dr.attaby's sheet.2

8/17/2019 Dr.Attaby's sheet.2

1/14

,.

i,

..)

-Y'>

s,--n11

t\.

\i{o

Ain

Shorns

University

Foculty

of Engineering

Theory

of Structures

2"d Yeor

Civil

2007

-

2008

heet

(t

-

s)

For

the

shown

structures,

drow

(S.F.D

ond

B.M.D.)

using

the

Slope

deflection method.

10t

F--B

m

-----+-3m

-*-sm

-*

*_3m___t___6m___{

__

6t

LJ--r--9--)

6t

l__s_l__sm___J

1

6

t

I

4

+

3

.t

3

_{

12t

I

I

6

l

l2rn.t

t/m


2/14

Exomple:

t-Bm

-*-3pn

-l-Jp

J

Swoy shope

Fixed end moments

48 m.t

10t

__

;

11.25

m.t

"#)

*

M

:

-48

-c

M

:

11.25

b-c

-3tl

A

64

EI

+

3G

A

xF,

_

o

Yo

*48+"'O-Yu:0-0

y.

:y

*58

DO

f__am

_f_3m _+_rm

_1

YoI

M

o-"

(

a t/m

Yo

For

member

(o-.)

By

o

+6x8x4-M

:0.0

o-c

M

o-c

yo:

;

-24

:

-30-0.005859375

El

A

z


3/14

For

mernber

(U-.)

Uyu

-10x3-Mo_":0.0

M

u-"

Yb-

U

+5:6'875

Yb:Yo

+58

+

0.013BBBBE|

A

6.875 +0.01388

El

A

:-30-0.005859575

il

A

+58

El

A:1

069.714285

M

:

-98.142

m.t

o-c

M

-

+100.39

m.t

b-c

98.142

m.t

100.39 m.t

+__Bm

______t_Jm _*_Jm

J

5


4/14

tM

b:

0

0.91

66

0"

XF*

:

0

-0.166A

60

(1)

EI

xo

€

-0

Wh

ere,

bo

-T

I

6m

-[Muo*Moul

^o-L- 6

J

X

o:

o.i

66El

q

-o.o55El

A

xo*

v

ob

o.166El

6t

-o.os5El

201,4

lt-

-r

bLt

A_

748

EI

M

OD

M.:

DO

M._

bc

-57.5

m.t

9.6

m.t.

-21.65

m.t

lr

21.65


5/14

Exomple:

Drow

the

B.M.D

for

the

shown

frome

a

t/m

I

4t

I

12m.t

72m.t

)

/A

b\S

t

Mob:0

+

o

+

zyob-6*

^

o5-l- ob

-

.5*

^

,'iuo

M_

bo

M._

DC

M

oo:

-72+

12

5

Xs

o

rA-u


6/14

Exomple:

.Drow

th

e

B.

M.

D

6t

for the

shown

frome

F.E.M

l__._+_em___]

.T

dL

\-/

j

\-/

30.375 m.t

):

w)

V(u^

m.t

'+

40.5m.

t

.

r)

/^,

M_

ob

M_

cb

M

ccl

JO,J75+

3x3

f-t

0

+

4+0-

bv

rl

0

+

2-;- 0.

+0

3*^

$0"

*u%

*u%

_

dc


7/14

EM

c:

0

1

.667

0"

*

0.1

66

EF*

_

0

M

A

.+M

=0

b

CCI

-30.375

(r

)

EI

j

M

ob

cd

l

m

l

c

xo

X6

v

dc

xq

*xa

-0

Wh

ere,

x

o

-[tdo

]

Mou*Mca*Moc

El 0

+A.4166

Et

c

t,

o"

:

-23.97

v

-

[

M

.o*

M

a"

I

^d-

L

r- J

o

-0

A

-0

(2)

il

a

_

57.531

M

ob:

4.79

m.t

M

"b:

6.39

m.t.

M

"d:

-6.39

m.t

M

o":

1'6' m't

v

40.5

B.

M.D


8/14

Exomple:

I

4

+

a

___t

l__._l___sm__J

lJm

)

52m

)

.t

-1

J

m.

6m.t

lu.

t-

)-

6m.t

9m.

t

)

M

dc

M

cd

M:

ce

M_

ec

M

cb

FI

6

+

2+0^

bv

-6+

+*o^

bv

o

+

o*u.

+6+-^

Jb

+o$a

-u fo

-

6

E--l-^

A

tb

23

+

r*u.

