Draft

Chapter 13

ARCHES and CURVED

STRUCTURES

1 Thischapterwillconcentrateontheanalysisof arches.

2 Theconceptsusedareidenticalto theonespreviouslyseen,however themajor(andonly)

dierenceis thatequationswillbe writtenin polarcoordinates.

3 Like cables,archescanbe usedto reducethebendingmoment in longspanstructures. Es-

sentially, anarch canbe consideredas aninvertedcable,andis transmitstheloadprimarily

throughaxialcompression,butcanalsoresist
exurethroughits
exuralrigidity.

4 A parabolicarch uniformlyloadedwillbe loadedin compressiononly.

5 A semi-circular arch uni rmlyloaded willhave some
exural stresses in additiontothe

compressive ones.

13.1 Arches

6 In orderto optimizedead-loadeciency, longspanstructuresshouldhave theirshapes ap-

proximatethecorespondingmoment diagram,henceanarch, suspendedcable,or tendoncon-

gurationin a prestressedconcretebeamallarenearlyparabolic,Fig.13.1.

7 Longspanstructurescanbe builtusing
atconstructionsuch as girdersor trusses.However,

forspansin excessof 100ft, it is oftenmoreeconomicalto builda curved structuresuch as an

arch, suspendedcableor thinshells.

8 Sincethe dawnof history, mankindhastried tospandistances usingarch construction.

Essentiallythiswasbecauseanarch required materialstoresistcompressiononly (such as

stone,masonary, bricks),andlabourwas notanissue.

9 Thebasicissuesof staticin arch designareillustratedin Fig.13.2wheretheverticalloadis

per unithorizontalprojection(such as an externalloadbutnota self-weight).Dueto symmetry,

theverticalreactionis simplyV =

wL

2

, andthereis noshearacrossthemidspanof thearch

(nora moment).Takingmoment aboutthecrown,

M=Hh

wL

2



L

2

L

4



= 0 (13.1)