strength of materialprint

Norton University Academic Year: 2013-2014

Department: Civil Engineering

Subject: Strength of Material

Group: M8

Session: Morning

(7 ) 7 5 35AM kgf F d kgf m kgfm

B A5m

M(A)

10N10N

(10 ) 10 2 20AM N F d N m kNm

B

A

8m

M(A)

4kN

4kN

(4 ) 4 8 32

(4 ) 32

A

A

M kN F d kN m kNm

M kN kNm

I. Relocating a force Move force from A to B

a.

b.

c.

A B5m

M(A)

7kgf7kgf




Group: M8

Session: Morning

0

0

245 20 10 2

2

245 20 10 2

2

(20 ) (10 2 ) (10 2 )A A A

Fx Fx Cos ft

Fx Fx Sin ft

M ft M ft M ft

(20 ) (10 2 10 ) (10 2 10 )

(20 ) 0

A

A

M ft ft m ft m

M ft

A

B

60°

30°

30°

10m

40kN

20ft

(40 ) 40 9 360

(40 ) 360

A

A

M kN F d kN m kNm

M kN kNm

0tan 45 10 1 1010

dxdy m m

m

d.

slope:

+

e.

45°

ABFx

Fy

dx

dy

20ft

10m

20ftF

45°

45°




Group: M8

Session: Morning

A

BFy

Fx

F

12m

4

35

4

3

3tan 0.75

4

arctan(0.75) 36.869

4 3

Fx Fx

B A10m

M(A

)

6kN

6kN

(6 ) 6 10 60AM kN F d kN m kNm

A B4ft

M(A

)

7kips7kips

(7 ) 7 4 28 .AM kips F d kips ft kips ft

f. slope:

g.

h.




Group: M8

Session: Morning

A

B

7ft

3lb

3lb

(3 ) 3 7 21 .AM lb F d lb ft lb ft

50MN

A

B

6m50MN

60°

60°

45°

0

0

0

0

0

50 60 25

50 60 43.30

6 45 4.24

6 45 4.24

25 4.24 106

43.30 4.24 183.59

106 183.59 289.59

289.59

A

A

A

A

M

M Mx My

Fx Cos MN

Fy Sin MN

dx Cos m

dy Sin m

Mx Fx dy MNm

My Fy dx MNm

M MNm

M MNm

A B

30° 30°

20kips 20kips

30 tan 30 55

35 1.666 3

3

20A

dtan d ft

ft

d ft ft

M kips F d

20 1.666 3 33.333 3kips ft

20 33.333 3 .AM kips kips ft

i.

j.

k.




Group: M8

Session: Morning

A

54°

3MN

60°

B

54°

4m

0

0

0

0

3 54 1.76

3 54 2.42

4 60 2

4 60 3.46

1.76 3.46 6.08

2.42 2 4.84

6.08 4.84 1.24

1.24

A

A

A

M Mx My

Fx Cos MN

Fy Sin MN

dx Cos m

dy Sin m

Mx Fx dy MNm

My Fy dx MNm

M MNm

M MNm

l.




Group: M8

Session: Morning

II. Moment of Inertia

1. រក XI , YI , XYI

3

34

12

200 2013333333.33

12

X

h dI

cm

X

Y b

a

x250cm

300cm




Group: M8

Session: Morning

3

34

12

2000 20133333.33

12

Y

Y

hdI

I cm

0XYI ពីព្រោះ (X’X និង Y’Y ជាអកស័ឆ្លោះ) ដូចពនោះ 413333333.33XI cm , 4133333.33YI cm and 0XYI

2. រងវិលអកស ័ 11 ចូរក ; ;a b abI I I រមូមនតទូពៅ

2 2 2

2 2 2

2 2

cos ( ) sin ( ) sin (2 )

cos ( ) sin ( ) sin (2 )

sin( )cos( ) sin( )cos( ) (cos (2 ) sin (2 ))

m x y xy

n y x xy

mn x y xy

I I I I

I I I I

I I I I

ពោយ អកស័ថមីជាអកស័កាត់តាម ទី្រជលុំទុំងន់ររស់ចតលពកាណកកង ពេបាន

2 2 2

2 2 2

2 2

cos ( ) sin ( ) sin (2 )

cos ( ) sin ( ) sin (2 )

sin( )cos( ) sin( )cos( ) (cos (2 ) sin (2 ))

a X Y XY

b Y X XY

ab X Y XY

I I I I

I I I I

I I I I

ពោយ 413333333.33XI cm , 4133333.33YI cm and 0XYI 2 2 2

4

2 2 2

4

2

13333333.33cos (11 ) 133333.33sin (11 ) 0sin (22 )

