solution a

6 vDm Biolo

seog
↑
3.27 t ↑12
13.77 22.27
U.27

C42
* 134.7

6x8x4+15XY

Fy x6
out
#1242 Eg= b 1.
7] C
L↓42
Przil -bat If 1.) E
Af
f
*[eB
m
= 0
LE
↳
-> 10.55
Lao
↑3z
Ie** MEge vsipuz
pol
I to Co
blok A
32x3+ FEMOB +FicDLxIT=6XTX2
Ecosd

↳ <
No
* = 5/
it
-

↑ 15
F=18,7

N 1.
7T
⑧
12
V me
↑f ↳L u ↑

!
F
I
~ d
↑
↑

B
O 4. 17
&
pet This
-

&

I
I
I cott ↑

28 3.5T

~
is.7]
 I
wil nurs 50w
- -
I - -

in
t
7

#BF
= 26,59

[My =

i fyx Dyx7 50x4 70x3

= +

i
-
(Fy 7Dy 445
+
=

↑ &
*
Dy ky
=

85

>
+
+

-
->Dx ->

190
504375407
-
=
=

↑ Ey
Dy 4505 Dy 47.5
=
=

* 747x7-50x 70X
-

FAF2,71

↳
on
In
the
10.0.
 T
p7.8 c.
·
<f s I+
+7of t

alterat os p
enzs75.2
tt

zetinbo
BA:-RCEhd-d
27
eln InD ~

130.27
=

bon d fencei
-

MAS
-25527 ~ 189.2

M. isa ↑Var
-

↑VAn
209.5
-

MBA +
MDC = 8.. (1)

S
Mox: 2EF (200 18x-=/d) IEEmbo May=
LEF
(8n) + 23
12

FEMoA=
-160162x6=-2 May= 255,27

of-</p) he
168, 7T
MCD= zEF (8y) -

(2E+ g
MBc=2
EF d

#
FEMbc=25X9=160,7 Vayx12 +209.5=160x6R55L7 e

↓ UcoNESTE2wXSn5toe
0
1) - 168.7f
EF En-238
LEF Osois
+ Ar +
=

"lettress
*
 rate isa E
roated &B

of =E
↑ X

A D

Are you motSttthgeSma

evrld mas

· i
8..
MBA + Mdc (1) f

EF fr. 67. LEI Ay tET8z

=
+ 66.67 =

Mcs+McD = 0 ...
(2)

Moz:* (8s =) ·
sio. +Y=-o
exis
EFEC +EF oy-66.167 LIE
+

/ 28s+Ec) 2x20
LEF
MBc= +

A
66.
67
-
o+b 66.6
=

McD=LF(28C+8n) - 66.B 7 -

22.T@
2 S
=-233.0fT
Oc==107.9
(8) O
zEF EI
-

Mcs= Eg=
 ⑤
⑧_
*
-

I TK 1dot
g redfred

I
-for
B= 0,07m

8x10"
nowi
stmer beon eas = 1
26.67
resa+mose =

(283EA-3P)
-

FErin
Gopios
(1)
2
EF A UBc
mpA: +
·
v
Ba
+ = 0 . . .

-
10 x 16
=

MDA = E1 (80 +
0.09/8) -
26.67
12
P = =
0,07
H
3 <
1f 6

M3c= (8n-P)
f

i A
=
+
FEs
= 0,04

MBc:EFC1.TAy-oon
6

EF (2.580-0101125) -

16.67 = 0

8g = 3,58x10" rad

May:
LEE (28A+4.40x
I +0109) + 1667
 *DD
PPC volw
me

It + 2
hi

Disretnature
-
fee
imme L
idG
Sar

~
MyD
saf -
MpA+Myp +24 =

MBA:GEE (2ED) +FEm OLT #

#
<

↑ if-
by
Mag = P

-> O
(83) medit
of
+FEM 12.02
MiD=LEF MacISEI last total
=
me

I1Do, 7080)
-
54 +24 =
*:
zot
= -

#3 = 38.46 / EF

enter
G
M=B= IEE (As) + Th = 62.55
forzurem S

f it 3 t

I f
h & Sar a M

plus 309
ngh 15F

↑
gat
t

~
b15j P "Ornot 12

13.73-2x= 0

= 5.715
x
 t
says
↳M
↳ I
->

ow
-> MextMpaze

fOEfozD
A

i
LS &
L

↑
~
Bu
MBL -
-
S VCD

MBA MCD
Mcr3 +Mcg = f
S I

* ⑦MAB c
vcs +UB = 6

chee
t
-An

MBc=EF
3
(283+4C EF
(zen EC +Ex+f
+

RCD+RDC
VCD =

A8
278s +88c 0
18
+ =

MBA: +
LE (283+
Mon MED
VDA = +

mc==*(2e2+)
128283) (28c +Ee +8 ot
Mas= EX -
O 12

6Ec +1283 + b
3 = 0
 *D=0,02
attrohelped
a
*

2)7 Ax

#
 behaldowo
Support Dsettes
A staff
down on Een->
stiffness
using disturbutter
the moment Member AB;
LET
retod find the elevent

E=
([I]
EI
forces KAy
E= 100Kr 1m3 and
body event
diagon
= =
over

= 1600 Ehmm
I
FEM
Member BC
M= 16+3 =22K0m
3ET
A ⑬ C
M3a=-16+6 = -1 m KBC =
(*)= /n =
0, FTEE

I
1
-

I I
* 8 iF 0,77
Mic 6-6=0 b0m
Distribution factor.
=

FEM 22 -

10 W
*

*
ist. 51 4.3
c >
st
DAReTTI-EF
W RE
com 2. 85 =
of
by 6.3
*
5 <v)
23.8T
-

t A

-f DFisc: se
AECETEF
~

m0r juel- 2.97

3 px 1xftty G
4. T

↓su 9.47 G

In
st 9.4)
↑ 5.02 ↑ 1.97 DAs =
DTas=) FEmdueed
5.8 FEM due to Du
↳ TrHz 13th
a

-
-

~
*
cm) state-ree est Pas (L+9)=6lr
ELI
m

Man*: zEF2 )-(**)): burn MBt=

S
1EF1-801) :- bur m

Ex. 3.3 GYN

MBA =
m
 CE 383 Structural Analysis
-
-(w)
Fall 2022-2023
Assignment #3

Due Date: November 20th, 2022 – 5:00 pm

I
Q1) Analyze the given structures using the slope deflection method, sketch the deformed shape, calculate
the support reactions, and draw the internal force diagrams. Assume that all members are axially rigid
and have the same EI. I

I
I
↳

I
I

⑰
o

I ↑

·
Q2) Analyze the given structure using the slope deflection method and calculate the axial force on truss
member CB. Assume that members ABE and DC are axially rigid. All frame members have the same EI and
EA of members CB and DB is equal to EI of the frame member in magnitude.

