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Schema.agsr.001REAZIONI 877947 Agosti Riccardo

@ Adolfo Zavelani Rossi, Politecnico di Milano, vers.27.03.13 06.09.19

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Schema.agsr.001AZIONI INTERNE 877947 Agosti Riccardo


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Schema.agsr.001PROCEDIMENTO E RISULTATI 877947 Agosti Riccardo


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o

b(1 -2 x/b + x2/b2 ) 1/EJ dx = [ x - x2/b +1/3 x3/b2 ]o

b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(-1/2 x2/b2 ) Fb 1/EJ dx = [-1/6 x3/b2 ]o

b Fb 1/EJ

= (-1/6 b ) Fb 1/EJ = -1/6 Fb2/EJ

LXoBA = ∫

o

b(-1/2 + x/b -1/2 x2/b2 ) Fb 1/EJ dx = [-1/2 x +1/2 x2/b -1/6 x3/b2 ]o

b Fb 1/EJ

= (-1/2 b +1/2 b -1/6 b ) Fb 1/EJ = -1/6 Fb2/EJ

A = 540. mm2

Ju = 154030. mm4

Jv = 37908. mm4

yg = 36.6 mmN = 500. NTy = -1500. NMx = -885000. Nmmxm = 18. mmum = -3. mmvm = -36.6 mmσm = N/A-Mv/Ju = -209.4 N/mm2

xc = 21. mmyc = 15. mmvc = -21.6 mmσc = N/A-Mv/Ju = -123.2 N/mm2

τc = 4.251 N/mm2

σo = √σ2+3τ2 = 123.4 N/mm2

S* = 2619. mm3mm 0 18 24 42x

0

48

54

y

15σc,τc

σm

u

v

Schema.agsr.001


Schema.agsr.001


Schema.agsr.001


Schema.bldd.002REAZIONI 912028 Baldin Daniele


5/4F 5/4F5/4Fb

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Schema.bldd.002AZIONI INTERNE 912028 Baldin Daniele


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Schema.bldd.002PROCEDIMENTO E RISULTATI 912028 Baldin Daniele


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(1/2 x2/b2 ) Fb 1/EJ dx = [1/6 x3/b2 ]o

b Fb 1/EJ

= (1/6 b ) Fb 1/EJ = 1/6 Fb2/EJ

LXoBA = ∫

o

b(1/2 - x/b +1/2 x2/b2 ) Fb 1/EJ dx = [1/2 x -1/2 x2/b +1/6 x3/b2 ]o

b Fb 1/EJ

= (1/2 b -1/2 b +1/6 b ) Fb 1/EJ = 1/6 Fb2/EJ

A = 756. mm2

Ju = 165564. mm4

Jv = 74844. mm4

yg = 39. mmN = -725. NTy = -1450. NMx = -928000. Nmmxm = 18. mmum = -3. mmvm = -39. mmσm = N/A-Mv/Ju = -219.6 N/mm2

xc = 21. mmyc = 17. mmvc = -22. mmσc = N/A-Mv/Ju = -124.3 N/mm2

τc = 4.541 N/mm2

σo = √σ2+3τ2 = 124.5 N/mm2

S* = 3111. mm3mm 0 18 24 42x

0

42

54

y

17σc,τc

σm

u

v

Schema.bldd.002


Schema.bldd.002


Schema.bldd.002


Schema.bltt.003REAZIONI 893013 Beltran Toledo Italo Jose


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Schema.bltt.003AZIONI INTERNE 893013 Beltran Toledo Italo Jose


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Schema.bltt.003PROCEDIMENTO E RISULTATI 893013 Beltran Toledo Italo


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(-1/2 x2/b2 ) Fb 1/EJ dx = [-1/6 x3/b2 ]o

b Fb 1/EJ

= (-1/6 b ) Fb 1/EJ = -1/6 Fb2/EJ

LXoBA = ∫

o


b Fb 1/EJ

= (-1/2 b +1/2 b -1/6 b ) Fb 1/EJ = -1/6 Fb2/EJ

A = 864. mm2

Ju = 251424. mm4

Jv = 62208. mm4

yg = 33. mmN = 835. NTy = -2505. NMx = -1753500. Nmmxm = 18. mmum = -6. mmvm = -33. mmσm = N/A-Mv/Ju = -229.2 N/mm2

xc = 24. mmyc = 14. mmvc = -19. mmσc = N/A-Mv/Ju = -131.5 N/mm2

τc = 3.627 N/mm2

σo = √σ2+3τ2 = 131.7 N/mm2

S* = 4368. mm3mm 0 18 30 48x

0

48

54

y

14σc,τc

σm

u

v

Schema.bltt.003


Schema.bltt.003


Schema.bltt.003


Schema.bnda.004REAZIONI 888197 Bendo Alessandro


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Schema.bnda.004AZIONI INTERNE 888197 Bendo Alessandro


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Schema.bnda.004PROCEDIMENTO E RISULTATI 888197 Bendo Alessandro


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o

b(1 -2 x/b + x2/b2 ) b2 1/EJ dx = [ x - x2/b +1/3 x3/b2 ]o

b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoBC = ∫

o

b(-1/2 + x/b -1/2 x2/b2 ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ

= [-1/2 x +1/2 x2/b -1/6 x3/b2 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (-1/2 b +1/2 b -1/6 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -7/6 Fb3/EJ

LXoCB = ∫

o

b(-1/2 x2/b2 ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ = [-1/6 x3/b2 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (-1/6 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -7/6 Fb3/EJ

A = 1080. mm2

Ju = 276955. mm4

Jv = 116640. mm4



τc = 3.778 N/mm2

σo = √σ2+3τ2 = 137.7 N/mm2

S* = 5022. mm3mm 0 18 30 48x

0

42

54

y

15σc,τc

σm

u

v

Schema.bnda.004


Schema.bnda.004


Schema.bnda.004


Schema.brnr.005REAZIONI 868395 Bernasconi Riccardo


7/4F 7/4F7/4Fb

A B

5/4F

7/4F5/4Fb

5/4F

7/4F

B

C

5/4F

1/2F1/2Fb

5/4F

1/2F

B D

2F

1/2F

F

1/2F3/2Fb

D

E

F

1/2F1/2Fb

F

1/2F

EF

1/2F

F

B

FFG

G

A

Schema.brnr.005AZIONI INTERNE 868395 Bernasconi Riccardo


0

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Schema.brnr.005PROCEDIMENTO E RISULTATI 868395 Bernasconi Riccardo


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(1/2 x2/b2 ) Fb2 1/EJ dx = [1/6 x3/b2 ]o

b Fb2 1/EJ

= (1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

LXoBA = ∫

o

b(1/2 - x/b +1/2 x2/b2 ) Fb2 1/EJ dx = [1/2 x -1/2 x2/b +1/6 x3/b2 ]o

b Fb2 1/EJ

= (1/2 b -1/2 b +1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

A = 468. mm2

Ju = 136587. mm4

Jv = 14364. mm4



τc = 1.824 N/mm2

σo = √σ2+3τ2 = 117.2 N/mm2

S* = 2300. mm3mm 0 12 18 30x

0

48

54

y

14σc,τc

σm

u

v

Schema.brnr.005


Schema.brnr.005


Schema.brnr.005


Schema.brss.006REAZIONI 887236 Berselli Samuele


31/16F 15/16F23/16Fb

A B

23/16F

15/16F23/16Fb

23/16F

15/16F

B

C

23/16FB D

F

FFb

D

EF

EF

F

B

FFGG

A

Schema.brss.006AZIONI INTERNE 887236 Berselli Samuele


0 0

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Schema.brss.006PROCEDIMENTO E RISULTATI 887236 Berselli Samuele


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(-1/2 x2/b2 +1/2 x3/b3 ) Fb 1/EJ dx = [-1/6 x3/b2 +1/8 x4/b3 ]o

b Fb 1/EJ

= (-1/6 b +1/8 b ) Fb 1/EJ = -1/24 Fb2/EJ

LXoBA = ∫

o

b(-1/2 x/b + x2/b2 -1/2 x3/b3 ) Fb 1/EJ dx = [-1/4 x2/b +1/3 x3/b2 -1/8 x4/b3 ]o

b Fb 1/EJ

= (-1/4 b +1/3 b -1/8 b ) Fb 1/EJ = -1/24 Fb2/EJ

A = 612. mm2

Ju = 149427. mm4

Jv = 27756. mm4

yg = 36.88 mmTy = -980. NMx = -842800. Nmmxm = 12. mmum = -3. mmvm = -36.88 mmσm = -Mv/Ju = -208. N/mm2

xc = 15. mmyc = 16. mmvc = -20.88 mmσc = -Mv/Ju = -117.8 N/mm2

τc = 3.031 N/mm2

σo = √σ2+3τ2 = 117.9 N/mm2

S* = 2773. mm3mm 0 12 18 30x

0

42

54

y

16σc,τc

σm

u

v

Schema.brss.006


Schema.brss.006


Schema.brss.006


Schema.brmm.007REAZIONI 829837 Bormolini Matteo


5/4F 5/4F5/4Fb

A B

7/4F

1/4F7/4Fb

7/4F

1/4F

B

C

7/4F

F1/2Fb

7/4F

B D

F

FFb

D

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F

B

FFG

G

A

Schema.brmm.007AZIONI INTERNE 829837 Bormolini Matteo


0

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1

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1

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Schema.brmm.007PROCEDIMENTO E RISULTATI 829837 Bormolini Matteo


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(1/2 x2/b2 ) Fb 1/EJ dx = [1/6 x3/b2 ]o

b Fb 1/EJ

= (1/6 b ) Fb 1/EJ = 1/6 Fb2/EJ

LXoBA = ∫

o


b Fb 1/EJ

= (1/2 b -1/2 b +1/6 b ) Fb 1/EJ = 1/6 Fb2/EJ

A = 792. mm2

Ju = 225759. mm4

Jv = 30240. mm4

yg = 31.36 mmTy = -1740. NMx = -1583400. Nmmxm = 12. mmum = -6. mmvm = -31.36 mmσm = -Mv/Ju = -220. N/mm2


