Draft

13.1Arches 213

SolvingforH

H=

wL

2

8 h

(13.2)

We recallthata similarequationwas derivedforarches.,andH is analogousto theCT

forcesin a beam,andhis theoverallheight of thearch, Sincehis much largerthand,Hwill

be much smallerthanCTin a beam.

10 SinceequilibriumrequiresHto remainconstant acrosstheearch, a paraboliccurve would

theoreticallyresultin nomoment onthearch section.

11 Three-hingedarchesarestaticallydeterminatestructureswhich shape canacomodatesup-

portsettlements andthermalexpansionwithoutsecondaryinternalstresses.Theyarealsoeasy

to analysethroughstatics.

12 Anarch carriestheverticalloadacrossthespanthrougha combinationof axialforcesand

exuralones. A welldimensionedarch willhave a smallto negligiblemoment, andrelatively

highnormalcompressive stresses.

13 Anarch is farmoreecient thana beam,andpossiblymoreeconomicalandaestheticthan

a trussin carryingloadsover longspans.

14 If thearch hasonlytwo hinges,Fig.13.3, or if it hasnohinges,thenbendingmoments may

existeitherat thecrownor at thesupportsor at bothplaces.

APPARENT LINE

OF PRESSURE WITH

ARCH BENDING

EXCEPT AT THE BASE

h

h’

V V

M

w

h

H’=wl /8h’<

2

wl /8h

2

H’

H’<H

APPARENT LINE OF

PRESSURE WITH

ARCH BENDING

INCLUDING BASE

V V

H’<H

M

w

h

L

crown

M

M

base

h’ base

H’<H

Figure13.3:Two HingedArch, (LinandStotesbury1981)

15 SinceH variesinverselyto the riseh, it is obviousthatoneshoulduseas higha riseas

possible.For a combinationof aestheticandpracticalconsiderations,a span/riseratioranging

from5 to 8 or perhapsas much as 12,is frequentlyused.However,as theratiogoes higher,we

may have bucklingproblems,andthesectionwouldthenhave a highersectiondepth,andthe

arch advantagediminishes.

16 In a parabolicarch subjectedto a uniformhorizontalloadthereis nomoment. However,in

practiceanarch is notsubjectedto uniformhorizontalload. First,thedepth(andthusthe

weight) of anarch is notusuallyconstant, thendueto theinclinationof thearch theactual

selfweight is notconstant. Finally, live loadsmay actonportionof thearch, thus thelineof

actionwillnotnecessarilyfollow thearch centroid.Thislasteectcanbe neglectedif thelive

loadis smallin comparisonwiththedeadload.