Note that member ABE is a continuous member. CB and DB are truss members.

Sign Convention

Assignment Submission

• Submit your own work. The improper collaboration will be penalized.

• Submit the digital version of your assignment to the ODTUClass, CE 383 All Sections
webpage
• The name of the submitted file should have the following form:
NameSurname_ID_Assignment#.pdf
e.g., AliYıldırım_1234567_#1.pdf
 80
⑧E
=

01 Xp= ↓ due + -

off
Los
Ar
-
·

symetry
BB 8E
-

=
fil
8
-modified
↓ I

#
NX
00 En N
I
red
120)
=

e
↑PzE
NT MEC Member AB 25xzxy" 22.22
=

Gaze
~

(aff+Xm .
+
++1
-
Up 0) FEMA
VEL
MAR
1 *8p2
EF
(2 >
E I(83 b) 2222
- +
+
= +

↓
=

VCD

↑
↓
->VyA
MBA
2 ven - VEF
MFF
(28B 8(7
MCD
MBA EEF
=
+
-

34) -
1.1) =

EF(28p 9/2)
-

1.
Eslaw
+

->
25a

=E(283 8)
Member B C

xMAy M3
287
=

(283 81
+
-

3() = +
+
6

#
*
N
I
M(z E7(y(281 0B) 64 Member EF
A +
-

D
=

(1) Member CD FEM

EEF(28e 8( 34)
e.
nyc
MBA MEE
=
-

=
+
- +

sEF((y)
F
mc =

e
+

Member
)
CE
MTF 64.37
E*(28z
+ 87
=

- +

MCE 2E1 2xc

287(2fa 8y 0).
= +
= +

mrz
E
= (28- 8E
1) 22.22
=
+
-
-

2EF
8D
=

I
 201- ->
A
<-1 souly MDE

throw
#
1 + on D
->

at
t

↳8.
**
-

T
=
-

I ↑nou
zm
-

On D a
&
&|

adfind
M =s
A ~ Q

5
m
↑
2def. mifusa

-
Le
dimessingan overse
5 E
ig
Way =-135
·

MBE = SEF (8B -90) + FEMsa

5+HFE tOES
#

ti f**->Y).**
ostfeitfo
f of
t

mas=e5 (280+x+)