τc = 2.491 N/mm2

σo = √σ2+3τ2 = 128.9 N/mm2

S* = 3879. mm3mm 0 12 24 36x

0

48

54

y

13σc,τc

σm

u

v

Schema.brmm.007


Schema.brmm.007


Schema.brmm.007


Schema.brsa.008REAZIONI 891317 Borsani Alessio


23/16F 23/16F23/16Fb

A B

15/16F

23/16F23/16Fb

31/16F

23/16F

B

C

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F

B

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Schema.brsa.008AZIONI INTERNE 891317 Borsani Alessio


0

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Schema.brsa.008PROCEDIMENTO E RISULTATI 891317 Borsani Alessio


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(-1/2 x2/b2 ) Fb2 1/EJ dx = [-1/6 x3/b2 ]o

b Fb2 1/EJ

= (-1/6 b ) Fb2 1/EJ = -1/6 Fb3/EJ

LXoBA = ∫

o

b(-1/2 + x/b -1/2 x2/b2 ) Fb2 1/EJ dx = [-1/2 x +1/2 x2/b -1/6 x3/b2 ]o

b Fb2 1/EJ

= (-1/2 b +1/2 b -1/6 b ) Fb2 1/EJ = -1/6 Fb3/EJ

LXoBC = ∫

o

b(-1/2 +3/2 x/b -3/2 x2/b2 +1/2 x3/b3 ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ

= [-1/2 x +3/4 x2/b -1/2 x3/b2 +1/8 x4/b3 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (-1/2 b +3/4 b -1/2 b +1/8 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -9/8 Fb3/EJ

LXoCB = ∫

o


b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (-1/8 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -9/8 Fb3/EJ

Schema.brsa.008PROCEDIMENTO E RISULTATI 891317 Borsani Alessio


A = 936. mm2

Ju = 248849. mm4

Jv = 52704. mm4

yg = 33.46 mmTy = -1760. NMx = -1707200. Nmmxm = 12. mmum = -6. mmvm = -33.46 mmσm = -Mv/Ju = -229.6 N/mm2


τc = 2.62 N/mm2

σo = √σ2+3τ2 = 133.6 N/mm2

S* = 4446. mm3mm 0 12 24 36x

0

42

54

y

14σc,τc

σm

u

v

Schema.brsa.008


Schema.brsa.008


Schema.brnl.009REAZIONI 889394 Brandizi Leonardo


1/2F

7/4F

1/2F

7/4F7/4Fb

A B

5/4F

3/4F5/4Fb

5/4F

3/4F

B

C

7/4F

1/2F1/2Fb

7/4F

1/2F

B D

3/2F

1/2F

3/2F

1/2F3/2Fb

D

E

3/2F

1/2F3/2Fb

3/2F

1/2FFb

EF

3/2F

F

B

3/2F

F

3/2F1/2Fb

FG

1/2F1/2Fb

1/2F

G

A

Schema.brnl.009AZIONI INTERNE 889394 Brandizi Leonardo


-1/2

3/4

-7/4

1/2

3/2

-3/2

3/23/2

0

F

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Schema.brnl.009PROCEDIMENTO E RISULTATI 889394 Brandizi Leonardo


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(1/2 x2/b2 ) Fb2 1/EJ dx = [1/6 x3/b2 ]o

b Fb2 1/EJ

= (1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (1/2 b -1/2 b +1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

A = 936. mm2

Ju = 248849. mm4

Jv = 52704. mm4

yg = 20.54 mmN = 580. NTy = -1740. NMx = -1774800. Nmmxm = 24. mmym = 54. mmum = 6. mmvm = 33.46 mmσm = N/A-Mv/Ju = 239.3 N/mm2

xc = 18. mmyc = 40. mmvc = 19.46 mmσc = N/A-Mv/Ju = 139.4 N/mm2

τc = 2.59 N/mm2

σo = √σ2+3τ2 = 139.5 N/mm2

S* = 4446. mm3mm 0 12 24 36x

0

12

54

y

40σc,τc

σm

u

v

Schema.brnl.009


Schema.brnl.009


Schema.brnl.009


Schema.brga.010REAZIONI 881254 Broggi Andrea


5/4F 5/4F5/4Fb

A B

7/4F

1/4F7/4Fb

7/4F

1/4F

B

C

7/4F

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7/4F

1/2F

B D

F

1/2F

F

1/2FFb

D

E

F

1/2FFb

F

1/2FFb

EF

1/2F

F

B

FFG

G

A

Schema.brga.010AZIONI INTERNE 881254 Broggi Andrea


0

1/4

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11

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1

0

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5/4

-7/4

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Schema.brga.010PROCEDIMENTO E RISULTATI 881254 Broggi Andrea


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoBC = ∫

o

b(1/2 - x/b +1/2 x2/b2 ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ

= [1/2 x -1/2 x2/b +1/6 x3/b2 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (1/2 b -1/2 b +1/6 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -5/6 Fb3/EJ

LXoCB = ∫

o

b(1/2 x2/b2 ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ = [1/6 x3/b2 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (1/6 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -5/6 Fb3/EJ

A = 468. mm2

Ju = 136587. mm4

Jv = 14364. mm4

yg = 19.62 mmN = -740. NTy = -1480. NMx = -799200. Nmmxm = 18. mmym = 54. mmum = 3. mmvm = 34.38 mmσm = N/A-Mv/Ju = 199.6 N/mm2


τc = 4.154 N/mm2

σo = √σ2+3τ2 = 117.9 N/mm2

S* = 2300. mm3mm 0 12 18 30x

0

6

54

y

40σc,τc

σm

u

v

Schema.brga.010


Schema.brga.010


Schema.brga.010


Schema.crlm.011REAZIONI 893348 Carlino Mauro


1/2F

7/4F

1/2F

7/4F7/4Fb

A B

5/4F

7/4F5/4Fb

5/4F

7/4F

B

C

3/4F

1/2F1/2Fb

3/4F

1/2F

B D

3/2F

1/2F

3/2F

1/2F3/2Fb

D

E

3/2F

1/2F3/2Fb

3/2F

1/2FFb

EF

1/2F

F

B

3/2FFG

1/2F

1/2F

G

A

Schema.crlm.011AZIONI INTERNE 893348 Carlino Mauro


1/2

7/4

-3/4

1/2

3/2

-1/2

3/200

F

7/4

-5/4

-1/2

-3/2

1/2

0

0

1/2

-1/2

F

0 7/4

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Schema.crlm.011PROCEDIMENTO E RISULTATI 893348 Carlino Mauro


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(-5/2 x2/b2 ) Fb2 1/EJ dx = [-5/6 x3/b2 ]o

b Fb2 1/EJ

= (-5/6 b ) Fb2 1/EJ = -5/6 Fb3/EJ

LXoBA = ∫

o

b(-5/2 +5 x/b -5/2 x2/b2 ) Fb2 1/EJ dx = [-5/2 x +5/2 x2/b -5/6 x3/b2 ]o

b Fb2 1/EJ

= (-5/2 b +5/2 b -5/6 b ) Fb2 1/EJ = -5/6 Fb3/EJ

LXoBC = ∫

o

b(-2 +4 x/b -2 x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [-2 x +2 x2/b -2/3 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-2 b +2 b -2/3 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 1/3 Fb3/EJ

LXoCB = ∫

o

b(-2 x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ = [-2/3 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-2/3 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 1/3 Fb3/EJ

Schema.crlm.011PROCEDIMENTO E RISULTATI 893348 Carlino Mauro


A = 864. mm2

Ju = 251424. mm4

Jv = 62208. mm4

yg = 21. mmN = 895. NTy = -2685. NMx = -1584150. Nmmxm = 30. mmym = 54. mmum = 6. mmvm = 33. mmσm = N/A-Mv/Ju = 209. N/mm2

xc = 24. mmyc = 40. mmvc = 19. mmσc = N/A-Mv/Ju = 120.7 N/mm2

τc = 3.887 N/mm2

σo = √σ2+3τ2 = 120.9 N/mm2

S* = 4368. mm3mm 0 18 30 48x

0

6

54

y

40σc,τc

σm

u

v

Schema.crlm.011


Schema.crlm.011


Schema.csrf.012REAZIONI 879105 Caserta Francesco


7/4F 7/4F7/4Fb

A B

5/4F

7/4F5/4Fb

5/4F

7/4F

B

C

5/4F

1/2F1/2Fb

5/4F

1/2F

B D

2F

1/2F

2F

1/2F2Fb

D

E

2F

1/2F2Fb

2F

1/2F3/2Fb

EF

F

1/2F1/2Fb

1/2F

F

B

FFG

G

A

Schema.csrf.012AZIONI INTERNE 879105 Caserta Francesco


0

7/4

-5/4

1/2

2

-1/2

-1/2

1

0

F

7/4

-5/4

-1/2

-2

1/210

0

0

F

0 7/4

5/4

0

1/2 0

0-2

-2-3/2

-1/2

0

0000

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Schema.csrf.012PROCEDIMENTO E RISULTATI 879105 Caserta Francesco


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(1/2 x2/b2 ) Fb2 1/EJ dx = [1/6 x3/b2 ]o

b Fb2 1/EJ

= (1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (1/2 b -1/2 b +1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

A = 612. mm2

Ju = 149428. mm4

Jv = 27756. mm4


xc = 15. mmyc = 38. mmvc = 20.88 mmσc = N/A-Mv/Ju = 124. N/mm2

τc = 4.268 N/mm2

σo = √σ2+3τ2 = 124.2 N/mm2

S* = 2773. mm3mm 0 12 18 30x

0

12

54

y

38σc,τc

σm

u

v

Schema.csrf.012


Schema.csrf.012


Schema.csrf.012


Schema.cste.013REAZIONI 877793 Castiglione Ettore


7/4F 7/4F7/4Fb

A B

5/4F

7/4F5/4Fb

5/4F

7/4F

B

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D

E

F

1/2F3/2Fb

F

1/2FFb

EF

1/2F

F

B

FFG

G

A

Schema.cste.013AZIONI INTERNE 877793 Castiglione Ettore


0

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Schema.cste.013PROCEDIMENTO E RISULTATI 877793 Castiglione Ettore


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(1/2 x2/b2 ) Fb2 1/EJ dx = [1/6 x3/b2 ]o

b Fb2 1/EJ

= (1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (1/2 b -1/2 b +1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

