tunnel while keeping Geon as small as possible. Station 12 - 00, PVT Bridge deck elevation 140 ft Tunnel fioor elevation 100 ft Station 0 00. PVc, Design speed (miles/hour) Rate of vertical curvature (K) Sag curves Crest curves pVIc PVT. 15 3 10 20 7 17 Ge 4= 140-1o0 = 25 12 26 40A 30 19 37 35 29 49 40 44 64 45 61 79 50 84 96

Expert Solution

Step 1

$D e s i g n s p e e d = 35 m i l e / h r F r o m t h e g i v e n p r o f i l e v i e w L_{s} + L_{c} = 12000$

Assume G_con as grade of constant grade section

$G_{2 s} = G_{1 C} = G_{c o n} G_{1 S} = G_{2 C} 0 G_{c o n} = A_{s} = A_{c} = A$

Equation for vertical alignment

$\frac{A L_{s}}{200} + \frac{A L_{c}}{200} + \frac{A (1200 - L_{s} - L_{c})}{100} = (140 - 100) W K T, L = K A \Rightarrow L_{s} = K_{s} A a n d 2_{c} = K_{c} A$

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