MOB=LOFORtbAE
 Ba
↑D1 jur

->ote I tCE aptottAE

8 *
ther 1
Cv3
55

It
* I
-

=>

it -> 10
If
↑
I.e
~-
-
a

us
i

A
* *
*
1
&
mit PKNM
? If

& aP
&
up
&
& 1o
x
-> DI D5 T
f
*
if
of lax =
-
Ds[D2 ↓ xD6
x
=0
z = s
↳by C

I
(lox-522)
&ee=
-hoto
E
T &ze=ef -

2
·

no
o

EF7-40x45XER
&
E= &

"If 5X --5xresis
2.
EF)-10x + +extfel
8 =

IfEX-Ix"+xtce)
=
# U o Id=
fo &

D2 (1.31
-2
=
g
=
 -Eq modfire
NFEe
Meat MetMyc
= -

MaBt MCD -

-meated
=

Et B
*
t
( MDE
A
a

↳
C
M32C
c

to man
-A
↳ Grece -A
~

~Pl -
DE
MBA=
LEI 183-P) FEM a
+

↳roofed85
pe
 E T

Member 2D DC

asa
D
↑ ↑ DY ↑D2 A
↳xf ↓
Ta ↳is
↳
C
B
D ↳
DS D5
FBA
0
2 MD =

FLEXL+ 5
B.d =
0
y
= v

15TEE
FastFcE=30
x

A 6T
M

12. 12

crpeta
5-6X
5 X :a
og/dy: B/EE

P
↑

*
A
t
s
C

OEDEE12+
25Kr
blowh )
-3x2)
· 5 s ->

Mx
↑FLE Gurl
↑
12
↑ '
-↓
Bi it isto the It S

&flax 1ex
-

↑ ↑ ske -

6x -xtc
f
i =0 t
↑ EBA=5T D 5
3 ·
It +

st2+12t

i
I

Member BA i-y=v5x1=z=Dc
⑧ eff-6x +29e** +x+2)
-
x
-
↑

-
3
1) I EI

↑
19DY 3 12
-

x
-ITTE
=

3
=5 Dy c=- 25 (=-12
=

↳in DS X = I

=0=dydx
x
=
-

LAGEE Dc= T delax e y=b/EE

(5x.exi
de E = =3
x
dyda: -IHE DC:- R/ET

x'+a)
&of (EX
-

3
:
Pee
(EX'-*taxtal - c=

-> c =-22.5
-
5

3
 Af Member X (
Eze
=
23 X = f =
3
SML = 0
By =
144

A D
↓

↑cy=24
*
yx4+Eg
x12

168
= 864
&3 = (24x-Ris x =
b
= uh
↑M By + Ag
=

↑ By: 1944
(1247-2x+c, 21=
1728 /
&de= yt
Ag

offere
D D6
Di
((x-+cix+ce) C-192
&
↳_ E
# 3
=

# *
a

gt gh
neald pule per * 0
Oy Ida: ITLEE
=

If +
A + + LAY sd ↑ot It

oo
*

i er
↑ You
↳
dyidkE54ly
x =

Y
x 835
Member Ba
=

Member AB x
Py=o ·

122x-6xh)
DI ↑D5
Az in
delax-R/ET: I
x

u
by
=

2561F
deldx 112x2-2x39) io di 1d=-
*

D5
18
=

g==
0
]
=
x= 0 =

(TN-I"+ax+p) &
3z=1)-192+72x-6x
H92X+S6X-ext
2 =

& G = &

dy/K
dolx YE
x = 0 =
0
=

8 dyidx=-254E5-D2 =-253107
&"+ax142)
x=

IEE (-964 + 12X -

3 =

4=-256
 (ioins-11(8)
3 Member BC
B 3
C
10x6x3 =
6Af
↑

10
&
↳↑ ↑
-
D
- -> Dy
Pe
1003dse
Eas Y D5

-a
*
st To &

a *
-> 0 ( 6 (
30 y

doe
=
C
D3
x x= =

gf y
=
=

D
now By = 30
50 <12210
↑
+0x-x
de= (-100
a
↑ xo
dyldx
Ele
By-39
Eze
A
-

4 so
dyf
(-100x +
154-Extal x= 6
didle
↑Az =30
⑱ 21 3= (Et
(-50x
+54-Etaxta) by
↑ jo siBIE 557/E
at0 (x)D d Member PC

~noag
↓

De
45
bdof-

↑
4.
Dy

xM i ↓ ↑
~oole x =2 dydx:
f
* I

0
-> D2 =x
x
y =

---
AB ⑧ 1015 A (50x
Member
&) I
i 1 &
PI de f =

& 5
g2-5BB/EE
0
x= 22=
+ c)
* *
Ex
↓D2 ↓Dy Bldx= YEI T25X2 <=-317
x =5
dylax= 21%Et D1=05/E
fr E50(3x =

+R y =
YEI (5x+1x+2) g= E
c = 85 D2=
d /dx=
YEE (150x-25X2+ h) aelax 1E=POX Ph
=55YEE
x= -

c:-181lis
3 = lzz (75x2-25T ) + 21x +22)
 fatter
2\r

& MA = 0

proper
12 + 18:
1Cy
c = 5 I m

Ag = =>

I 5

Tag ↑ cy

ii)
DI D2
& 2S
& x= B

Echetc
A B
in
122.5+2)
Member AC 31X16 *E

(-1(x-2) ( 18
zz f C) (
- =
=

+12)
;yn)
7-3x
30.5 +3x, +12 19+3k>
Ef(***+12xtcl
=
8
dx
T1.5=sk--4)
3 =
Gt (* +6x"+xt22) 2x16 yee
+c2

0xx 1] x= 0 f
108 + 621 +2 = 0 c2 =-22.T
y
=

fg "ef'x c -13,25
=

cy= 8

& 1+) as 3, 75
=

3
= HEt(x) +csx +c)
 -B_) rA &4) (3)
A

out* I
on.
⑳

warped
I
**s +
=

-
+

i
&modified =
1x
D
free-
+

- -
Or
↳mes mes ⑮
4 +
+

(2)
+ +++
↓RBA 2
-> mc
VDA VCD
-

VBA + VCD = 100

-
maRas +mcD+Y +
0
mas
* Max + Mco+mc = (2) 225 =

u
I
-
MBA +

MDc 0 =

(3) 10
10 -
u

Member AB
y=
-

b/, Member CE

-225 Jet
Man
2,(80 31/) McE BEI (EC) 18 x102
= =

0
+

+
+

(2feteif-=
10

"oswo)-
-
-

0
man -

(27 3/10)
+

MEL=GE
45
10

Member BL Member (D S 475 13/10 0

x) id
met(see
-x
4(2+x
=

4(28 0D) e
Yarn
+

mc
=
 <x+ D Member (D
0

C r

⑦B or

modified
I do f
Max=SEF (8c +
p)
↑

othe *

-Biale
M
↳ goe T

2 mez ~S
~ crs Mxc+Maa = R (I)
MDAT Vasa MCD ->
0 (7)
Mcrs+MCD =

->
Med VATVcD = 0
(3)

of
cam
& At

Member AB --
(8n +8
MAD:
LEF
Me:
IF (28s+301,)
member BC
05
bd P=0.00=0,00625

LET10 (280+2e-3x10006it)
MBc = +96

Mc3 2511 (152+8y-3x10,00515)) 36

-

=
 Member Ay ↑ 1D = D/6 Mender BC A ↑

F =
-

D/p
LEF (Er -1D) Mrc=1EF (s +8)
MAn= + 30

MDA:
*I 1270 12 heFOY-bED tRIES TED+OF
+
-

0B_) ↑
A
1.1283 -

0,11379b =-30
St · #
I
modkin

EPTEetCrostoftRo-joptErso
e
o EFP-EE
for
am not
ver

fist
f
I I
E 0,0701 =
0.11979 8m =-
13,75

59,5"
*
B= /EE v
-

o
W
* =

267,350/ EI
-

MontMDc =
0 (1
Tex +Uxc=VgA =
12)
PXOKEl +
Msc +40
(Mustmon) 0
-

* =
Fr x6
x Fop = DxO/EE
0.1 EF 6
 (1) El8x + 1.8+E18D +05 ETED - lEI8DtiTelEp #135

12)EIOD +O5ET8x +EFfy + 3 75 EFfy =-$8

2.75EFFy + OWEEEx=-58

①R
-

HEIES-EIOD:#2
EF53=ME
fr E
EDTTF
tr

IET (p)
I MD: + 13.5
womped
P T
I t
&R

Paper
b
↑

&30
DiLEF

= 2
=
Y
L28D

(28r+83)
+01)

-BizetOnToEEE
Inagred +18
f
icrl-
Upc=
IFF (s 1
ir- Imet p
MBA: (83)
met EI
names
↑ pol

-
↳ f
->

↑ DA

MDEF MDB = S

Mootmpc +iDA= 0
*
 *E
o C
asic
sprey A
Ac
=
- *E *
*Lodfed C
#
E ged
*

F
1def.