A = 756. mm2

Ju = 165564. mm4

Jv = 74844. mm4

yg = 15. mmN = 460. NTy = -920. NMx = -966000. Nmmxm = 24. mmym = 54. mmum = 3. mmvm = 39. mmσm = N/A-Mv/Ju = 228.2 N/mm2

xc = 21. mmyc = 37. mmvc = 22. mmσc = N/A-Mv/Ju = 129. N/mm2

τc = 2.881 N/mm2

σo = √σ2+3τ2 = 129.1 N/mm2

S* = 3111. mm3mm 0 18 24 42x

0

12

54

y

37σc,τc

σm

u

v

Schema.cste.013


Schema.cste.013


Schema.cste.013


Schema.crra.014REAZIONI 914406 Corradino Andrea


31/16F 15/16F23/16Fb

A B

23/16F

15/16F23/16Fb

23/16F

15/16F

B

C

23/16FB D

F

FFb

D

E

FFb

FFb

EF

F

B

FFGG

A

Schema.crra.014AZIONI INTERNE 914406 Corradino Andrea


0 0

15/1

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0

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Schema.crra.014PROCEDIMENTO E RISULTATI 914406 Corradino Andrea


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(-1/2 x2/b2 +1/2 x3/b3 ) Fb 1/EJ dx = [-1/6 x3/b2 +1/8 x4/b3 ]o

b Fb 1/EJ

= (-1/6 b +1/8 b ) Fb 1/EJ = -1/24 Fb2/EJ

LXoBA = ∫

o

b(-1/2 x/b + x2/b2 -1/2 x3/b3 ) Fb 1/EJ dx = [-1/4 x2/b +1/3 x3/b2 -1/8 x4/b3 ]o

b Fb 1/EJ

= (-1/4 b +1/3 b -1/8 b ) Fb 1/EJ = -1/24 Fb2/EJ

A = 792. mm2

Ju = 225759. mm4

Jv = 30240. mm4

yg = 22.64 mmTy = -2300. NMx = -1725000. Nmmxm = 24. mmym = 54. mmum = 6. mmvm = 31.36 mmσm = -Mv/Ju = 239.6 N/mm2

xc = 18. mmyc = 41. mmvc = 18.36 mmσc = -Mv/Ju = 140.3 N/mm2

τc = 3.293 N/mm2

σo = √σ2+3τ2 = 140.4 N/mm2

S* = 3879. mm3mm 0 12 24 36x

0

6

54

y

41σc,τc

σm

u

v

Schema.crra.014


Schema.crra.014


Schema.crra.014


Schema.dlsf.015REAZIONI 772937 D’Alessio Francesca


5/4F 5/4F5/4Fb

A B

7/4F

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7/4F

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7/4F

B D

F

FFb

D

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FFb

FFb

EF

F

B

FFG

G

A

Schema.dlsf.015AZIONI INTERNE 772937 D’Alessio Francesca


0

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Schema.dlsf.015PROCEDIMENTO E RISULTATI 772937 D’Alessio Francesca


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(1/2 x2/b2 ) Fb 1/EJ dx = [1/6 x3/b2 ]o

b Fb 1/EJ

= (1/6 b ) Fb 1/EJ = 1/6 Fb2/EJ

LXoBA = ∫

o


b Fb 1/EJ

= (1/2 b -1/2 b +1/6 b ) Fb 1/EJ = 1/6 Fb2/EJ

A = 1080. mm2

Ju = 276955. mm4

Jv = 116640. mm4


xc = 24. mmyc = 39. mmvc = 20.4 mmσc = -Mv/Ju = 115.2 N/mm2

τc = 2.916 N/mm2

σo = √σ2+3τ2 = 115.3 N/mm2

S* = 5022. mm3mm 0 18 30 48x

0

12

54

y

39σc,τc

σm

u

v

Schema.dlsf.015


Schema.dlsf.015


Schema.dlsf.015


Schema.dnsg.016REAZIONI 845411 Danesi Gabriele


23/16F 23/16F23/16Fb

A B

15/16F

23/16F23/16Fb

31/16F

23/16F

B

C

15/16FB D

F

FFb

D

E

FFb

FFb

EF

F

B

FFGG

A

Schema.dnsg.016AZIONI INTERNE 845411 Danesi Gabriele


0

23/1

623

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-15/16

0

1

0

1

0

F

23/16

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16-3

1/16

0

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0

0

0

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F

0 23/16

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A

B C

D

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F

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Schema.dnsg.016PROCEDIMENTO E RISULTATI 845411 Danesi Gabriele


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoBC = ∫

o

b(-1/2 x/b + x2/b2 -1/2 x3/b3 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [-1/4 x2/b +1/3 x3/b2 -1/8 x4/b3 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-1/4 b +1/3 b -1/8 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 23/24 Fb3/EJ

LXoCB = ∫

o

b(-1/2 x2/b2 +1/2 x3/b3 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [-1/6 x3/b2 +1/8 x4/b3 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-1/6 b +1/8 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 23/24 Fb3/EJ

A = 540. mm2

Ju = 154030. mm4

Jv = 37908. mm4


xc = 21. mmyc = 39. mmvc = 21.6 mmσc = -Mv/Ju = 123. N/mm2

τc = 2.891 N/mm2

σo = √σ2+3τ2 = 123.1 N/mm2

S* = 2619. mm3mm 0 18 24 42x

0

6

54

y

39σc,τc

σm

u

v

Schema.dnsg.016


Schema.dnsg.016


Schema.dnsg.016


Schema.grts.017REAZIONI 917200 Gritcul Serghei


1/2F

5/2F

1/2F

5/2F5/2Fb

A B

2F

3/2FFb

2F

3/2FFb

B

C

5/2F

3/2F3/2Fb

5/2F

3/2F

B D

3/2F

3/2F

3/2F

3/2F3/2Fb

D

E

3/2F

3/2F3/2Fb

3/2F

3/2F

EF

5/2F

F

B

3/2F

F

3/2F1/2Fb

FG

1/2F1/2Fb

1/2F

G

A

Schema.grts.017AZIONI INTERNE 917200 Gritcul Serghei


-1/2

3/2

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3/2

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27.0

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B

C

D

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G

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F

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27.0

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Qua

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Schema.grts.017PROCEDIMENTO E RISULTATI 917200 Gritcul Serghei


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(-3/2 x2/b2 ) Fb 1/EJ dx = [-1/2 x3/b2 ]o

b Fb 1/EJ

= (-1/2 b ) Fb 1/EJ = -1/2 Fb2/EJ

LXoBA = ∫

o

b(-3/2 +3 x/b -3/2 x2/b2 ) Fb 1/EJ dx = [-3/2 x +3/2 x2/b -1/2 x3/b2 ]o

b Fb 1/EJ

= (-3/2 b +3/2 b -1/2 b ) Fb 1/EJ = -1/2 Fb2/EJ

LXoBC = ∫

o

b( x/b - x2/b2 ) Fb 1/EJ dx + 1 (-1) (-1) Fb2/EJ

= [1/2 x2/b -1/3 x3/b2 ]o

b Fb 1/EJ + 1 (-1) (-1) Fb2/EJ

= (1/2 b -1/3 b ) Fb 1/EJ + 1 (-1) (-1) Fb2/EJ = 7/6 Fb2/EJ

LXoCB = ∫

o

b( x/b - x2/b2 ) Fb 1/EJ dx + 1 (-1) (-1) Fb2/EJ

= [1/2 x2/b -1/3 x3/b2 ]o

b Fb 1/EJ + 1 (-1) (-1) Fb2/EJ

= (1/2 b -1/3 b ) Fb 1/EJ + 1 (-1) (-1) Fb2/EJ = 7/6 Fb2/EJ

Schema.grts.017PROCEDIMENTO E RISULTATI 917200 Gritcul Serghei


A = 498. mm2

Ju = 141019. mm4

Jv = 31734. mm4



τc = 2.87 N/mm2

σo = √σ2+3τ2 = 123.7 N/mm2

S* = 2491. mm3mm 0 18 24 42x

0

48

53

y

15σc,τc

σm

u

v

Schema.grts.017


Schema.grts.017


Schema.dmcm.018REAZIONI 870485 D’Amico Michele Francesco


2F 2F2Fb

A B

5/2F

F3/2Fb

5/2F

FFb

B

C

5/2F

1/2F1/2Fb

5/2F

1/2F

B D

F

1/2F

F

1/2FFb

D

E

F

1/2FFb

F

3/2F

EF

3/2F

F

B

FFG

G

A

Schema.dmcm.018AZIONI INTERNE 870485 D’Amico Michele Francesco


0

1

-5/2

1/2

11

-3/2

1

0

F

2

-5/2

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0

0

0

F

0 2

3/2

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0-1

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27.0

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Qua

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X=

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→M

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Schema.dmcm.018PROCEDIMENTO E RISULTATI 870485 D’Amico Michele


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(-1/2 x2/b2 ) Fb2 1/EJ dx = [-1/6 x3/b2 ]o

b Fb2 1/EJ

= (-1/6 b ) Fb2 1/EJ = -1/6 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (-1/2 b +1/2 b -1/6 b ) Fb2 1/EJ = -1/6 Fb3/EJ

LXoBC = ∫

o

b(-1 + x/b ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ = [- x +1/2 x2/b ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/E

= (- b +1/2 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -3/2 Fb3/EJ

LXoCB = ∫

o

b(- x/b ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ = [-1/2 x2/b ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (-1/2 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -3/2 Fb3/EJ

Schema.dmcm.018PROCEDIMENTO E RISULTATI 870485 D’Amico Michele


A = 714. mm2

Ju = 156210. mm4

Jv = 68670. mm4

yg = 38.15 mmN = 495. NTy = -990. NMx = -940500. Nmmxm = 18. mmum = -3. mmvm = -38.15 mmσm = N/A-Mv/Ju = -229. N/mm2