12852746.74

133333.33cos (11 ) 13333333.33sin (11 ) 0sin (22 )

613919.88

13333333.33cos(11 )sin(11 ) 133333.33cos(11 )sin(11 ) 0(cos (2

a

b

ab

I

cm

I

cm

I

2

4

2 ) sin (22 ))

2472403.517 cm




Group: M8

Session: Morning

ដូចពនោះ 4

4

4

12852746.74

613919.88

2472403.517

a

b

ab

I cm

I cm

I cm

3. រកមង្កិលអកស័ពី C(a,b) មក (0,x,y)។ ចូររក ; ;x y xyI I I

ររូមនតរកមង្កិល

2

2

2

2

x X X

y Y Y

xy XY Y X

I I aQ a A

I I bQ b A

I I aQ bQ abA

ពោយ

23

23

4

4

2

20 200400000

2

20 20040000

2

250

300

13333333.33

133333.33

0

200 20 4000

X

X

X

Y

XY

Q cm

Q cm

b cm

a cm

I cm

I cm

I

A cm

ពេបាន

2

4

13333333.33 2 300 400000 300 4000

613333333.33

xI

cm

2

4

133333.33 2 250 40000 250 4000

270133333.33

yI

cm

4

0 300 40000 250 400000 300 250 4000

412000000

xyI

cm




Group: M8

Session: Morning

ដូចពនោះ 4

4

4

613333333.33

270133333.33

412000000

x

y

xy

I cm

I cm

I cm




Group: M8

Session: Morning

III. Truss Analysis by Method of Joints

1.កុំលុំង្រតិកមមររស់ទុំរ Ax; Ay; By

តាម(1)

2.សិកាលុំនឹងតុំន

តុំណ(A)

តាមSlope

0 ; Fx

0xA

0 ; Fy

6 4 4 2 0

20 (1)

0;

12 8 3 8 6 4 9 0

8 3 8 6 4 99

12

y y

y y

A

y

y

A B KN KN KN KN

A b KN

M

B m KN m KN m KN m

KN m KN m KN mB KN

m

20 9 11yA KN KN KN

2 2 3 22 3

3 213

yx

yx

yx

ACACAC

ACACAC

ACACAC

FFF

AC AH CH

FFF

FFF

2KN4KN

6KN

4KN4KN

A

C

D

E

B

FGH

Ax=0

Ay=11KN By=9KN

2M

2M

3M 3M 3M3M

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

A

11KN

?AHF

?yACF

?xACF




Group: M8

Session: Morning

តុំណ(H)

តុំណ(C)

0 ; Fy

11 0

11

13

2

13 = 11 19.83

2

311 16.5

2

y

y

y

x

AC

AC

AC AC

AC

F KN

F KN

F F

KN KN

F KN KN

0 ; Fx

0

16.5

xAH AC

AH

F F

F KN

0 ; Fy

4 0

4

HC

HC

F KN

F KN

0 ; Fx

16.5 0

16.5

HG

HG

F KN

F KN

H16.5KN

4KN

?HCF

?HGF




Group: M8

Session: Morning

តាម(1)&(3)ពយើងបាន

0 ; Fy

4 4 11 0

3 (1)

y y

y y

CD CG

CD CG

F F KN KN KN

F F KN

0 ; Fx 16.5 0

16.5 (2)

x x

x x

CD CG

CD CG

F F KN

F F KN

2 2

2 2 16.5

8.25 (3)

x x y y

y y

y y

CD CG CD CG

CD CG

CD CG

Slope F F F F

F F KN

F F KN

3 (1)

8.25 (3)