↑Y
-..........
up wir w/ o

Fsont
Ap = 0
18
↓
N

-S
14
s'mce
-

-
=

Myc 00
mcb
(et
0
+ Mck * jozn
=
=

80 ·mc

3
80 the

(x)
mcn =
-

0x2582+ B7.3 0
=

OC
&c 021.T70
3
~

&e
= =

MCE F 2E+(27c + bx) + 53.3) t8

-abmcx 45
c++12+ yb (q)
5x 4B
·(-
1x
=

+
=
-

+
=

-
 A
= >

↓ 10 MDA ↳s0kN. m
f ↑ ↑
o
ene
-

Im I
↑
* D m

nodged On MDX
VsC
->

1-
Cx + 1 = -

K
-

152m

3-
2. dof
(1) ReA+Mic=38 & <x= MCStMDLUT
-mar 6
1 Ho 1 Ho

<Ex

Member AB

JEF/S (8n)

EfOp-GEIDEALTs=-EreTetTOTE
MoA =
-

11.25 EIOD
&

EID
*
=JO
G 6

MBc=2E1/6 REs +
317 + 11.25

mcr= 2=716 <8p+1)-11.25

Upc 1, 5
Mectar E= @ &or =-
=
+

8y = =0.75
 ~NM4,1(MDE+M=
an
&B -> D &
->I 3e

I Y ·4
2 C
I) matm
(1) VBFVDE
3
+

=
0
=

-> -> VRF

VBE
MCF
Metmet
MBE

↳MED ~MFL
it A it A
D

51P = -

4/5(1) GEIO+deID
+ +REEL
Member BE
+2E10, +hE 3 =

5 36
(283 1)
Mb
=
+
25

220008y + 1600D 5000 =

+
-
40

Me:
2F (*1 + (t)
(2)) +

6E +
42 + 5406- 45 30 0
=

·,
+

Member BC G 25 36

22000 + 1600 10
+ 50008y = -

Mb
(2+y 0
1) 45 13) 6EI ILEIA+GEIEL+REID I
=
+
= +

+
+

25 125 25 125

Man
(2f+ 1) 45 3600 y + 3600 c 2880D e
=
=
+
-
+

Member (F
5
0
+

=
-

D/y * =

-13/612008c
=
-

31/1200 1 1/288
=

D 0,003472
2,F(28c 5) 0,00227
=

9,000507
-

McF
-

= +

Mr 28/5(fc
=
+

3)
 A

n**
-

BF

v
Dist

kA
3EF, k3 4El, kB=3E5
=

Y 3
200x280x10
DFBA 3x
Reg
=

6
0,163
=

200x200x1e"(8 1)

1
440x10 200x1

3y
+
+
x

x
+

200x NOx10"
DFBc= 0,326
=

200x200x1e"(8 1)+ 440x10 200x1

+
x

DFBz 1
=
-

10,326 +

0,163) 0,511
=

1)rm)
interle
5
-

i is
I
2015,
it a
-
9x1x2(5)
9x
+ =
- 2x12
5 49
=
+

-
 "f koolm method Distributia
Use moment disturbation
factor
·

·Draw

C
FBD and moment diagrams 1
i 1) FAz = 0.0
-

bu. Yo ·
E=20050a Trbc=280x103 Isp=740x183 3x100x18/ 6000
A DFoa =

e
TX28oXIo6 FxGhox
t glo ex20x180x86

A B D
#gun a 600

I irinicisa I I
is W
toxl
0.326 0.51)
D
1m
DE 0, 163 -
s

# -bo
=>
FEM (DF)xB=)
DM DFRc=4x200x18" 1200 = 0,326

com 17x106
(D #cB=-
Due
P

Total O DFay =
3x100xunox04000 = 0.511
A2x103

~epim ss gel com

Y s
~" FEM's
ustule
I
~

Re
|\

You we ↓ "stal
102.52
ao-the come
a
t
B Mos*=-RXbT
8
= -
282.5100m

(S)-enFle 177.30
C80:74

11.2 2
↳Bes C
M:
EXLI bowt

EMMB
Nc =-69 bo m

Es
↳

msp"EKK=gr
N

157M
*
t

Muze, hel
 B S D

usfitpoit e
DF I

C
*
FER
cor
emitic,
2)
-

A
D)is t 6.25 =
6,22
*
-

D
5
&difed &
magied D

tal -
18,75 28, 75
-
45 y8 ↓Howl- Lo
zourv
5) (
bE
d).
I
↳ *

m
↳ D D

EF
kDc=EI,kco
=

& FBC= sEt/c = 8.5

2xTET /
6

1) Fcp =
0.5
 A B C

DF o 067 0.3) L
EM
* 10 s 80 170 ⑧

D)
is t -
167,5-0715

10,000
m Com -83,74
-1000
m

total
16.77-871 8715 D

KAD=
GXEl Koc
SEE
=

EF
DFoz =
= 0,67
EI+EI

DFBc=0,37

FEM's due to loads woul

GB deK 15. 180

FErr's due to settlement.

mAs:I13x0000) 4-pheRec=set1-0000
Ye
gown
51 on
=

.
.
.

.
10,000
MDA = 90kNk
 KEC DFcE= 3E6 ⑪Bc "16EF
L 0,43 0,76
= = =
=

** (/5 +"/s) (916+3/s 41s)

# +

kc = GEI
G Fcm =
0.57
1FoF = 1-10,56 +0,36)
knD =

LEE D) Fob "/sEF

=
0,28
=
= 0.36

E(716 + 313 +h(b)

kost:
LEE
E C #
3 (

Paris P
DE I 0,43 057
0.3010,20 I

I
EM
* 8 -
GT
#
13.5
57)
-

13,5 O

Pit glow fit

Birln Dict 3) My 9
-

BC 19.55 25.65 3. 24 2.5 T 1, 24

3***
35 45 Cor O
↳S S

1,62 12.8]
1,67
-

6715 1) is 7 -

0,7 0,91 -

3,62-3,59-4.62
X
e Y-2.2)