τc = 3.057 N/mm2

σo = √σ2+3τ2 = 132.8 N/mm2

S* = 2894. mm3mm 0 18 24 42x

0

42

53

y

16σc,τc

σm

u

v

Schema.dmcm.018


Schema.dmcm.018


Schema.dcml.019REAZIONI 877976 Di Camillo Lorenzo


1/2F

5/2F

1/2F

5/2F5/2Fb

A B

2F

5/2FFb

2F

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B

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3/2F3/2Fb

3/2F

3/2F

B D

3/2F

3/2F

3/2F

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D

E

3/2F

3/2F3/2Fb

3/2F

3/2F

EF

3/2F

F

B

3/2FFG

1/2F

1/2F

G

A

Schema.dcml.019AZIONI INTERNE 877976 Di Camillo Lorenzo


1/2

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3/2

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3/200

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Schema.dcml.019PROCEDIMENTO E RISULTATI 877976 Di Camillo Lorenzo


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(1/2 x2/b2 ) Fb2 1/EJ dx = [1/6 x3/b2 ]o

b Fb2 1/EJ

= (1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (1/2 b -1/2 b +1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

LXoBC = ∫

o


b Fb2 1/EJ - 1 (-1) (-1) Fb3/E

= (- b +1/2 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -3/2 Fb3/EJ

LXoCB = ∫

o


b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (-1/2 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -3/2 Fb3/EJ

Schema.dcml.019PROCEDIMENTO E RISULTATI 877976 Di Camillo Lorenzo


A = 816. mm2

Ju = 230061. mm4

Jv = 52992. mm4

yg = 31.79 mmN = -1740. NTy = -1740. NMx = 1740000. Nmmxm = 18. mmum = -6. mmvm = -31.79 mmσm = N/A-Mv/Ju = 238.3 N/mm2

xc = 24. mmyc = 13. mmvc = -18.79 mmσc = N/A-Mv/Ju = 140. N/mm2

τc = 2.487 N/mm2

σo = √σ2+3τ2 = 140.1 N/mm2

S* = 3946. mm3mm 0 18 30 48x

0

48

53

y

13σc,τc

σm

u

v

Schema.dcml.019


Schema.dcml.019


Schema.lbtt.020REAZIONI 850296 Labate Tommaso


5/2F 5/2F5/2Fb

A B

2F

5/2FFb

2F

5/2FFb

B

C

2F

3/2F3/2Fb

2F

3/2F

B D

2F

3/2F

2F

3/2F2Fb

D

E

2F

3/2F2Fb

2F

3/2F1/2Fb

EF

F

3/2F1/2Fb

3/2F

F

B

FFG

G

A

Schema.lbtt.020AZIONI INTERNE 850296 Labate Tommaso


0

5/2

-2

3/2

2

-3/2

-3/2

1

0

F

5/2

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-3/2

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0

0

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0 5/2

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0-2

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00

00

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00

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00

00

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00

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Schema.lbtt.020PROCEDIMENTO E RISULTATI 850296 Labate Tommaso


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(1/2 x2/b2 ) Fb2 1/EJ dx = [1/6 x3/b2 ]o

b Fb2 1/EJ

= (1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (1/2 b -1/2 b +1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

LXoBC = ∫

o


b Fb2 1/EJ - 1 (-1) (-1) Fb3/E

= (- b +1/2 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -3/2 Fb3/EJ

LXoCB = ∫

o


b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (-1/2 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -3/2 Fb3/EJ

Schema.lbtt.020PROCEDIMENTO E RISULTATI 850296 Labate Tommaso


A = 1032. mm2

Ju = 260495. mm4

Jv = 107424. mm4



τc = 4.236 N/mm2

σo = √σ2+3τ2 = 117.8 N/mm2

S* = 4630. mm3mm 0 18 30 48x

0

42

53

y

14σc,τc

σm

u

v

Schema.lbtt.020


Schema.lbtt.020


Schema.lgml.021REAZIONI 835162 Ligammari Luca


5/2F 5/2F5/2Fb

A B

2F

5/2FFb

2F

5/2FFb

B

C

2F

3/2F3/2Fb

2F

3/2F

B D

2F

3/2F

F

3/2F3/2Fb

D

E

F

3/2F3/2Fb

F

3/2F

EF

3/2F

F

B

FFG

G

A

Schema.lgml.021AZIONI INTERNE 835162 Ligammari Luca


0

5/2

-2

3/2

3/21

-3/2

1

0

F

5/2

-2

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-2-13/2

0

0

0

F

0 5/2

1-1

3/2 0

0-3

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0

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Sch

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lgm

l.021

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I 835

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27.0

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27.0

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00

00

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00

00

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00

00

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00

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Schema.lgml.021PROCEDIMENTO E RISULTATI 835162 Ligammari Luca


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoBC = ∫

o

b(3/2 -2 x/b +1/2 x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [3/2 x - x2/b +1/6 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (3/2 b - b +1/6 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 5/3 Fb3/EJ

LXoCB = ∫

o

b( x/b +1/2 x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [1/2 x2/b +1/6 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (1/2 b +1/6 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 5/3 Fb3/EJ

A = 438. mm2

Ju = 124871. mm4

Jv = 12114. mm4

yg = 33.08 mmN = 920. NTy = 1380. NMx = -800400. Nmmxm = 12. mmum = -3. mmvm = -33.08 mmσm = N/A-Mv/Ju = -209.9 N/mm2


τc = 4.034 N/mm2

σo = √σ2+3τ2 = 120.4 N/mm2

S* = 2190. mm3mm 0 12 18 30x

0

48

53

y

14σc,τc

σm

u

v

Schema.lgml.021


Schema.lgml.021


Schema.lgml.021


Schema.mnrs.022REAZIONI 878035 Manrique Silvera Gerald


43/16F 27/16F35/16Fb

A B

35/16F

27/16F19/16Fb

35/16F

27/16FFb

B

C

35/16F

FFb

35/16F

F

B D

F

F

F

FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

G

A

Schema.mnrs.022AZIONI INTERNE 878035 Manrique Silvera Gerald


0 0

27/1

6

-35/16

1

1

-1

1

0

F

43/16 27/16

-35/

16

-1

-1

1

0

0

0

F

0 35/16

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6-1

1 0

0-1

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0

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00

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00

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00

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16F

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Schema.mnrs.022PROCEDIMENTO E RISULTATI 878035 Manrique Silvera


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(- x2/b2 +1/2 x3/b3 ) Fb2 1/EJ dx = [-1/3 x3/b2 +1/8 x4/b3 ]o

b Fb2 1/EJ

= (-1/3 b +1/8 b ) Fb2 1/EJ = -5/24 Fb3/EJ

LXoBA = ∫

o

b(-1/2 +1/2 x/b +1/2 x2/b2 -1/2 x3/b3 ) Fb2 1/EJ dx

= [-1/2 x +1/4 x2/b +1/6 x3/b2 -1/8 x4/b3 ]o

b Fb2 1/EJ

= (-1/2 b +1/4 b +1/6 b -1/8 b ) Fb2 1/EJ = -5/24 Fb3/EJ

LXoBC = ∫

o

b(1/2 -1/2 x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [1/2 x -1/6 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (1/2 b -1/6 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 4/3 Fb3/EJ

LXoCB = ∫

o

b( x/b -1/2 x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [1/2 x2/b -1/6 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (1/2 b -1/6 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 4/3 Fb3/EJ

Schema.mnrs.022PROCEDIMENTO E RISULTATI 878035 Manrique Silvera


A = 582. mm2

Ju = 140714. mm4

Jv = 25506. mm4



τc = 4.166 N/mm2

σo = √σ2+3τ2 = 126.8 N/mm2

S* = 2567. mm3mm 0 12 18 30x

0

42

53

y

15σc,τc

σm

u

v

Schema.mnrs.022


Schema.mnrs.022


Schema.mrna.023REAZIONI 835477 Maranga Andrea


2F 2F2Fb

A B

5/2F

F3/2Fb

5/2F

FFb

B

C

5/2F1/2Fb

5/2F

F

B D

F

F

F

FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

G

A

Schema.mrna.023AZIONI INTERNE 835477 Maranga Andrea


0

1

-5/2 -5/2

1

1

-1

1

0

F

2

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0-1

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27.0

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Qua

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iper

stat

ica

X=

VC

→M

x(x)

Mo(

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xMo

MxM

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xMo/

EJd

x∫X

MxM

x/E

Jdx

AB

b-x

Fx

-Fx2

x2

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Fb3 /E

J1/

3Xb3 /E

JB

A b

b-x

-Fb+

Fx

-Fb2 +

2Fbx

-Fx2

b2 -2bx

+x2

BC

b-b

+x

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2Fbx

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+x2

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JC

B b

xF

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2Fx

Fbx

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Fx2

x2

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b0

1/2F

b-1/

2qx2

00

00

DB

b0

-Fx+

1/2q

x20

0

DE

b0

-Fx

00

00

ED

b0

Fb-

Fx

00

EF

b0

-Fb+

Fx

00

00

FE

b0

Fx

00

FB

b0

00

00

0B

F b

00

00

FG

b0

00

00

0G

F b

00

00

GA

b0

00

00

0A

G b

00

00

BC

elon

gazi

one

asta

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Cε B

CL B

CF

b3 /EJ

tota

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3Fb3 /E

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iper

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X=

VC

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Svi

lupp

i di c

alco

lo ip

erst

atic

a

Schema.mrna.023PROCEDIMENTO E RISULTATI 835477 Maranga Andrea


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(- x2/b2 ) Fb2 1/EJ dx = [-1/3 x3/b2 ]o

b Fb2 1/EJ

= (-1/3 b ) Fb2 1/EJ = -1/3 Fb3/EJ

LXoBA = ∫

o

b(-1 +2 x/b - x2/b2 ) Fb2 1/EJ dx = [- x + x2/b -1/3 x3/b2 ]o

b Fb2 1/EJ

= (- b + b -1/3 b ) Fb2 1/EJ = -1/3 Fb3/EJ

LXoBC = ∫

o

b(-1/2 +2 x/b -3/2 x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [-1/2 x + x2/b -1/2 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-1/2 b + b -1/2 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = Fb3/EJ

LXoCB = ∫

o

b( x/b -3/2 x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [1/2 x2/b -1/2 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (1/2 b -1/2 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = Fb3/EJ

Schema.mrna.023PROCEDIMENTO E RISULTATI 835477 Maranga Andrea


A = 756. mm2

Ju = 207276. mm4

Jv = 26352. mm4



τc = 3.613 N/mm2

σo = √σ2+3τ2 = 131.4 N/mm2

S* = 3841. mm3mm 0 12 24 36x

0

48

53

y

47σc,τc

σm

u

v

Schema.mrna.023


Schema.mrna.023


Schema.mrtm.024REAZIONI 846219 Martignoni Matteo


35/16F 35/16F35/16Fb

A B

27/16F

35/16F19/16Fb

43/16F

35/16FFb

B

C

27/16F

FFb

27/16F

F

B D

F

F

F

FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

G

A

Schema.mrtm.024AZIONI INTERNE 846219 Martignoni Matteo


0

35/1

635

/16

-27/16

1

1

-1

1

0

F

35/16

-27/

16-4

3/16

-1

-1

1

0

0

0

F

0 35/16

19/1

6-1

1 0

0-1

-100

0

0000

Fb

Sch

ema.

mrt

m.0

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Mat

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no, v

ers.

