3. Derive the formula for the following; show all sketches and relevant assumptions:(i)(ii)Length of tangentChord length(iii)External distance(iv)Middle ordinateT- RunE- Rwe -RR-radius of circular curveT- tangent lengthA - internection angleM- middle ordinatePC - point of curvePT - point of tangentP= point of intenectionE - extemal distanceE - R-cosM -R- Ron- a(1 - a) 1. (Simple Curve) Refer to problem Example 15.6 (textbook Garber and Hoel) and re-do with thefollowing changes to the given information:(a) Intersectional angle for 1 station = 3degrees(b) Sta of PC is 800+25.5860 deg.(c) Inscribed angle for entire curve is800+25.5860 degrees50%25% L75%PCPTCalculate length of curve. Determine thestations at 25% Lc, 50% Lc, 75% Le (L, is lengthof the curve) then calculate the chords anddeflection angles at these points; show all yoursolution then summarize the results into atabulation. Calculate also the following: MiddleOrdinate and External Distance. Determine stationing of PT.2. (Compound Curve) Refer to problemExample 15.7 (textbook Garber and Hoel) and re-do with the following changes to the giveninformation:PC(a) The two simple curves are joined atSta. 238 + 80(b) First curve: R1 = 550' & A¡=40deg(c) Second curve: R2 = 450' & A2=25degR.R radii of simple curves forming compound curveA.4, - intersection angles of simple curvesA- intersection angle of compound curve1.t - tangent lengths of simple curvesT,T; = tangent lengths of compound curvePCC = point of compound curvePI = point of intersectionPC - point of curvePT - point of tangentCalculate the individual length of curves.Determine stationing of PC and PT. At eachcurve's mid-length, compute the deflection angleand chord length.

Answered: Image /qna-images/answer/057b9862-be11-4c44-b884-10868fbe7cb1.jpg

3. Derive the formula for the following; show all sketches and relevant assumptions: Length of tangent Chord length (i) (ii) (iii) (iv) External distance Middle ordinate T- Run E- Rwe -R PC- point of curve R-radius of circular curve T-tungent length A internection angle M- middle ordinate PT- point of tangent H- point of intenection E- etemal distance cos M-R-Ron -(1 - )

3. Derive the formula for the following; show all sketches and relevant assumptions: Length of tangent Chord length (i) (ii) (iii) (iv) External distance Middle ordinate T- Run E- Rwe -R PC- point of curve R-radius of circular curve T-tungent length A internection angle M- middle ordinate PT- point of tangent H- point of intenection E- etemal distance cos M-R-Ron -(1 - )

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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Concept explainers

Length and Length related Variables

Length can de defined as the measurement or extent of physical quantities or objects from one terminal to another terminal. Stone age humans used finger length, step length, and so on to measure the size or displacement of an object. Nowadays, depending on how precise the measurement requires to be and the object’s size is measured, we use measuring devices for measurements like rulers and steel tape. Most people have used a ruler or tape measure to measure a particular distance or the size of an object. For more precise measurements of tiny objects, the development of measurement tools such as the Vernier caliper, which permits us to measure dimensions within 1/1000 of an inch. In the last few decades, electronic distance measuring instruments (EDMI) have been implemented that permit us to measure distances from a few feet to many miles with reasonable accuracy.

Question

3. Derive the formula for the following; show all sketches and relevant assumptions:
(i)
(ii)
Length of tangent
Chord length
(iii)
External distance
(iv)
Middle ordinate
T- Run
E- Rwe -R
R-radius of circular curve
T- tangent length
A - internection angle
M- middle ordinate
PC - point of curve
PT - point of tangent
P= point of intenection
E - extemal distance
E - R-
cos
M -R- Ron
- a(1 - a)

1. (Simple Curve) Refer to problem Example 15.6 (textbook Garber and Hoel) and re-do with the
following changes to the given information:
(a) Intersectional angle for 1 station = 3
degrees
(b) Sta of PC is 800+25.58
60 deg.
(c) Inscribed angle for entire curve is
800+25.58
60 degrees
50%
25% L
75%
PC
PT
Calculate length of curve. Determine the
stations at 25% Lc, 50% Lc, 75% Le (L, is length
of the curve) then calculate the chords and
deflection angles at these points; show all your
solution then summarize the results into a
tabulation. Calculate also the following: Middle
Ordinate and External Distance. Determine stationing of PT.
2. (Compound Curve) Refer to problem
Example 15.7 (textbook Garber and Hoel) and re-
do with the following changes to the given
information:
PC
(a) The two simple curves are joined at
Sta. 238 + 80
(b) First curve: R1 = 550' & A¡=40deg
(c) Second curve: R2 = 450' & A2=25deg
R.R radii of simple curves forming compound curve
A.4, - intersection angles of simple curves
A- intersection angle of compound curve
1.t - tangent lengths of simple curves
T,T; = tangent lengths of compound curve
PCC = point of compound curve
PI = point of intersection
PC - point of curve
PT - point of tangent
Calculate the individual length of curves.
Determine stationing of PC and PT. At each
curve's mid-length, compute the deflection angle
and chord length.

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