or
Com O ill <
-

0,46
S

0, 17 O, 17
Dist 8
99 1,32 0, 17

com O
0.005) b4 > O,
-000s
pict -0.057-0,000024 -
-

0, 18 -024

com -O,L
⑮ -

0,047
I
~
0,12

↑
ictl ( 56.56-112 11,00 17.2]
19,6
718.6
~
 10,307
↓Bc = YEI DFxc EF
=

=
01675 xF(p 1
=
- +
0,455) =

Y
e=((315) DFcr = 0,242
kDE= JEI

5
FDE
x =
1 -
0.675 =
0,375 DFcD = YEE(n = 0,303
Use |cy = 4ET
Y
kcg = JEI
kCF =
YEI e(1 4 32) + +

2 5
70 3/2
(modified DF( 0,455
a
+ = =

(1 3(z+
+

4(t)
E B 2B CcD CF F D

~
((r)-
*F
I 8,3750,675 0303 0,455 0,242 W ↳

So be EM
F O 53576,25-76,775 5 30
-
- -

D
20 Dist -

17,33
=

20,9) 25,38 30,11 20.27

L - -
com 12,69 Milb 10,14

EM's
↑ de to settalant. Bis7 -

4,76 -

8,57
4.786,583,5
Com L S 1.75-
2,19 -
4.29
Mx
2EF(3(0,0) 56,77 Dist
= =

56,25
M(n
2EF( 3(0,0)))
=

=
-
=

↓
 DS 5'/m
B
Distination I IfvdO T
D) T Y
A # ↓7.
A
Sau ↳ v 18
↓

Nathan
↑

⑰4 R
·to Member AB
↑ FisD
↓ 7.5
↑
I
-
=
cy
& Ma =
0
↑

5x 6 x 6 =
Fpox 3
2
#
Dp = 22.5 (2)

CUS
x
W
=
7.z
=
m

↑
+ I
-

i -

mix
If
a

-
 lotkr 1= 3000KN/m
~w 1xxxxU
*
↑

To An
im
↓
Lon
1
T

3
b = 0,0150
Member BC
de 1x
f

zE1 (7enteptex 0.010 +

I Mrc:
ar
f OB

* S
↳
A fo
↓A 0,015m
Mas=L+E xto) + we

modified =

-
E Elfy +
FEy-og 0,005675ez
=
+

ERP
So Tphet o
Grindor ↑
prese
vis
12800 03-125 W = =
06

setox--those
Var ew & F 75ier
=

Mec+Mcy-200 + 180 =0

Member BA MDC+MCD = 28

MDA =
SEF (8b) -
we

3 g

128a+83) T
cl
man= =
· ede = Ma = 0 - 110x6

Dx 125.5
+17TX5=67x5+Dxx10

:
=

↑
⑧
~
a
pty eghe
oorestor to

act
I
-

us 12
-
a
43 ↑

*
by ↑ 19.7 di
 modified 10/m
damped modal
deformation
#"A
All codes
only
&3 C
*

are
2 Y
↑ D modaped ~ 10kr/m
! B
a
Luc ze
D* *
-

↳ 5D KANaPhR + ↓

cog Loz00s
-

* *
=
hm 5m ↳m
20101 coogh
F=
3st
Only
iiii os) (7
by others are zero to
121) =
zEIR by:
thet Ectuut
y
*U &

S #Toe
1

..if the -

K=
3EF YEz
+ K21: CEE
5
member-and
force (Option (use SDE)

worCEFL LECt)TFh7
Only EC + 2003
K22
neEl5

15 isil of
DYEC
Le
is (8) Iiiy-li)
&
EFl
12
4 = 2EE
5 xz= ("*+IEF)

1. M + = ==
 def
ONEfor"I
I0KN/m All body damped model
only
FEI ciD
~
or

ic
- -

ofA " So
i
EE
5m
=

snorter Storowleret a S
↓
Solrf
f
2. EE
LEE

Discetication Member- and K.:LE

↑DB
Forces K21= EE
↳LP
#
it t
↳ - ⑧

Only
whereOEEI)
AB
En

()+Feg)
815
-

zur)e 1Ize
-

Ezkz

sil V.OE E
12
Ef

=a Yet E
Le K2

for
i4
In

are
=

41 =-EFK22:SE
h
ET.
(3)=7507
-
Le n ar

# -az
br D All modes are clamped
E += L**EL

risty↑
11 = :200
Disrefication
-
0,24

"the
ex
Fic
-

2EI
y EEK
=

e1=
K On =
-10.94 /EF Db =
-188.7 /EI
bE1
/g
=
zEzle
K
a
1
=

↓ In K1z
Onl By
= EIs

on * nodal defination Only Di Only De K22= 2EE - K13

S r
1x k23

jet
NIC
Pht
"Ya
Runken=6)g 13

ofsie
Goo key ↑

-)
40"
Foggy were
v
a
T
It

was
SEI

feeS
see
E
K13: LEEly
YEE
- S

I -
YfcEg Rc=reEakz
 17.2TIEE
-

↳ Go 1297/ EE

EtOso pain-li
I
·

D= 27.22)EF
=

less is]lis?) +il=i

~

0.3) 2 Y/6
De =
1.57 /EF

D 19,AS/ Ef
=

onlyvocal defore
in DF-1
25 Only
All nodes clamped
~solwin
a re

104 /m

i &
"T-Kel K1
~

LEE
c
atif (B.
=
=
is t
↳ ↳
If *I modifed

PIGET- see K SEE/ec

Vitana

E
=

Sm =
-

-A me
5 *

Im

more P2 =)
Discretization Only

#i3f]/3) -fony
"SP2 2Kic
-> K22
Yo
-

T
me

·next
3 sEEE
S
·

FEEE K1z =
6EFf5

t
K 22:
IEF/125
↑SEE
D= fy = 148, h4 / EF C

Di = D = -

371.09 / EE

Member-and forces
Onn/EE
&

-isone noise7+ (8)

·
↓s EI =
233
 trait l rodd,deforation

freeofthereform
a

sour 2in All rodes are

clamped did
As ~
10 m
=
i
be 3
112KrI-
+ $ b -a

fety
8m
F:

EF =
2000010mEA=10000km

modified
is retination
&

it Drple KII:
REFLEE I
+
1407, T
-

K =-5988
,
-LEF TE

Only Pheztn U BEE

LEF
-
12
↳* ↳In
Ih
Kin =

LettoF=-55889
4z
Et+SEF=10416.3
=
 deferee
gode
came, in
cesel: model deformation
odour

tire
no

(iii)
solvin

Latourtime
my F:
Lev
In =

our *
-
SJo B Tem "
0

↳m Solution Cel
*B =

1, 8x = 0

130) liii)
To, 342875
# -0,0525
GE 11) gEE
I
6EI)25
= ↳ ↑ G Ee
th
D)
is retination in
2.3 of25
-0,0525
↓ Gif↓ ↑ 3EE
g8I

D_modified IEE
-

FEF+SEE
by
-

↑
=zEF 42
it saDsndtia E
be:
-EEOS As:
tot ↓
*
Pl "LEF +EE+IE
Case I
= 0,642875 EI
member-end force AB to=1
=

12 (Rof)-> (fl- 0.040-

165 =

met:
↳
↑SE
&

I
as**)1
th ↑
Ken
I

its & ↳ otzzEF

-
VDEE &
=rO
EE
RNz=
tEFLGEt
Kzz:
GEF EEE +IEF=2.3E
+
 Only D1=1, D2 -0.6
0
= Cord =

/5 =

3T000
EAF70x5000 =

co - 012x4V2 Pu=39750m S22 =

0.6 0nix 5
Siizt
=

·usit
=A 263,000
=
=>
EA= JT080 1800 340000
" DI "
↑t DI 3)720 P27 =
72,000
#E r o
428T
Nimm"
>Ke KI =
56/35.9 Z

↑12 K21
=
2663,08

Only
fig
1, D1= 58135,57
0
D2 =
2634.08

120330/500 azure
51.2: 1= PXUV no
(u=es. e
& 15000

D2 = 1 9 = 43750

12z= 142 235.92

D1= 317]
x16"Y
K2I
1: 0x 4
0: 63500
2 6600
0

D) i = -
7.55 x 10
MDe

sind== 00
t5 +P=30
=
=

:By E
 cax), D1 1x2 0
=
=

EA= 90000 In -> D P.

-
g
12
k9 Pab4 E 3 8A45
=
=

1
=
=

Soool
CD2 90000
↑ Du
-

(x)D
t Pcurinte
scp -> PCD =
11250 un
PAD 14408
PBb 27500
= = =
=

11750
r

95
R1 419fy. kn

2011
=

L 121= 685.05 kn

(ax2, Dz 1P 1 =
=
11480

11250
3 =

t =

PcourEPco-e T

A *
->K12 k12 685107
=

=3 Pao x5
EPAD 1000 -(1222 &22 14494.85
=

sind:
=
=

can 90060 18000

!..

u1sH15ov(i) 3 303
=

P1 1.564x15
=

D2
= -
308x1%/
 def

Partorre
no modal

1 5-x - 0-5
-

def
to
=
wall
only

4
-5an(5) T
Discretination 111 2El
=

Sohere -
12 0 =

I
ky1*kTEI

S 1 I 1)
20
-
1.5
1
Oypz =

0 Y b =

mas
(
= -

) = 16+ xb+-

Di = 3.33
-

IfI
nbflat orin

Mix D2 167/EI
15 k12 0 =
=

xj
= -

1(1/FI 122: GEI

132-6ET

t(t 3(,)()) c))

CebEEF
mob
=
+
-
=

②
↑
↓yy -.5EI
=

12) =
bEI

(x) 17.[EI
=
 No
deformation 02 rodal def ayb1 1
=

83000kw." Ax 301m
- Y42
r(4
EF =
~ 1

KN/mad
ran to me B I 3608
x4
br ↑25 +

T
3
F (33
1Ly 1937.5
- =
=

12: 15750
-

1
isrefication
xy.D
& =

acCon
12
L 1.7(c) 13)
-offel
-

3987.5 15750
= 3
asdified
1
~

15750 10750
=

-
# -22
=

126000

r
PoolTry
Member- and
forces

mon
( 25x100
0,0165) 90.0x
fu
-

10
=
-

+ =

A
Y

mxc
() 2.54x10) + 6x
=
=
-
-108
 -def casel
only real
sof only (1 1
~xxrln
=

20
K21
15
111 ↓

1↳20
- + ->
z I to

i
EESEFi
EF: 1.2x103 kwm"

=1200krm"

⑭ # 11)
t
ca
- ⑱

&
c
-
L

D1 0,15m
=

1
3
Can I
only D2 = 0.0 = =Px5

keyE.
A
P
0.0EA
=

1)
is cretization
~

·DcENEE
medified en k12 =

6EI/9 kn
kEF PE
=

+
A

e &
122 =
2.087 EI

ku
=
3350 0,15X00
1,
=
=

p =
81(c)

Econo 901 (i z
=

6EE

15

89(n
[xcx cuss J
10
=

+12000 79.3395 + 19200A +

- 0089.3
120 + 2439.6xD2 = - 20 15200A= 64.8065

38.406-809Dn 6.4 0.003375m"

=
A
- =

1375mm
~
 No deformation
only model
def
3225
i
5) I(IH)
T
=
4,
5

at
+ A ↳

9)
-
F =

t -

Disrefication 1
QyD1
1
&lyDz
=
=

DC
) -> D -> D

*
I 131 122 1232
=_rifed
T 5.
3/15
DL
↓(I
S
xic) LetincS
- T
*
·IO-T So I

3 E
aku = ~S

S 3
EETE
h 1
↑ ENER
E k1c bEF/1ZY
=

122 0.86667EI
=

↑bET kz =
-

14Y 134 1y1 E16 =

-
ky1 0=

P/123

Ic, ( f)
e1yn O
Only Dy 1
=

EI v
6
M4 P15 16 a D1 = x]]
uE1"x)
=

12]

V T
*
O
lu- D =

V
e k
0
=

D =

123 EF/6
=

13) EF/y
=
 Nodeformation ore.
Only nodal def Atel ALIML1 alyD1
1
=

Bz Dy 0
=
=

2285188
T I
s
27
i
s 13)
ag
o -S

26.67 kx> K2
T

FESoroks+c) (583
# -x
-

Y
--
. .