27.0

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A

B

C

DEF

G

W

F

X

q

Sch

ema

di c

alco

lo ip

erst

atic

o

03/

2

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10

0-1

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00 0 0

Mo

fless

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0-1

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0

00

00 0 0

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Mx

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X=

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ers.

27.0

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Qua

dro

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ribut

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per

iper

stat

ica

X=

HD

→M

x(x)

Mo(

x)M

xMo

MxM

x∫M

xMo/

EJd

x∫X

MxM

x/E

Jdx

AB

b-x

3/2F

x-3

/2F

x2x2

-1/2

Fb3 /E

J1/

3Xb3 /E

JB

A b

b-x

-3/2

Fb+

3/2F

x-3

/2F

b2 +3F

bx-3

/2F

x2b2 -2

bx+

x2

BC

b-b

+x

1/2F

b-F

x-1/

2qx2

-1/2

Fb2 +

3/2F

bx-1

/2F

x2 -1/2

qx3

b2 -2bx

+x2

-1/2

4Fb3 /E

J1/

3Xb3 /E

JC

B b

xF

b-2F

x+1/

2qx2

Fbx

-2F

x2 +1/

2qx3

x2

BD

b0

Fb-

Fx

00

00

DB

b0

-Fx

00

DE

b0

-Fx

00

00

ED

b0

Fb-

Fx

00

EF

b0

-Fb+

Fx

00

00

FE

b0

Fx

00

FB

b0

00

00

0B

F b

00

00

FG

b0

00

00

0G

F b

00

00

GA

b0

00

00

0A

G b

00

00

BC

elon

gazi

one

asta

N1B

Cε B

CL B

CF

b3 /EJ

tota

li11

/24F

b3 /EJ

2/3X

b3 /EJ

iper

stat

ica

X=

HD

-11/

16F

Svi

lupp

i di c

alco

lo ip

erst

atic

a

Schema.mrtm.024PROCEDIMENTO E RISULTATI 846219 Martignoni Matteo


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(-3/2 x2/b2 ) Fb2 1/EJ dx = [-1/2 x3/b2 ]o

b Fb2 1/EJ

= (-1/2 b ) Fb2 1/EJ = -1/2 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (-3/2 b +3/2 b -1/2 b ) Fb2 1/EJ = -1/2 Fb3/EJ

LXoBC = ∫

o

b(-1/2 +3/2 x/b -1/2 x2/b2 -1/2 x3/b3 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [-1/2 x +3/4 x2/b -1/6 x3/b2 -1/8 x4/b3 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-1/2 b +3/4 b -1/6 b -1/8 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 23/24 Fb3/EJ

LXoCB = ∫

o

b( x/b -2 x2/b2 +1/2 x3/b3 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [1/2 x2/b -2/3 x3/b2 +1/8 x4/b3 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (1/2 b -2/3 b +1/8 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 23/24 Fb3/EJ

Schema.mrtm.024PROCEDIMENTO E RISULTATI 846219 Martignoni Matteo


A = 900. mm2

Ju = 233812. mm4

Jv = 48816. mm4



τc = 3.595 N/mm2

σo = √σ2+3τ2 = 135.7 N/mm2

S* = 4311. mm3mm 0 12 24 36x

0

42

53

y

14σc,τc

σm

u

v

Schema.mrtm.024


Schema.mrtm.024


Schema.mccg.025REAZIONI 867110 Mecacci Giorgia


1/2F

FFb

1/2F

F2Fb

A B

1/2F1/2Fb

1/2F

B

C

F

3/2F3/2Fb

F

3/2F

B D

3/2F

3/2F

3/2F

3/2F3/2Fb

D

E

3/2F

3/2F3/2Fb

3/2F

3/2F

EF

5/2F

F

B

3/2F

F

3/2F1/2Fb

FG

1/2F1/2Fb

1/2F

G

A

Schema.mccg.025AZIONI INTERNE 867110 Mecacci Giorgia


-1/2

0

-1

3/2

3/2

-5/2

3/23/2

0

F

1

-1/2

-3/2

-3/2

3/2

0

-10

1/2

F

1 2

1/2

0

3/2 0

0-3

/2

-3/200

0

0-1/2

-1/2

0

Fb

Sch

ema.

mcc

g.02

5P

RO

CE

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EN

TO

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ISU

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27.0

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01

1 000

00

00 0 0

00 0 0

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27.0

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Qua

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iper

stat

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X=

VA

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Mo(

x)M

xMo

MxM

x∫M

xMo/

EJd

x∫X

MxM

x/E

Jdx

AB

bx

Fb

Fbx

x2

1/2F

b3 /EJ

1/3X

b3 /EJ

BA

b-b

+x

-Fb

Fb2 -F

bxb2 -2

bx+

x2

BC

bb-

x-1

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b+1/

2Fx

-1/2

Fb2 +

Fbx

-1/2

Fx2

b2 -2bx

+x2

-1/6

Fb3 /E

J1/

3Xb3 /E

JC

B b

-x1/

2Fx

-1/2

Fx2

x2

BD

b0

3/2F

b-3/

2Fx

00

00

DB

b0

-3/2

Fx

00

DE

b0

-3/2

Fx

00

00

ED

b0

3/2F

b-3/

2Fx

00

EF

b0

-3/2

Fb+

3/2F

x0

00

0F

E b

03/

2Fx

00

FB

b0

00

00

0B

F b

00

00

FG

b0

-Fx+

1/2q

x20

00

0G

F b

01/

2Fb-

1/2q

x20

0

GA

b0

-1/2

Fb+

1/2F

x0

00

0A

G b

01/

2Fx

00

BC

elon

gazi

one

asta

N1B

Cε B

CL B

C-F

b3 /EJ

tota

li-2

/3F

b3 /EJ

2/3X

b3 /EJ

iper

stat

ica

X=

VA

F

Svi

lupp

i di c

alco

lo ip

erst

atic

a

Schema.mccg.025PROCEDIMENTO E RISULTATI 867110 Mecacci Giorgia


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b( x/b ) Fb2 1/EJ dx = [1/2 x2/b ]o

b Fb2 1/EJ

= (1/2 b ) Fb2 1/EJ = 1/2 Fb3/EJ

LXoBA = ∫

o

b(1 - x/b ) Fb2 1/EJ dx = [ x -1/2 x2/b ]o

b Fb2 1/EJ

= ( b -1/2 b ) Fb2 1/EJ = 1/2 Fb3/EJ

LXoBC = ∫

o


= [-1/2 x +1/2 x2/b -1/6 x3/b2 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ


LXoCB = ∫

o


b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (-1/6 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -7/6 Fb3/EJ

Schema.mccg.025PROCEDIMENTO E RISULTATI 867110 Mecacci Giorgia


A = 924. mm2

Ju = 235641. mm4

Jv = 52560. mm4



τc = 2.746 N/mm2

σo = √σ2+3τ2 = 115.1 N/mm2

S* = 4349. mm3mm 0 12 24 36x

0

12

53

y

39σc,τc

σm

u

v

Schema.mccg.025


Schema.mccg.025


Schema.mssf.026REAZIONI 889516 Messa Federico


1/2FFb

1/2F3/2Fb

A B

F

1/2FFb

F

1/2F

B

C

F

1/2F1/2Fb

F

1/2F

B D

F

1/2F

F

1/2FFb

D

E

F

1/2FFb

F

3/2F

EF

3/2F

F

B

FFG

G

A

Schema.mssf.026AZIONI INTERNE 889516 Messa Federico


0

-1/2

-1

1/2

11

-3/2

1

0

F

1/2

-1

-1/2

-1

1/23/2

0

0

0

F

1 3/2

10

1/2 0

0-1

-100

0

0000

Fb

Sch

ema.

mss

f.026

PR

OC

ED

IME

NT

O E

RIS

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27.0

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D

EF

G

W

FX

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1/2 01/2

0

0-1

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01

1 000

00

00 0 0

00 0 0

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27.0

3.13

06.0

9.19

Qua

dro

cont

ribut

i PLV

per

iper

stat

ica

X=

VA

→M

x(x)

Mo(

x)M

xMo

MxM

x∫M

xMo/

EJd

x∫X

MxM

x/E

Jdx

AB

bx

Fb

Fbx

x2

1/2F

b3 /EJ

1/3X

b3 /EJ

BA

b-b

+x

-Fb

Fb2 -F

bxb2 -2

bx+

x2

BC

bb-

x1/

2Fb-

1/2F

x1/

2Fb2 -F

bx+

1/2F

x2b2 -2

bx+

x2

1/6F

b3 /EJ

1/3X

b3 /EJ

CB

b-x

-1/2

Fx

1/2F

x2x2

BD

b0

1/2F

b-1/

2Fx

00

00

DB

b0

-1/2

Fx

00

DE

b0

-Fx

00

00

ED

b0

Fb-

Fx

00

EF

b0

-Fb+

1/2F

x+1/

2qx2

00

00

FE

b0

3/2F

x-1/

2qx2

00

FB

b0

00

00

0B

F b

00

00

FG

b0

00

00

0G

F b

00

00

GA

b0

00

00

0A

G b

00

00

BC

elon

gazi

one

asta

N1B

Cε B

CL B

C-F

b3 /EJ

tota

li-1

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b3 /EJ

2/3X

b3 /EJ

iper

stat

ica

X=

VA

1/2F

Svi

lupp

i di c

alco

lo ip

erst

atic

a

Schema.mssf.026PROCEDIMENTO E RISULTATI 889516 Messa Federico


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b( x/b ) Fb2 1/EJ dx = [1/2 x2/b ]o

b Fb2 1/EJ

= (1/2 b ) Fb2 1/EJ = 1/2 Fb3/EJ

LXoBA = ∫

o

b(1 - x/b ) Fb2 1/EJ dx = [ x -1/2 x2/b ]o

b Fb2 1/EJ

= ( b -1/2 b ) Fb2 1/EJ = 1/2 Fb3/EJ

LXoBC = ∫

o

b(1/2 - x/b +1/2 x2/b2 ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ

= [1/2 x -1/2 x2/b +1/6 x3/b2 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ


LXoCB = ∫

o

b(1/2 x2/b2 ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ = [1/6 x3/b2 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (1/6 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -5/6 Fb3/EJ

Schema.mssf.026PROCEDIMENTO E RISULTATI 889516 Messa Federico


A = 462. mm2

Ju = 129608. mm4

Jv = 14346. mm4



τc = 2.753 N/mm2

σo = √σ2+3τ2 = 123.2 N/mm2

S* = 2253. mm3mm 0 12 18 30x

0

6

53

y

39σc,τc

σm

u

v

Schema.mssf.026


Schema.mssf.026


Schema.mnta.027REAZIONI 887897 Montagner Alessio


1/2F

FFb

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1/2F

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Schema.mnta.027AZIONI INTERNE 887897 Montagner Alessio


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Schema.mnta.027PROCEDIMENTO E RISULTATI 887897 Montagner Alessio


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b( x/b +1/2 x2/b2 ) Fb2 1/EJ dx = [1/2 x2/b +1/6 x3/b2 ]o

b Fb2 1/EJ

= (1/2 b +1/6 b ) Fb2 1/EJ = 2/3 Fb3/EJ

LXoBA = ∫

o

b(3/2 -2 x/b +1/2 x2/b2 ) Fb2 1/EJ dx = [3/2 x - x2/b +1/6 x3/b2 ]o

b Fb2 1/EJ

= (3/2 b - b +1/6 b ) Fb2 1/EJ = 2/3 Fb3/EJ

A = 852. mm2

Ju = 238569. mm4

Jv = 62064. mm4



τc = 2.644 N/mm2

σo = √σ2+3τ2 = 125.4 N/mm2

S* = 4277. mm3mm 0 18 30 48x

0

6

53

y

39σc,τc

σm

u

v

Schema.mnta.027


Schema.mnta.027


Schema.mnta.027


Schema.mntm.028REAZIONI 844334 Montemarano Mauro


FFb

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3/2F2Fb

2F

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EF

F

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FFG

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A

Schema.mntm.028AZIONI INTERNE 844334 Montemarano Mauro


0

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Schema.mntm.028PROCEDIMENTO E RISULTATI 844334 Montemarano Mauro


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(- x/b -1/2 x2/b2 ) Fb 1/EJ dx = [-1/2 x2/b -1/6 x3/b2 ]o

b Fb 1/EJ

= (-1/2 b -1/6 b ) Fb 1/EJ = -2/3 Fb2/EJ

LXoBA = ∫

o

b(-3/2 +2 x/b -1/2 x2/b2 ) Fb 1/EJ dx = [-3/2 x + x2/b -1/6 x3/b2 ]o

b Fb 1/EJ

= (-3/2 b + b -1/6 b ) Fb 1/EJ = -2/3 Fb2/EJ

A = 606. mm2

Ju = 141406. mm4

Jv = 27738. mm4



τc = 2.805 N/mm2

σo = √σ2+3τ2 = 132.5 N/mm2

S* = 2587. mm3mm 0 12 18 30x

0

12

53

y

38σc,τc

σm

u

v

Schema.mntm.028


Schema.mntm.028


Schema.mntm.028


Schema.mttv.029REAZIONI 853842 Motta Valentina


FFb

F2Fb

A B

1/2F

F1/2Fb

1/2F

F

B

C

1/2F

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B D

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3/2F3/2Fb

D

E

F

3/2F3/2Fb

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EF

3/2F

F

B

FFG

G

A

Schema.mttv.029AZIONI INTERNE 853842 Motta Valentina


0

1

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1

0

F

1

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Schema.mttv.029PROCEDIMENTO E RISULTATI 853842 Motta Valentina


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b( x/b +1/2 x2/b2 ) Fb2 1/EJ dx = [1/2 x2/b +1/6 x3/b2 ]o

b Fb2 1/EJ

= (1/2 b +1/6 b ) Fb2 1/EJ = 2/3 Fb3/EJ

LXoBA = ∫

o

b(3/2 -2 x/b +1/2 x2/b2 ) Fb2 1/EJ dx = [3/2 x - x2/b +1/6 x3/b2 ]o

b Fb2 1/EJ

= (3/2 b - b +1/6 b ) Fb2 1/EJ = 2/3 Fb3/EJ

A = 750. mm2

Ju = 156599. mm4

Jv = 74826. mm4

yg = 14.69 mmN = 650. NTy = 975. NMx = -975000. Nmmxm = 24. mmym = 53. mmum = 3. mmvm = 38.31 mmσm = N/A-Mv/Ju = 239.4 N/mm2


τc = 3.019 N/mm2

σo = √σ2+3τ2 = 139.9 N/mm2

S* = 2910. mm3mm 0 18 24 42x

0

12

53

y

37σc,τc

σm

u

v

Schema.mttv.029


Schema.mttv.029


Schema.mttv.029


Schema.nzza.030REAZIONI 881418 Nuzzo Arianna


19/16FFb

3/16F27/16Fb

A B

11/16F

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F

B D

F

F

F

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Schema.nzza.030AZIONI INTERNE 881418 Nuzzo Arianna


0 0

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Schema.nzza.030PROCEDIMENTO E RISULTATI 881418 Nuzzo Arianna


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b( x/b -1/2 x3/b3 ) Fb2 1/EJ dx = [1/2 x2/b -1/8 x4/b3 ]o

b Fb2 1/EJ

= (1/2 b -1/8 b ) Fb2 1/EJ = 3/8 Fb3/EJ

LXoBA = ∫

o

b(1/2 +1/2 x/b -3/2 x2/b2 +1/2 x3/b3 ) Fb2 1/EJ dx

= [1/2 x +1/4 x2/b -1/2 x3/b2 +1/8 x4/b3 ]o

b Fb2 1/EJ

= (1/2 b +1/4 b -1/2 b +1/8 b ) Fb2 1/EJ = 3/8 Fb3/EJ

LXoBC = ∫

o


= [-1/2 x +1/2 x2/b -1/6 x3/b2 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ


LXoCB = ∫

o


b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (-1/6 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -7/6 Fb3/EJ

Schema.nzza.030PROCEDIMENTO E RISULTATI 881418 Nuzzo Arianna


A = 780. mm2

Ju = 214152. mm4

Jv = 30096. mm4



τc = 3.797 N/mm2

σo = √σ2+3τ2 = 116.9 N/mm2

S* = 3797. mm3mm 0 12 24 36x

0

6

53

y

40σc,τc

σm

u

v

Schema.nzza.030


Schema.nzza.030


Schema.ptre.031REAZIONI 888074 Pietrobelli Eleonora


1/2FFb

1/2F3/2Fb

A B

F

1/2FFb

F

1/2F

B

C

F1/2Fb

F

F

B D

F

F

F

FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

G

A

Schema.ptre.031AZIONI INTERNE 888074 Pietrobelli Eleonora


0

-1/2

-1 -1

1

1

-1

1

0

F

1/2

-1

0-1

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Schema.ptre.031PROCEDIMENTO E RISULTATI 888074 Pietrobelli Eleonora


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(- x/b +1/2 x2/b2 ) Fb 1/EJ dx = [-1/2 x2/b +1/6 x3/b2 ]o

b Fb 1/EJ

= (-1/2 b +1/6 b ) Fb 1/EJ = -1/3 Fb2/EJ

LXoBA = ∫

o

b(-1/2 +1/2 x2/b2 ) Fb 1/EJ dx = [-1/2 x +1/6 x3/b2 ]o

b Fb 1/EJ

= (-1/2 b +1/6 b ) Fb 1/EJ = -1/3 Fb2/EJ

A = 1068. mm2

Ju = 262174. mm4

Jv = 116496. mm4



τc = 4.2 N/mm2

σo = √σ2+3τ2 = 120.5 N/mm2

S* = 4913. mm3mm 0 18 30 48x

0

12

53

y

38σc,τc

σm

u

v

Schema.ptre.031


Schema.ptre.031


Schema.ptre.031


Schema.ppvy.032REAZIONI 849430 Popova Yulia


11/16FFb

11/16F27/16Fb

A B

3/16F

11/16F11/16Fb

19/16F

11/16F

B

C

3/16F

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3/16F

F

B D

F

F

F

FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

G

A

Schema.ppvy.032AZIONI INTERNE 849430 Popova Yulia


0

11/1

611

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1

1

-1

1

0

F

11/16

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Schema.ppvy.032PROCEDIMENTO E RISULTATI 849430 Popova Yulia


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b( x/b ) Fb2 1/EJ dx = [1/2 x2/b ]o

b Fb2 1/EJ

= (1/2 b ) Fb2 1/EJ = 1/2 Fb3/EJ

LXoBA = ∫

o

b(1 - x/b ) Fb2 1/EJ dx = [ x -1/2 x2/b ]o

b Fb2 1/EJ

= ( b -1/2 b ) Fb2 1/EJ = 1/2 Fb3/EJ

LXoBC = ∫

o

b(1/2 x/b - x2/b2 +1/2 x3/b3 ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ

= [1/4 x2/b -1/3 x3/b2 +1/8 x4/b3 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ


LXoCB = ∫

o

b(1/2 x2/b2 -1/2 x3/b3 ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ

= [1/6 x3/b2 -1/8 x4/b3 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (1/6 b -1/8 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -23/24 Fb3/EJ

Schema.ppvy.032PROCEDIMENTO E RISULTATI 849430 Popova Yulia


A = 534. mm2

Ju = 146122. mm4

Jv = 37890. mm4

yg = 16.99 mmN = 1400. NTy = -1400. NMx = -882000. Nmmxm = 24. mmym = 53. mmum = 3. mmvm = 36.01 mmσm = N/A-Mv/Ju = 220. N/mm2


