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Solution of Mid First Term 2012/2015 Second Year Page 1 of 14 Question ONE: ( ) ( ( ) ) ( ( ) ) ( ( ) ) ( ( )( )) { } [ ]{ }{ } () () () ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) . .

Mid First Term - Question ONE

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Page 1: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 1 of 14

Question ONE:

(

) ( (

)

)

(

(

)

) ( (

)

)

( (

) (

))

{

}

[

] {

} {

}

( )

( )

( )

( )

( )

(

)

(

)

(

)

(

)

(

)

(

)

𝑤𝑥 𝑧

. .

𝐿

𝐿

𝑧

𝑥

Page 2: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 2 of 14

B.Cs:-

At

At

At

At

At

At

At

Similary

( )

( )

( )

( )

( )

(

)

(

)

(

)

(

)

(

)

(

)

B.Cs:-

At

(

) (

)

Page 3: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 3 of 14

(

)

(

)

(

)

(

)

Bending moment and Shear force and Reactions

(

) (

)

Max

(

) (

)

(

)

(

)

Page 4: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 4 of 14

( )

N.A

1

2

3

4

0 5 10 15 20 25 30 35 40 45-4000

-3000

-2000

-1000

0

1000

2000

z

My

0 5 10 15 20 25 30 35 40 45-1000

-500

0

500

1000

z

Sx

0 5 10 15 20 25 30 35 40 45 50-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

z

u

0 5 10 15 20 25 30 35 40 45 50-0.2

-0.15

-0.1

-0.05

0

0.05

z

v

Page 5: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 5 of 14

𝑥

𝑦

𝐶

Page 6: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 6 of 14

Anathor Solution

(

) ( (

)

)

(

(

)

) ( (

)

)

( (

) (

))

{

}

[

] {

} {

}

𝑤𝑥 𝑧

. .

𝐿

𝐿

𝑧

𝑥

𝑤𝑥 𝑧

.

𝐿

𝐿

𝑧

𝑥

𝑚

𝑅𝐴 𝑅𝐵

Page 7: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 7 of 14

(

)

(

)

(

(

) )

(

)

(

(

)

)

(

)

(

(

)

)

B.Cs:-

At

At

At

At

At

At

At

Similary

Page 8: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 8 of 14

(

)

(

(

)

)

(

)

(

(

)

)

Bending moment and Shear force and Reactions

(

)

Max

(

) (

)

(

)

(

)

Page 9: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 9 of 14

( )

N.A

1

2

3

4

0 5 10 15 20 25 30 35 40 45-4000

-3000

-2000

-1000

0

1000

2000

z

My

0 5 10 15 20 25 30 35 40 45-1000

-500

0

500

1000

z

Sx

0 5 10 15 20 25 30 35 40 45 50-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

z

u

0 5 10 15 20 25 30 35 40 45 50-0.2

-0.15

-0.1

-0.05

0

0.05

z

v

Page 10: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 10 of 14

𝑥

𝑦

𝐶

Page 11: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 11 of 14

Anathor Solution

(

) ( (

)

)

(

(

)

) ( (

)

)

( (

) (

))

[ ] [ ]

[ ] [

]

{

}

[

] {

} {

}

𝑤𝑥 𝑧

. .

𝐿

𝐿

𝑧

𝑥

𝑤𝑥 𝑧

.

𝐿

𝐿

𝑧

𝑥

𝑚

𝑅𝐴 𝑅𝐵

Page 12: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 12 of 14

( [ ] [ ]

[ ] [

])

( [ ]

[ ]

[ ]

[

]

)

(

[ ]

[ ]

[ ]

[

]

[ ] )

B.Cs:-

At

At

At

At

At

(

[ ]

[ ]

[ ]

[

]

)

Similary

(

[ ]

[ ]

[ ]

[

]

)

Bending moment and Shear force and Reactions

[ ]

[ ]

[ ]

[

]

[ ]

[ ]

[

]

Page 13: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 13 of 14

Max

(

) (

)

(

)

(

)

0 5 10 15 20 25 30 35 40 45-4000

-3000

-2000

-1000

0

1000

2000

z

My

0 5 10 15 20 25 30 35 40 45-1000

-500

0

500

1000

z

Sx

0 5 10 15 20 25 30 35 40 45 50-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

z

u

0 5 10 15 20 25 30 35 40 45 50-0.2

-0.15

-0.1

-0.05

0

0.05

z

v

Page 14: Mid First Term - Question ONE

Solution of Mid First Term 2012/2015 Second Year

Page 14 of 14

( )

N.A

1

2

3

4

𝑥

𝑦

𝐶