FreeST
kv +
=

216 27

F
=

· kz1 =
EI/jEFly
L

D)
is crefication Xy1 0
=

In
m

rodified
-
alB 1 =
Di=DIES

I ixc)
-

c) S
0,167
0.1670
Dy -

6p
+ C
⑳

EF 01672.1670,75
- =

(5)
ASEE
~

mN1k
3
O 0.25 as
-

36.67
>+
H ~
1,e ↳kn4 YEI
8

fit↑ i
T
10.664/E+ D2 - 10.664Cc kiz Et(t j)
62,000/EE
=

x1
E
-
=
=
= -

②I
k( Et(t 5=
+ +
1)
Member -
and foxel ksz =
EF/y

onlyDs 1x1 Dc
= 0
=

Man
Et)
=

64
-
+
3x(104)) + 0 =
-
9.x2u -
11
zEF1O uEF18
I
177 x(p 0
=

->
4 12T
+
4y & 121: EFY
MBA
66) 3x(5))
F(2x/ 15.55 knw E12
=

+ kyy
= =

6+ (- 6480)) 533)
zEt(2x(
27.9964-
=

myp =

+
 .
-

(2x) 000) (62))

N

Mpb =
+ - 57.1) = -

90 wrm

Mpc =

EFObbYo (- 1866,) =
-12.42 wro
pinhteningour l

69130
gO

sign
convention +It
re 1 -

4.17q(15.55
47.7565
↑ go
Monet Diagon
at*It
77.7505
-> 4.147
- 9,372

t hire
res
12.4Y t

~ -

15.55

↓
27.996
-

Igo gour

9.391
 No
deformation modal def. Case 1:D1 1 Dz Dj P
Only
=
= =

--
M
132
F
I -
4xx
Disretization >30
41.25 67. - M

modified e
67.5

↳Sam
a

K2 6 8EI

s
kei=
- 56
Pa-> an
k2 =
?

An
E

E f)
==
2
Ky EI/C
=

Case 2 D2= 1 D1 D3 ==

Cax]: Dy 1 Dz D1 0
= =
=

5
x045 1 Px6k
=
=
=

I 0.25EI
Member-end forces
↑
X
EI/4t

ne
p
=

x*/23
all
(2x I 4)) (x43) -
Max 103,061
"
+ =

=
113 K12
-
↓ 4EF16 ↓
122] /(3]
y-
3 r
-
k22
- >
E -

Mar
(- /5)) 3 119.5055 2EF/6 X
=
=

+
+

k1y EI/] N
W

?? P EI/48
I
=
I
=

t(2-(s) (s))
S

mas =

+ = -20,00 K23 = -

E/12 E
213

kc =7/6 1 12
EE16
=

Ni
Mor
(2x))) (-)-- As
+

k2 +
+ x2y
~

-(()) 3s,

I i): (I
57.5 6.776 116 "3
Roc
5( K12 E/12
=
= =

El 116 0,09891-1112
D1 -
=
49.346/EI
- a
3 6x
I D2 815.729
p=16.95 /EE
=
=

**
=

De 12.509_/e7
=
~
 to
Meet Diagram
OEEHOctor
in

eflected shape
& L

f
- > b0

12.995 x.c-

to
+
MWOS/x
83.66I 26.773

actionon
=
↓

5004-561.129
ofthe
-
b.2M 6.776 mon

Go
10.061
vS6.2M 12.0216.995
-> 17.095 ↑s1.on
#

x,b) -
f
<15.TOST x &
6.2'
s7.0sfal102
->
t12.02

v
*19.5095
-

-> i9

19,569T ↓58063
 Case 1: de = 1 d2 =
dy dy = = 0
Case 2: dz =
1d1 dx dz
=
= 0
=

k11
G
11.63EF/ 12.27EF/ KiL l.3EF/12 4. GEFL 137
all
d

&
mI ↑ p
soit so141 6My
S 414t
*

bE
- w
67JEI
L

k2z 6.7312
El
1y 23.6
=
k2 11.3JEI
=

↓12 11.35EI/2
= =

L3 22
isretitation
D)
d] 23.6E k32
-

11.33E k42 48E5/L

=

kx = kv
12.27E
- =
=

If 4t
Ay Caxe4d =) dz = dy =d1 =0 Case 3: dy = 1 de =d1 =
dy 0
=

sEFIL +
E 133

fuair
1217
437
p
7.
↑ i ↑

6.41.18 4n 3 194%
- T

23.6/p 11.33/7-23.6/p 12/p us

E ↑

EE
#

11) = - 23.6EI 1723

=

tE
11.33/12 6.51c-11.56 40/L L3

keu
E27
=

El /2 23,67/13 12.27EF/(2
-
23.61 23.6/4-12.27/17 kyy ku)
=

=
-

kz =
-

2 (2x) 7.68EF/2
=

12.27/ Yobk
-

12th F.60E/
-
-

synety is obtained
 deformation
Only deferreter
No
cal

O 12.75

·
- -
d
*

F
Stirin
=

isrefination
1)

~modified Dual pe

Si,= Si
-

I D1 = -
7,068/E5
ET
D2 = - 17.772/EE
Cage 1: Dil Dire

3IsEE
o
alldie ER
IF
213

bEz/y
=
EF/12
-

21EI kz1
k1 gzz/y)
= = -

+
~
216

2 D2 1 Di =0
Cage
=

MIL as
SEE
Gen4
28/6
*
o
e
for

112
E ↓22 BEF
-

=
=

E
 no
deformatio only rodal def

t
to D1 1 =

↓Early
N

or
4
R "Or
+ I
111 2.3]E

if
is refination
7)
=

Sr - + xD1
2.3t
= - 8.54
I
D *

(1 = -

3,64/

A
In

IR
(N1E
F
EM's due to settlement F =

Sl ol
#

-
↓oio Y 1500
457 !
*
-.