τc = 4.097 N/mm2

σo = √σ2+3τ2 = 129.6 N/mm2

S* = 2566. mm3mm 0 18 24 42x

0

6

53

y

38σc,τc

σm

u

v

Schema.ppvy.032


Schema.ppvy.032


Schema.pzzm.033REAZIONI 891221 Pozzoni Marco


1/2F

7/4F

1/2F

7/4F7/4Fb

A B

5/4F

3/4F5/4Fb

5/4F

3/4F

B

C

7/4F

3/2F1/2Fb

7/4F

3/2FFb

B D

3/2F

3/2F

3/2F

3/2F3/2Fb

D

E

3/2F

3/2F3/2Fb

3/2F

3/2F

EF

5/2F

F

B

3/2F

F

3/2F1/2Fb

FG

1/2F1/2Fb

1/2F

G

A

Schema.pzzm.033AZIONI INTERNE 891221 Pozzoni Marco


-1/2

3/4

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3/2

3/2

-5/2

3/23/2

0

F

7/4

-5/4

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3/2

0

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1/2

F

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0

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Schema.pzzm.033PROCEDIMENTO E RISULTATI 891221 Pozzoni Marco


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(-3/2 x2/b2 ) Fb2 1/EJ dx = [-1/2 x3/b2 ]o

b Fb2 1/EJ

= (-1/2 b ) Fb2 1/EJ = -1/2 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (-3/2 b +3/2 b -1/2 b ) Fb2 1/EJ = -1/2 Fb3/EJ

LXoBC = ∫

o

b(-1 +2 x/b - x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [- x + x2/b -1/3 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (- b + b -1/3 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 2/3 Fb3/EJ

LXoCB = ∫

o

b(- x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ = [-1/3 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-1/3 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 2/3 Fb3/EJ

Schema.pzzm.033PROCEDIMENTO E RISULTATI 891221 Pozzoni Marco


A = 582. mm2

Ju = 166519. mm4

Jv = 44082. mm4



τc = 4.093 N/mm2

σo = √σ2+3τ2 = 130.8 N/mm2

S* = 2870. mm3mm 0 18 24 42x

0

48

55

y

16σc,τc

σm

u

v

Schema.pzzm.033


Schema.pzzm.033


Schema.prva.034REAZIONI 853194 Previtali Alessia


5/4F 5/4F5/4Fb

A B

7/4F

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7/4F

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7/4F

1/2FFb

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F

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D

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F

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F

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EF

3/2F

F

B

FFG

G

A

Schema.prva.034AZIONI INTERNE 853194 Previtali Alessia


0

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x/E

Jdx

AB

b-x

1/2F

x-1

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x2x2

-1/6

Fb3 /E

J1/

3Xb3 /E

JB

A b

b-x

-1/2

Fb+

1/2F

x-1

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b2 +F

bx-1

/2F

x2b2 -2

bx+

x2

BC

b-b

+x

Fb-

Fx

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2Fbx

-Fx2

b2 -2bx

+x2

-1/3

Fb3 /E

J1/

3Xb3 /E

JC

B b

x-F

x-F

x2x2

BD

b0

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Fb-

1/2F

x0

00

0D

B b

0F

b-1/

2Fx

00

DE

b0

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00

00

ED

b0

Fb-

Fx

00

EF

b0

-Fb+

1/2F

x+1/

2qx2

00

00

FE

b0

3/2F

x-1/

2qx2

00

FB

b0

00

00

0B

F b

00

00

FG

b0

00

00

0G

F b

00

00

GA

b0

00

00

0A

G b

00

00

BC

elon

gazi

one

asta

N1B

Cε B

CL B

CF

b3 /EJ

tota

li1/

2Fb3 /E

J2/

3Xb3 /E

J

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Svi

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Schema.prva.034PROCEDIMENTO E RISULTATI 853194 Previtali Alessia


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(-1/2 x2/b2 ) Fb2 1/EJ dx = [-1/6 x3/b2 ]o

b Fb2 1/EJ

= (-1/6 b ) Fb2 1/EJ = -1/6 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (-1/2 b +1/2 b -1/6 b ) Fb2 1/EJ = -1/6 Fb3/EJ

LXoBC = ∫

o


= [- x + x2/b -1/3 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ


LXoCB = ∫

o


b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-1/3 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 2/3 Fb3/EJ

Schema.prva.034PROCEDIMENTO E RISULTATI 853194 Previtali Alessia


A = 798. mm2

Ju = 175127. mm4

Jv = 81018. mm4



τc = 4.165 N/mm2

σo = √σ2+3τ2 = 136.8 N/mm2

S* = 3194. mm3mm 0 18 24 42x

0

42

55

y

17σc,τc

σm

u

v

Schema.prva.034


Schema.prva.034


Schema.prft.035REAZIONI 867435 Prifti Tomas


1/2F

7/4F

1/2F

7/4F7/4Fb

A B

5/4F

7/4F5/4Fb

5/4F

7/4F

B

C

3/4F

3/2F1/2Fb

3/4F

3/2FFb

B D

3/2F

3/2F

3/2F

3/2F3/2Fb

D

E

3/2F

3/2F3/2Fb

3/2F

3/2F

EF

3/2F

F

B

3/2FFG

1/2F

1/2F

G

A

Schema.prft.035AZIONI INTERNE 867435 Prifti Tomas


1/2

7/4

-3/4

3/2

3/2

-3/2

3/200

F

7/4

-5/4

-3/2

-3/2

3/2

0

0

1/2

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F

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b+F

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1-2x

/b+

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CB

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2

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00

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00

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x-1/

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CF

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Schema.prft.035PROCEDIMENTO E RISULTATI 867435 Prifti Tomas


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(-1/2 x2/b2 ) Fb 1/EJ dx = [-1/6 x3/b2 ]o

b Fb 1/EJ

= (-1/6 b ) Fb 1/EJ = -1/6 Fb2/EJ

LXoBA = ∫

o


b Fb 1/EJ

= (-1/2 b +1/2 b -1/6 b ) Fb 1/EJ = -1/6 Fb2/EJ

A = 912. mm2

Ju = 272448. mm4

Jv = 71424. mm4



τc = 2.74 N/mm2

σo = √σ2+3τ2 = 117. N/mm2

S* = 4558. mm3mm 0 18 30 48x

0

48

55

y

14σc,τc

σm

u

v

Schema.prft.035


Schema.prft.035


Schema.prft.035


Schema.rttl.036REAZIONI 892357 Rattaggi Lorenza


7/4F 7/4F7/4Fb

A B

5/4F

7/4F5/4Fb

5/4F

7/4F

B

C

5/4F

3/2F1/2Fb

5/4F

3/2FFb

B D

2F

3/2F

2F

3/2F2Fb

D

E

2F

3/2F2Fb

2F

3/2F1/2Fb

EF

F

3/2F1/2Fb

3/2F

F

B

FFG

G

A

Schema.rttl.036AZIONI INTERNE 892357 Rattaggi Lorenza


0

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3/2

2

-3/2

-3/2

1

0

F

7/4

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0

0

F

0 7/4

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AB

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00

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BC

bb-

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b+1/

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Fbx

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b2 -2bx

+x2

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J1/

3Xb3 /E

JC

B b

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2Fx

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x2

BD

b0

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b0

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DE

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Fx-

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F b

01/

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00

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Schema.rttl.036PROCEDIMENTO E RISULTATI 892357 Rattaggi Lorenza


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoBC = ∫

o


= [-1/2 x +1/2 x2/b -1/6 x3/b2 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ


LXoCB = ∫

o


b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (-1/6 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -7/6 Fb3/EJ

A = 1128. mm2

Ju = 293725. mm4

Jv = 125856. mm4


xc = 24. mmyc = 15. mmvc = -21.21 mmσc = N/A-Mv/Ju = -122. N/mm2

τc = 2.845 N/mm2

σo = √σ2+3τ2 = 122.1 N/mm2

S* = 5168. mm3mm 0 18 30 48x

0

42

55

y

15σc,τc

σm

u

v

Schema.rttl.036


Schema.rttl.036


Schema.rttl.036


Schema.rsse.037REAZIONI 917955 Rossi Edoardo


7/4F 7/4F7/4Fb

A B

5/4F

7/4F5/4Fb

5/4F

7/4F

B

C

5/4F

3/2F1/2Fb

5/4F

3/2FFb

B D

2F

3/2F

F

3/2F3/2Fb

D

E

F

3/2F3/2Fb

F

3/2F

EF

3/2F

F

B

FFG

G

A

Schema.rsse.037AZIONI INTERNE 917955 Rossi Edoardo


0

7/4

-5/4

3/2

3/21

-3/2

1

0

F

7/4

-5/4

-3/2

-2-13/2

0

0

0

F

0 7/4

5/4

0

1/2-1

0-3

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0

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00

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00

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00

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Schema.rsse.037PROCEDIMENTO E RISULTATI 917955 Rossi Edoardo


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(1/2 x2/b2 ) Fb2 1/EJ dx = [1/6 x3/b2 ]o

b Fb2 1/EJ

= (1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (1/2 b -1/2 b +1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

A = 498. mm2

Ju = 147997. mm4

Jv = 16614. mm4

yg = 35.6 mmN = 650. NTy = 975. NMx = -906750. Nmmxm = 12. mmum = -3. mmvm = -35.6 mmσm = N/A-Mv/Ju = -216.8 N/mm2


τc = 2.776 N/mm2

σo = √σ2+3τ2 = 125. N/mm2

S* = 2529. mm3mm 0 12 18 30x

0

48

55

y

15σc,τc

σm

u

v

Schema.rsse.037


Schema.rsse.037


Schema.rsse.037


Schema.slrm.038REAZIONI 896150 Salari Mehdi


31/16F 15/16F23/16Fb

A B

23/16F

15/16F23/16Fb

23/16F

15/16F

B

C

23/16F

F

23/16F

FFb

B D

F

F

F

FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

G

A

Schema.slrm.038AZIONI INTERNE 896150 Salari Mehdi


0 0

15/1

6

-23/16

1

1

-1

1

0

F

31/16 15/16

-23/

16

-1

-1

1

0

0

0

F

0 23/16

23/1

60

0-1

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0

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00

DB

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00

00

ED

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00

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00

00

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b0

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00

FB

b0

00

00

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F b

00

00

FG

b0

00

00

0G

F b

00

00

GA

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00

00

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00

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Schema.slrm.038PROCEDIMENTO E RISULTATI 896150 Salari Mehdi