2 5.25

2.625

5.625

y y

y y

y

y

y

CD CG

CD CG

CG

CG

CD

F F KN

F F KN

F KN

F KN

F KN

22

2 2

35.625 8.438

2

3 2.625 3.938

2

(8.438) 5.625 10.14

3.938 2.625 4.732

x

x

CD

CG

CD

CG

Slope F KN KN

F KN KN

F KN

F KN

?yCDF

?yCGF

?xCDF

?xCGF

C

4KN

4KN

16.5KN

11KN




Group: M8

Session: Morning

តុំណ(D)

តុំណ(G)

0 ; Fx

8.438 0

8.438

x

x

DE

DE

F KN

F KN

28.438 5.625

3

13 8.438 10.14

3

yDE

DE

Slope F KN KN

F KN KN

0 ; Fy

6 5.625 5.625 0

5.25

DG

DG

F KN KN KN

F KN

0 ; Fy

5.25 2 5.25 0

2

y

y

GE

GE

F KN KN KN

F KN

3

2 32

13 F 2 3.605

2

xGE

GE

Slope F KN KN

KN KN

0 ; Fx

3.938 16.5 3 0

15.562

GF

GF

F KN Kn

F KN

D

6KN

5.625KN

8.438KN

G

2KN

16.5KN

3.938KN

5.25KN

5.25KN

?yGEF

?xGEF

?GFF

?DGF

?xDEF

?yDEF




Group: M8

Session: Morning

តុំណ(E)

តុំណ(F)

របារ កម្្ុំងកនលង របាររង AC 19.83KN Compression

AH 16.5KN Tension

HC 4KN Tension

HG 16.5KN Tension

CD 10.14KN Compression

CG 4.732KN Compression

DE 10.14KN Compression

DG 5.25KN Tension

GE 3.605KN Tension

0 ; Fx

8.438 3 0

11.438

x

x

EB

EB

F KN KN

F KN

211.438 7.625

3

13 11.438 13.747

3

yEB

EB

Slope F KN KN

F KN KN

0 ; Fy

4 5.625 7.625 2 0

0

EF

EF

F KN KN KN KN

F

0 ; Fx 15.562 0

15.562

FB

FB

F KN

F KN

E

4KN

3KN

2KN

3.938KN

5.625KN

?EFF

?yEBF

?xEBF

F15.562KN

0KN

?FBF




Group: M8

Session: Morning

GF 15.562KN Tension

EB 13.747KN Compression

EF 0KN No Tension or

Compression

FB 15.562KN Tension




Group: M8

Session: Morning

IV. Truss analysis by Method of Section

Reaction

10t10t

2t

2t

0.8t

0.8t

0.4t

N P

K M

H

F

D

BA

C

E

G

10t10t

2t

2t

0.8t

0.8t

0.4t

N P

K M

H

F

D

BA

C

E

G

1

2

2

1

3

4 4

5

5

3




Group: M8

Session: Morning

0

3 0.4 6 0.8 9 0.8 12 2 15 2 4 10 4 0

3 0.4 6 0.8 9 0.8 12 2 15 2 4 10

4

26.8

A

y

y

m t m t m t m t m t m t B

m t m t m t m t m t m tB

m

t

M

0 ( )

20 26.8 0

6.8

0 ( )

0.4 0.8 0.8 2 2 0

6

y

y

x

x

Y

A t t

A t

X

t t t t t A

A t

Section (1-1)

26.8t6.8t

6t BA

FAC

FCBXFDB

FCBY

3

4

5

section (1-1)




Group: M8

Session: Morning

0

4 ( 6.8 ) 0

6.8 ( )

0 ( )

6 0

36 , 6 4.5

4

5 306 7.5 ( )

4 4

X

X y

B

AC

AC

BC

BC BC

BC

m F t

F t Tension

X

F t

F t F t t

N t Compress

M

0 ( )

6.8 6.8 26.8 4.5 0

22.3 ( )

DB

DB

Y

F t t t t

F t Compress

Section (2-2)

26.8t

D

B

FDF

6t

4.5t

FBA

FDC

section (2-2)




Group: M8

Session: Morning

0 ( )

