Draft

13.1Arches 219

2. Theexpressionforthehorizontaldisplacement ofCis

1

|{z}

P

Ch = 2

Z

B

C

M

M

EI

ds+ 2

Z

B

C

V

V

AwG

ds+ 2

Z

B

C

N

N

AE

ds (13.17)

3. FromFig.13.9, fortheribfromCtoB,

M =

P

2

(100Rcos) (13.18-a)

M = 1(Rsin 125 :36) (13.18-b)

V =

P

2

sin (13.18-c)

V = cos (13.18-d)

N =

P

2

cos (13.18-e)

N = sin (13.18-f)

ds = Rd (13.18-g)

4. If theabove valuesaresubstitutedin Eq.13.17andintegratedbetweenthelimitsof 0.898

and=2, theresultwillbe

Ch= 22:55 + 0: 023 0 : 003 = 22: 57 (13.19)

5. TheloadP is now assumedto be removedfromtherib,anda realhorizontalforceof

1 k is assumedto acttowardtheright atCin conjunctionwiththe ctitioushorizontal

forceof 1 k actingto theright at thesamepoint. Thehorizontaldisplacement ofCwill

be givenby

ChCh = 2

Z

B

C

M

M

EI

ds+ 2

Z

B

C

V

V

AwG

ds+ 2

Z

B

C

N

N

AE

ds (13.20-a)

= 2 : 309 + 0: 002 + 0: 002 = 2: 313 in (13.20-b)

6. Thevalueof thehorizontalreactioncomponent willbe

HC=

Ch

ChCh

=

22 : 57

2 : 313

= 9.75k (13.21)

7. If only
   exuralstrainsareconsidered,theresultwouldbe

HC=

22 : 55

2 : 309

= 9.76k (13.22)

Comments

1. For thegivenribandthesingleconcentratedloadat thecenterof thespanit is obvious

thattheeectsof shearingandaxialstrainsareinsigni cant andcanbe disregarded.