+

,+0"

X6

d

/,.///

SWAY


9/14

XM

c

2.41

XF*

X6

_0

Er0

c

:0

-

0.208

El

A:

-17

(1

)

M

xe

a]>

ec

I

m

_1

xe-

B

-0

e

Wh

e re,

\,

I

M

""+

M

"J

e- L 4 )

X

":

O.375El

0"

-0.1875E1

A

xM"

-g

M"o

*Mo"

*

BxJ

_

6xo

v- [M"a*Ma"l++

^d- t 6

J

v

ce

M

cd

\\\\\

cll

Lq__t

l=J"

+4

x,__

t_

-(2)

dc

X

o-

0.166t1

0"+0.05581

-0.2083E10

-0.2+3

EIA-

c

A

4

El

0

_

-7.89

c

El

A

M

dc

M

ccl

M_

ce

M:

ec

M

cb

_

-

9.696

1.75m.t

-12.876

m.t.

-4.25

m.t

-.309

m.t

17

.OB m.

t

17.48

12.87

/l

I

I

I

I

I

7

.75

B.

M.D


10/14

EXAMPLE:

6t

o

r/^

12t

I

ton

:

,6=

r

4.5

sin

:0.

B

3

cos

:0.6

3

As-

A

Az

-0.6

Ar

-0.8

m.t

A

A

^

28.125

28.125

m.t

\-/

\e-l

F.E.M


11/14

M

ob:

o

*r*

ob

-6*xo.BA

M

M

bo:

o

*

aoa

ob

-

6*xo.B

A

.

_-

28.125

bc

.: 28.125

cb

+

12%u,

+6%

o"

+

18

t[ uxo.6

A

+

6

51

u'

+

1z|

o"

+

18

s-EIu

xo'6

A

7ru.-12

s+;

^

7,

u.-

12

rElr

o

M

M

-:0

cd

:

dc

+B

0+4

XM

b:

0

2.266

0o

*0.8

0c

M.

+M,

-0

o

Dc

+0.0586

A

:

^

8.125

EI

(1)

IM

:0

M

c

0.8

0o

+2.660c

+M

+M

,-0

cb

ce

co

-0.02133

A

:

re.875

EI

(2)

XF,

:

0

1

2l

I

-e

o

t/m

6t_

xo

xd

d

II

Xo*X

6

+6

-0

(3)


12/14

bo

l

m

l

b

For

member (ob)

6x o-1,'1

bdlM

ob

6x

o-

0s

-A.2GOO

A

For

member

(.d)

(r)

M

--0

M"a

*Md"

:

Then

we

hove

6x

6*

4.5y

a

to

get

ya

first

M

bc

(

yd

-3+.5*

[

Mcu*M

uc

7.5

.L/

o"

_rl

J:vo

v

6

t/m

M

"u

54

m't

121

I

\

(t-

t

'v

)

\j--

22.5+

[

M"u+Mu"

1 |

i.^,

1'v

'L--75-J

I

l12t

T[/,*r*

14s+tU#-J-(r..

34.5+

[

M.u*M

o"

L

7.5

lz


13/14

Another

woy

to get

y

6

dc

lv

7.sm__l_4.s,._'l

For

th

e

wh

ole

from

e

D/

;0

6x6*

6x7.SxJ.75+12x12+\A

ou

*M

ar:12ya

yo:

2e.oo+

t

U#*

t

(B)

sing

one volue

for

y

o

from

equotions

A

ond

B

in

M"a

*M

d":

6x6*

4.Syo

equ

otion

leods

to,

155.25+0.6(M

u"

*M

"u

)*6xo

_M"o

_Mo"

_o

6l.o:

-1.44

0u

*0.10

0"-0.6576

-155.25

EI

substituting

equction

(r)

ond

(il)

into

equotion

form

6x

o+6x

6

*J6

-O

(using

eq.

A)

(il)

(3)

in

the

-0.44

0o

*0.10

0"-0.923n

:H.ta

Solving

(1),(2)

ond

(3)

we

con

get

(3)

oo:

'+f

o_ €1q

cLl

_135.2

EI

A_

t3


14/14

Mob:

f

o'

Mui

?q

M

:2.4

+

?u^

''cb

5

D

LFI

M,

:-2.4

+

-i

0o

DCJ

t

Mo:

o'o

oEt

o,

-2.+

+

5D

M

+M

bc

bc

4Et

0,

5D

El

0b

:i.5

M

:

0.6m.t

ob

M

bc

M

bo

M

-3m.t

cb

E.IV.

D

dr.attaby's sheet.2

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