Advanced Methods of Structural Analysis

Appendix 579

Hingeless non-uniform parabolic archesIx

D

IC cos

̨

;

D

454

IC

A

C

f

;k 2

D

1

1

C

a

A

B

C l

f

a

Ix

HA

H

B

RA

RB

M

B

M

A

Ta b l e A. 2 0

Reactions and bending moments due to different types of loads

Loading

R

A

H

M

A

M

B

M

C

1

P

l/^2

P^2

1564

Plf

k

Pl^8



5 4

k



 1

Pl^8



5 4

k



 1

Pl^8



1



5 k 8



2

P

ul

P

2 .1

C

2 u

/



D

1



u

154

Plf

(^2) u

2 k
Pl
u

 2
5k^2
u

 1
Pl
(^2) u


5k^2


 1
u
0:5
Pl^2
(^2) u
^1

5k^2
(^2) 

3
q
l/^2
1332
ql
ql
2
16f
k

ql
2
192
.11

8k/
ql
2
192
.8k

5/
ql
2
48
.1

k/
4
j=
1

6 EI
C
(^2) l
152
EI
C lf
9 EI
C
l
3 EI
C
l

3 2
EI
C l
5
D=
1
0
454
EI
C
lf
2
152
EI
C
lf
152
EI
C
lf

154
EI
C
lf
6
Increase oftemperature
t° t°
0
454
EI
C
f
2
̨t
t
152
EI
C f
̨t
tk
152
EI
C f
̨t
tk

154
EI
C f
̨t
tk
aI
;AC
C
are moment of inertia and area of cross section at the crown
C

. If axial forces are neglected, then



D

0; k

D

1