2
8. PFr
↑ 750
c)
Disactivation
-

*T
DI 3x 1500
Y

GEF(05): 37xkE(-3x(0)
Mon: =- 1500
St
E
8 Y

(ax): D1 =),Dz0 =

Cn2;D2 =1 DiO

menexro(= Ft
·E

-tothee
xx 12) 112
u bee/10

Sa h
p 2

A
-
~ ->
12EE
x # Ju -

(1) 1.TEI
=

421 =

EE5 I=
M12=-EF18 122=GE
16
ment
 No deformation case Core 1A), Dn = 0

-ruwy-
o
22 6EE)108
6E1/100
45
11- 12000
·

97(90
k2p
= = -

<F
-
XIRE KDIEE +1
x
-
75

o 1000 12 5-

L
deformation
-

real 21
only are 117600

-EOSE
=

reser
1

&)iscetiction .

F-Sic
cri E5 x,
t
min 4
B sind
title

A4
=
= =

↑=192000 - -

④go Case 2: D2 = 1 D1 0
=

k12

7600519
-
4/10c
↑KIL

-
-

12000
: 6E7/100
112

112
=

=
YE)10
-

651/100
=

=
80000

-
12000

↑1 =
-

0,00103541

D 0.001741989
=

Man:
E(000nnesr ooxsh())
=

+ 201 = 266.5
 Disetivation
1-regoda
Case 1: ns
deformatbr
Cir cC3 +10
-> -> Di

xr D
7 p 7
r
80

IE
DI
· ↳10

I
-8 18
->
2.5
F
795
=

10
I
# * *

H I
i

Cex1iD1 1bz
=

0s
=
0
=

Caye 2: Dz 1 =
B1 Dc =
= 0

You
122 2EF
↓) (3) 1232

*E
x
"

i) T +
7
- ka
+

EEFE
=

ArtifoE
3 S
I 1b
f

21
K =
6E5164
68
To
1y1 6EF/16
=

Cre 3: Ds = 1 1,2 =

6EF/64
127
u
&-
113 -
121] =
6EF/16 122 =
EF
-> r

-Sa
EF1Y kyz EF
123
=

2EI =

1x 1.WEI =

oil coder ofy= 7.It

D1 44. 42
=

12 06.R
0 ,0S97T I -

A
=

-
 No
deformation a Carli D1 1 =

·it sou
28
3EF 3k
I"T
J,nT d p ↳ in
↑ KV f
=

Only model deformation R

t 2
A
=

90

to
. . .

. . .
1 Px2
=

=> ⑳
EA

i
·
=

23 1x
EF t5 A
=

+ + 5700
=

12) (EF/y 17(y 3608

= =

Discrefinate
-
-

pP ~medigre Cue 2.Dz = 1 D1 =

in f o
modified

i ↳o
3/2 set Kiz
EF SEF 36
-
+ = -

W
↑
&22 E 14400
=

lE +
=

SEElY

I 1)
mosc)
-

700 -

36x0 D1 =0,006075
=

Dz 0,00 2552
=
=

-
3600

Note: #of equations of

Peses of indeterminent is the et unhow reactions -

equilbem
 No
deformation are (x1:D1 1xz Dz=
=
0
=

28.125

↓*St"sSE
W-
Iewl-
IN
~

kEF IEF R
ftS LSor
La
" 11 =
+ +

SECTIS
P+ = 10 o

ad ↑ L
↑ Rz =

JEF-6F
=-

El
I ↑

↓==

·EEVEoinoioEE
k11=-AE/Y
↑
&1237
Case 2: D2 1 B1 Ds 0
= -
=

only nedal detonation

EEF AILabE
12x
E E
-

+
EF
=
=
-

280.625 o

K22
as 10) &
3EI
=
FEEl]

2E
x Rs 0
J
=

It
*
Core 3 Dy 1
=
D2 Dc = =

⑤ &(13

↑=DElY
SEEI9 4x =-AEY
Ricee

-IEMFoi-SEE
~

↑p
SETRE
I I
I

this
0
12
=

EI (x)
E+
=

11) 7 O
str
-
-AEly 0
 ~modifiedDJs
Discretization No
deformation ibute
case

D3
pall as
->
I
medifral
ST
32
-.
In *

is I re
-
E

stanonfic
A B

only model deformation

Ii
F =

⑤ ↓I - 13
-> A
-
E -

i
Es
319 ↳
Only DC= 1
↑
K9
->

gEE
=
-
K2=0
El
th
bet19
bes 1231 0
=

Sex/9
C alli S +3E7/g EE/y
* 14 = =

E
↓t
141
↑
JEF
-
27 E -
-

12 1
Only se/3 gE5/
=

112
k3 22
-
1 + 42 0 =

-> K31

K22 IEE
3/s
=

⑮ -> 431 1/0

=

bEE
T zFly
-
442 EF/2
=

ak
bit
 No
deformation cant
·y
rodal deforehe
w source

↳S-E)a bTON 916.67

10

B C I

SE

GF(3S= 2000

Discretivated DI
B3=903-rodefe
A - s

D1 1=
2.5EFx D1 = 916.67
uk/
124

x d *1 2.TE
=

s4-
GCEI
-

v I
wo
 is refinatio
* No deforather as

(ji)
48vla
~ F
CD
but
=

D 5
/
Con)) 300

*
radgred 54 a =

I
-

Boroswe DrIt I
(B Sum + ↓

10
-

i
↑

F
H-(,) 24
=

set
*
12(1
x I
ky JEF
<
=

o 2
1u EF =

(ii) (i)
x
=

fevi El

+
c m
+

exele 122: 6EF

h
+

&↓
4
-
wef
I Y
 D is refinafid
Use
OD
fr
reared d ↳me D

mpn
c

&B
Yo
soc
f
omen
L

-
t -
Bekdt
-

a modified MDF
MBF + Mx+Mop
= 160

Upc + VBE t8o-NO

t
↓
*
A
 Direct
stiffers examples -d att
d
- - Back subs
o
polr
-12301-
↓
the
-
3A12- at
la
O
is
- C
D D2
8-

↑010g
1 (vi)
E

x
12)GF-0.0Ta
-
R =

D
-B
234,375

F
=

ms
=

872, 3 6666,67
n
-

F=20000 uni 3750

234.375

ab
-

EA = 10000 kW

l
Discretination
+
T

As ALO I -

143

o As kxy xxxx + fo
f
=

#Arethe ti
72
ASED
of
I

55 gre
' ↑
as
axially ungid
 <DI

P2)
↑
↓ M