Analysis of Arches & Cables

By Sachin Singh|Updated : December 2nd, 2021

Through Champion Study Plan for GATE Civil Engineering (CE) 2022, we are providing Analysis of Arches and Cables study notes and other important materials on every topic of each subject.

These topic-wise study notes are useful for the preparation of various upcoming exams like GATE CivilIESBARCISROSSC-JEState Engineering Services examinations and other important upcoming competitive exams.

This article contains fundamental notes on the "Analysis of Arches and Cables" topic of the "Structural Analysis" subject.

Arches

Three Hinged Arches

(i) Three Hinged Parabolic Arch of Span L and rise 'h' carrying a UDL over the whole span

image001
image002

where, H = Horizontal thrust

VA = Vertical reaction at image003

image004 Simply supported beam moment i.e., moment caused by vertical reactions.

Hy = H-moment

DS = Degree of static indeterminacy

BMC = Bending Moment at C.

(ii) Three Hinged Semicircular Arch of Radius R carrying a UDL over the whole span.

image005

image006

image007

image008
Point of contraflexure = 0

(iii) Three Hinged Parabolic Arch Having Abutments at Different Levels

(a) When it is subjected to UDL over whole span.

image009

image010

(b) When it is subjected to concentrated load W at crown

image011

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(iii) Three Hinged Semicircular Arch Carrying Concentrated Load W at Crown

image013

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Temperature Effect on Three Hinged Arches

image015

(i) image016

Where, Δh = free rise in crown height

l = length of arch

h = rise of arch

α = coefficient of thermal expansion

T = rise in temperature in 0C

(ii) image018

Where, H = horizontal thrust

and h = rise of arch

(iii) % Decrease in horizontal thrust image019

Two Hinged Arches

image020

image021

DS = 1

Where, M = Simply support Beam moment caused by vertical force.

(i) Two hinged semicircular arch of radius R carrying a concentrated load 'w' at the town.

image022

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(ii) Two hinged semicircular arch of radius R carrying a load w at a section, the radius vector corresponding to which makes an angle α with the horizontal.

image024

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(iii) A two hinged semicircular arch of radius R carrying a UDL w per unit length over the whole span.

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(iv) A two hinged semicircular arch of radius R carrying a distributed load uniformly varying from zero at the left end to w per unit run at the right end.

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(v) A two hinged parabolic arch carries a UDL of w per unit run on entire span. If the span off the arch is L and its rise is h.

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(vi) When half of the parabolic arch is loaded by UDL, then the horizontal reaction at support is given by

image032

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(vii) When two hinged parabolic arch carries varying UDL, from zero to w the horizontal thrust is given by

image034

image033

(viii) A two hinged parabolic arch of span l and rise h carries a concentrated load w at the crown.

image035

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Temperature Effect on Two Hinged Arches

image037

image038

(i) image039

where H = Horizontal thrust for two hinged semicircular arch due to rise in temperature by T 0C.

(ii) image040

where l0 = Moment of inertia of the arch at crown.

H = Horizontal thrust for two hinged parabolic arch due to rise in temperature T 0C.

Reaction Locus for a Two Hinged Arch

(a) Two Hinged Semicircular Arch

Reaction locus is straight line parallel to the line joining abutments and height at image041

image042

(b) Two Hinged Parabolic Arch

image043

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Eddy's Theorem

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where, MX = BM at any section

y = distance between given arch linear arch

 

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