26.8 4.5 0

22.3 ( )

DF

DF

Y

F t t

F t Compress

0 ( )

6 ( )

D

BA

counterwise

F t Tension

M

0 ( )

6 6 0

0

DC

DC

X

F t t

F

Section (3-3)

0.8t

0.4t

26.8t6.8t

6t

F

D

BA

C

E

FGFX

FGFY

FFHFEG

3

4

5

section (3-3)




Group: M8

Session: Morning

0 ( )

(6 6 ) (3 0.4 ) (4 6.8 ) 4 0

36 1.2 27,2 4 0

1.9 ( )

F

EG

EG

EG

counterwise

m t m t m t m F

tm tm tm m F

F t Comprss

M

Section (4-4)

10t10t

2t N P

FN

MY

FN

MX

FNK FPM

3

4

5

section (4-4)

0 ( )

10 ( )

N

PM

counterwise

F t Compress

M




Group: M8

Session: Morning

0 ( )

2 0

32 ( 2 ) 1.5

4

5( 2 ) 2.5 ( )4

MNx

MNx MNy

MN

X

F t

F t F t t

F t t compression

0 ( )

10 20 1.5 0

5.5 ( )

NK

NK

Y

F t t t

F t Compression

Section (5-5)

10t10t

2t

2t

N P

K

1.5

t

2t

10t

FPM

FKM

section (5-5)

0 ( )

0

N

KM

counterwise

F

M




Group: M8

Session: Morning

របារ កុំលុំងកនលង (t) របាររង AB 6 (Tension)

AC 6.8 (Tension)

FC 0 (Not C and nor T)

DF 22.3 (Compression)

CB 7.5 (Compression)

EG 1.9 (Compression)

PM 10 (Compression)

NM 2.5 (Compression)

NK 8.5 (Compression)

KM 0 (Not C and nor T)




Group: M8

Session: Morning

V. Maxwell Cremona Diagram

Reaction

3000.0000 3000.0000 3000.0000 3000.0000

2000.0000

2000.0000

3kN

4kN

3kN

3kN

4kN

1kN

A B

C

D

E

H G F

7.5kN4.5kN

6kN 10 11

12 13

14 152

1 9 8

3

5

64




Group: M8

Session: Morning

0

(2 3 ) (3 4 ) (4 3 ) (6 4 ) (9 4 ) 12 0

907.5

12

0

12 7.5 4.5

0

3 3 6

A

y

y

y

y

x

x

M

m kN m kN m kN m kN m kN B

B kN

F

A kN

F

A kN kN kN

Scale: 1000mm/1kN




Group: M8

Session: Morning

From the Maxwell Cremona Diagram above

We obtain:

scale: 1000mm/1kN

9

12

10

8112.4904=8.112kN

8

12750.0000=12.750kN

11

3

4

12

5

6

13

14

3605.5513

15

7

13520.8173

1000.0000

6309.7147

5408.3269

5000.0000

3605.5513

11250.0000




Group: M8

Session: Morning

AC=2-10=8.112kN (C)

HA=10-9=12.750kN (T)

HG=11-8=12.750kN (T)

HC=10-11=1kN (T)

CD=4-12=6.310kN (C)

CG=12-11=5.408kN (C)

DE=6-13=9.915kN (Sh,C)

DG=13-12=5kN (T)

GE=13-14=3.606kN (C)

GF=14-8=11.250kN (T)

FE=14-15=0

FB=15-8=11.250kN

BE=15-7=13.521kN (C)

របារ កុំលុំងកនលង (kN) របាររង AC 8.112 (Compression)

AH 12.75 (Tension)

HG 12.75 (Tension)

HC 1 (Tension)

CD 6.31 (Compression)

CG 5.408 (Compression)

DE 9.915 (Compression)

DG 5 (Tension)

GE 3.606 (Compression)

GF 11.25 (Tension)

FE 0 (Not C and nor T)

FB 11.250

BE 13.521 (Compression)




Group: M8

Session: Morning

strength of materialprint

Education

kn fcgy

kn fhg

kn fdex

kn 360knm3040kndepartment

kn 3m3may

kn 12m1

kn f d

i x cos