Structure Analysis I

Structure Analysis I

Lecture 13Cables & Arches

Ch.5 in text book

Cables

• Cables are often used in engineering structure to support and or transmit loads from one member to another

Cables subjected to concentrated loads

Example 1Determine the tension in cables and what is the dimension h ?

kNT

TT

M

CD

CDCD

A

79.6

0)4(8)2(35.52

0

54

53

oBC

BC

BCBCy

BCBCx

T

TF

TF

3.32

82.4

0sin8)(79.60

0cos)(79.60

54

53

oBA

BA

BABAo

y

BABAo

x

T

TF

TF

8.53

90.6

0sin3)3.32(sin82.40

0cos)3.32(cos82.40

mh 74.28.53tan2

Cables subjected to a Uniform Distributed Load

0

0

2

L

R

R

y

x

L

wLR R F

H H H F

_

2

0 02 2

V=0

0 02 2

2

0

4

8

mid span x

y

wL L wL LH f M

wLH

wL

f

H

wLV F

H F

Analysis Procedure

_

2

2

2

0

0

02

8

4

2 2

.2

.2

2

02

V= 2

0mi s an x

y

d p

wL x wxH y M

w

wLH

ff x

wLwx

LH y wx x

wxH

V F

wLwx

y L x

w xy L x

y

H

L

F

x

H

H

L

@ 0

0 2 2.

0 0

V

=

0

L

L

R x

L

L

L y

L

M B

wL xR x H y

H y R wx x

R wx xH

y

R wx V F

R

H

wx

H F

General Case

max

max

2 2max

is at is maximum

cos

T

HT

T H V

Note

Example 2Determine the tension of the cable at points A, B, C

2

20 425 0 2

@ 0

1H

M C

x

x

2100

40 425 0 22

@

0

M A

xH

2

2

2

20 425 02

10040 425 0

2

200 10000 0

41.42

xH

xH

x x

x

100 x

2

2 2

2 2

42.4220 425 36459.2 36.46

2 425(41.42) 17.6

425(100) 17600 24900 24.9

36.46 24.

,

9 61.7

36.46 17.6

1

1

50.

0

0

7

0 0

Cy right part

y al A

A

A

C

Al

also from f

from f

V W

H I

x

V

b k

k

V Ib k

T k

T

from

W V

k

x100 x

2 2 2 2max

500 307500 Ib=7.5k

2 2

7.031 7.5 10.280

A B

A B

WLV V

T T T H V

Example 3Determine the tension of the cable at points A, B

2500 30

7031.258 8

H

2

8

wLH

f

HH

AVBV

Arches

Arches Types

Three hinge frame

Example 1Determine the internal forces at Section D

kNA

kNA

F

kNB

BM

kNB

BM

y

x

x

x

xRightC

y

yA

93

0F

86

0

86

0)20(67)8(60)6(0

67

0)28(60)10(100)40( 0

y

86

93

86 cos20

93 sin20

86 sin20

93 cos20

242

242

112.6

58

Example 1

Determine the internal forces at Section D

y

0 25

F 0

25

0 25 (50) (25) 25 (25) 0

25

0

25

A y

y

B xRight

x

x

x

M C kN

A kN

M C

C kN

F

A kN

yF 0

0

0

25

y

x

x

B

F

B kN

22

2

12

25

25

5025

250

25tan 2 25 0.5

50

26.6

x

o

y x

dyx

dxdy

dx

25cos 12.5sin 27.95

25 12.5cos 11.18

25(6.25) 12.5(12.5) 0

D

D

D

N

V sin

M

26.6o

Group Work 1 Determine the internal forces at B

Group Work 2 Determine the Tension at A & B