Arches & Cables GATE Civil Engineering Notes by Krishna Yadav Sir
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Arches & Cables GATE Civil Engineering Notes are very important for students preparing for the GATE Civil exam. This topic is scoring and mostly based on clear concepts and simple calculations. With regular practice, students can easily solve questions from arches and cables.
These Arches & Cables GATE Civil Engineering Notes are written in easy English and formal tone. They help students understand basic ideas, formulas, and exam-focused points without confusion.
What Are Arches and Why Do They Matter in GATE
Arches are curved structures used to carry loads safely to the supports. In GATE Civil Engineering, questions mostly come from three-hinged arches, because they are statically determinate and easy to analyze.
The most common types studied in Arches & Cables GATE Civil Engineering Notes are parabolic arches and semi-circular arches. These arches help reduce the bending moment by transferring load mainly through compression.
Types of Three-Hinged Arches
Before solving numerical problems, students must clearly know the types of arches asked in exams.
|
Type of Arch |
Key Feature |
Exam Importance |
|
Parabolic Arch |
Shape follows parabola |
Very high |
|
Semi-Circular Arch |
Half circle shape |
Moderate |
Three-hinged arches have hinges at both supports and one at the crown. This makes the calculation of support reactions simple using static equilibrium equations.
Support Reactions in Three-Hinged Arches
In Arches & Cables GATE Civil Engineering Notes, support reactions are always the first step. Reactions include vertical reaction (VA, VB) and horizontal reaction (HA, HB).
To find these reactions:
-
Use ∑Fy = 0
-
Use ∑Fx = 0
-
Take moment about one support or hinge
After finding vertical and horizontal reactions, the resultant reaction is calculated using Pythagoras theorem.
Resultant Reaction and Inclination
The resultant reaction makes an angle with the horizontal. This angle is important in GATE questions.
|
Term |
Formula |
|
Resultant Reaction |
√(V² + H²) |
|
Inclination Angle |
tan⁻¹(V/H) |
For a parabolic arch, the inclination at support is given by:
tan α = 2H / L
Internal Forces in Parabolic Arches
Internal forces are a core part of Arches & Cables GATE Civil Engineering Notes. These forces act at any point along the arch.
The main internal forces are:
-
Normal Thrust
-
Radial Shear
-
Bending Moment
To find these forces, the equation of a parabola is used.
Check: GATE Civil Engineering Notes
Equation of Parabolic Arch
The standard equation is:
y = (4H / L²) x (L − x)
The slope at any point is found by differentiating this equation.
|
Parameter |
Expression |
|
Slope (tan θ) |
(4H / L²)(L − 2x) |
|
Normal Thrust |
Hx cosθ + Vx sinθ |
|
Radial Shear |
Vx cosθ − Hx sinθ |
Bending Moment in Parabolic Arch
One important result from Arches & Cables GATE Civil Engineering Notes is that the bending moment is zero for a parabolic arch carrying a full-span UDL.
This result is very popular in GATE exams and often asked as a direct question.
|
Loading Condition |
Bending Moment |
|
Full UDL |
Zero at all points |
Semi-Circular Arch Analysis
Semi-circular arches have radius r and span L = 2r. The analysis method is similar to parabolic arches.
The key point in Arches & Cables GATE Civil Engineering Notes is that the resultant reaction at the support makes an angle of 45 degrees with the horizontal.
|
Feature |
Value |
|
Span |
2r |
|
Resultant Angle |
45° |
Basics of Cables in Civil Engineering
Cables are flexible structures that can carry only tension. They cannot resist compression or bending moment.
This makes cable problems easier compared to arches. In Arches & Cables GATE Civil Engineering Notes, cables are mainly studied under:
-
Point loads
-
Uniformly distributed load (UDL)
-
Self-weight
Important Cable Properties
-
Bending moment in cable is always zero
-
Shape depends on type of load
-
Maximum tension occurs at supports
Shapes of Cables Under Different Loads
Understanding cable shape helps in solving tension problems.
|
Loading Type |
Cable Shape |
|
Point Load |
Funicular polygon |
|
UDL on span |
Parabolic shape |
|
Self-weight |
Catenary shape |
These shapes are frequently mentioned in Arches & Cables GATE Civil Engineering Notes and asked in theory-based questions.
Cable Tension Analysis
Cable tension is found using static equilibrium and geometry. The horizontal component of tension remains constant throughout the cable.
When supports are at different elevations, the maximum tension occurs at the higher support. This is a very important GATE concept.
|
Case |
Key Result |
|
Same level supports |
Equal tension trend |
|
Different level supports |
Max tension at higher support |
Common Mistakes to Avoid
Students often lose marks due to small mistakes. Arches & Cables GATE Civil Engineering Notes highlight these error points:
-
Mixing angle with vertical instead of horizontal
-
Assuming bending moment in cables
-
Wrong derivative for slope
-
Ignoring hinge conditions
Quick Revision Tips for Topic Arches & Cables GATE Civil Engineering
These simple points help students revise faster and score better using Arches & Cables GATE Civil Engineering Notes.
-
Memorize parabola equation and slope formula
-
Always draw a neat diagram
-
Write equilibrium equations clearly
-
Practice numerical problems daily
These tips help students score better using Arches & Cables GATE Civil Engineering Notes.
Arches & Cables GATE Civil Engineering Notes play a key role in GATE preparation. With clear understanding of arches, cables, equations, and tension behavior, students can easily score marks from this topic. Regular practice and revision will help build confidence and accuracy for the exam.
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