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(1/2 x2/b2 -1/2 x3/b3 ) Fb2 1/EJ dx = [1/6 x3/b2 -1/8 x4/b3 ]o

b Fb2 1/EJ

= (1/6 b -1/8 b ) Fb2 1/EJ = 1/24 Fb3/EJ

LXoBA = ∫

o

b(1/2 x/b - x2/b2 +1/2 x3/b3 ) Fb2 1/EJ dx = [1/4 x2/b -1/3 x3/b2 +1/8 x4/b3 ]o

b Fb2 1/EJ

= (1/4 b -1/3 b +1/8 b ) Fb2 1/EJ = 1/24 Fb3/EJ

A = 642. mm2

Ju = 158306. mm4

Jv = 30006. mm4

yg = 37.71 mmN = -1380. NTy = -960. NMx = -950400. Nmmxm = 12. mmum = -3. mmvm = -37.71 mmσm = N/A-Mv/Ju = -228.5 N/mm2


τc = 2.882 N/mm2

σo = √σ2+3τ2 = 132.6 N/mm2

S* = 2852. mm3mm 0 12 18 30x

0

42

55

y

16σc,τc

σm

u

v

Schema.slrm.038


Schema.slrm.038


Schema.slrm.038


Schema.slvg.039REAZIONI 834781 Salvatori Gabriele


5/4F 5/4F5/4Fb

A B

7/4F

1/4F7/4Fb

7/4F

1/4F

B

C

7/4F1/2Fb

7/4F

FFb

B D

F

F

F

FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

G

A

Schema.slvg.039AZIONI INTERNE 834781 Salvatori Gabriele


0

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Schema.slvg.039PROCEDIMENTO E RISULTATI 834781 Salvatori Gabriele


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(- x2/b2 ) Fb2 1/EJ dx = [-1/3 x3/b2 ]o

b Fb2 1/EJ

= (-1/3 b ) Fb2 1/EJ = -1/3 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (- b + b -1/3 b ) Fb2 1/EJ = -1/3 Fb3/EJ

LXoBC = ∫

o


= [-3/2 x +3/2 x2/b -1/2 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ


LXoCB = ∫

o

b(-3/2 x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ = [-1/2 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-1/2 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 1/2 Fb3/EJ

Schema.slvg.039PROCEDIMENTO E RISULTATI 834781 Salvatori Gabriele


A = 828. mm2

Ju = 244195. mm4

Jv = 34128. mm4



τc = 2.487 N/mm2

σo = √σ2+3τ2 = 137.5 N/mm2

S* = 4262. mm3mm 0 12 24 36x

0

48

55

y

14σc,τc

σm

u

v

Schema.slvg.039


Schema.slvg.039


Schema.sccm.040REAZIONI 853403 Scoccimarro Martina


23/16F 23/16F23/16Fb

A B

15/16F

23/16F23/16Fb

31/16F

23/16F

B

C

15/16F

F

15/16F

FFb

B D

F

F

F

FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

G

A

Schema.sccm.040AZIONI INTERNE 853403 Scoccimarro Martina


0

23/1

623

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1

1

-1

1

0

F

23/16

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00

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00

00

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00

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00

00

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Schema.sccm.040PROCEDIMENTO E RISULTATI 853403 Scoccimarro Martina


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoBC = ∫

o

b(-1/2 x/b + x2/b2 -1/2 x3/b3 ) Fb 1/EJ dx + 1 (-1) (-1) Fb2/EJ

= [-1/4 x2/b +1/3 x3/b2 -1/8 x4/b3 ]o

b Fb 1/EJ + 1 (-1) (-1) Fb2/EJ

= (-1/4 b +1/3 b -1/8 b ) Fb 1/EJ + 1 (-1) (-1) Fb2/EJ = 23/24 Fb2/EJ

LXoCB = ∫

o

b(-1/2 x2/b2 +1/2 x3/b3 ) Fb 1/EJ dx + 1 (-1) (-1) Fb2/EJ

= [-1/6 x3/b2 +1/8 x4/b3 ]o

b Fb 1/EJ + 1 (-1) (-1) Fb2/EJ

= (-1/6 b +1/8 b ) Fb 1/EJ + 1 (-1) (-1) Fb2/EJ = 23/24 Fb2/EJ

A = 972. mm2

Ju = 264196. mm4

Jv = 56592. mm4



τc = 4.19 N/mm2

σo = √σ2+3τ2 = 113.4 N/mm2

S* = 4813. mm3mm 0 12 24 36x

0

42

55

y

15σc,τc

σm

u

v

Schema.sccm.040


Schema.sccm.040


Schema.sccm.040


Schema.shhe.041REAZIONI 809828 Shehu Elton


1/2F

7/4F

1/2F

7/4F7/4Fb

A B

5/4F

3/4F5/4Fb

5/4F

3/4F

B

C

7/4F

3/2F3/2Fb

7/4F

3/2F

B D

3/2F

3/2F

3/2F

3/2F3/2Fb

D

E

3/2F

3/2F3/2Fb

3/2F

3/2F

EF

5/2F

F

B

3/2F

F

3/2F1/2Fb

FG

1/2F1/2Fb

1/2F

G

A

Schema.shhe.041AZIONI INTERNE 809828 Shehu Elton


-1/2

3/4

-7/4

3/2

3/2

-5/2

3/23/2

0

F

7/4

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3/2

0

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Schema.shhe.041PROCEDIMENTO E RISULTATI 809828 Shehu Elton


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(1/2 x2/b2 ) Fb2 1/EJ dx = [1/6 x3/b2 ]o

b Fb2 1/EJ

= (1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (1/2 b -1/2 b +1/6 b ) Fb2 1/EJ = 1/6 Fb3/EJ

A = 948. mm2

Ju = 262515. mm4

Jv = 52848. mm4

yg = 20.97 mmN = -3098. NTy = -2655. NMx = 1593000. Nmmxm = 24. mmym = 55. mmum = 6. mmvm = 34.03 mmσm = N/A-Mv/Ju = -209.8 N/mm2

xc = 18. mmyc = 40. mmvc = 19.03 mmσc = N/A-Mv/Ju = -118.8 N/mm2

τc = 4.025 N/mm2

σo = √σ2+3τ2 = 119. N/mm2

S* = 4776. mm3mm 0 12 24 36x

0

12

55

y

40σc,τc

σm

u

v

Schema.shhe.041


Schema.shhe.041


Schema.shhe.041


Schema.smbm.042REAZIONI 886588 Simbula Marco


5/4F 5/4F5/4Fb

A B

7/4F

1/4F7/4Fb

7/4F

1/4F

B

C

7/4F

1/2F1/2Fb

7/4F

1/2F

B D

F

1/2F

F

1/2FFb

D

E

F

1/2FFb

F

3/2F

EF

3/2F

F

B

FFG

G

A

Schema.smbm.042AZIONI INTERNE 886588 Simbula Marco


0

1/4

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1/2

11

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1

0

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5/4

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00

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00

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CF

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Schema.smbm.042PROCEDIMENTO E RISULTATI 886588 Simbula Marco


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(-1/2 x2/b2 ) Fb2 1/EJ dx = [-1/6 x3/b2 ]o

b Fb2 1/EJ

= (-1/6 b ) Fb2 1/EJ = -1/6 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (-1/2 b +1/2 b -1/6 b ) Fb2 1/EJ = -1/6 Fb3/EJ

LXoBC = ∫

o


= [- x + x2/b -1/3 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ


LXoCB = ∫

o


b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-1/3 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 2/3 Fb3/EJ

Schema.smbm.042PROCEDIMENTO E RISULTATI 886588 Simbula Marco


A = 474. mm2

Ju = 143796. mm4

Jv = 14382. mm4



τc = 3.893 N/mm2

σo = √σ2+3τ2 = 126.1 N/mm2

S* = 2470. mm3mm 0 12 18 30x

0

6

55

y

40σc,τc

σm

u

v

Schema.smbm.042


Schema.smbm.042


Schema.stcm.043REAZIONI 886709 Steccanella Marco


1/2F

7/4F

1/2F

7/4F7/4Fb

A B

5/4F

7/4F5/4Fb

5/4F

7/4F

B

C

3/4F

3/2F3/2Fb

3/4F

3/2F

B D

3/2F

3/2F

3/2F

3/2F3/2Fb

D

E

3/2F

3/2F3/2Fb

3/2F

3/2F

EF

3/2F

F

B

3/2FFG

1/2F

1/2F

G

A

Schema.stcm.043AZIONI INTERNE 886709 Steccanella Marco


1/2

7/4

-3/4

3/2

3/2

-3/2

3/200

F

7/4

-5/4

-3/2

-3/2

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0

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27.0

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Schema.stcm.043PROCEDIMENTO E RISULTATI 886709 Steccanella Marco


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoBC = ∫

o

b(-1/2 + x/b -1/2 x2/b2 ) Fb 1/EJ dx - 1 (-1) (-1) Fb2/EJ

= [-1/2 x +1/2 x2/b -1/6 x3/b2 ]o

b Fb 1/EJ - 1 (-1) (-1) Fb2/EJ

= (-1/2 b +1/2 b -1/6 b ) Fb 1/EJ - 1 (-1) (-1) Fb2/EJ = -7/6 Fb2/EJ

LXoCB = ∫

o

b(-1/2 x2/b2 ) Fb 1/EJ dx - 1 (-1) (-1) Fb2/EJ = [-1/6 x3/b2 ]o

b Fb 1/EJ - 1 (-1) (-1) Fb2/EJ

= (-1/6 b ) Fb 1/EJ - 1 (-1) (-1) Fb2/EJ = -7/6 Fb2/EJ

A = 876. mm2

Ju = 264708. mm4

Jv = 62352. mm4



τc = 3.537 N/mm2

σo = √σ2+3τ2 = 135.1 N/mm2

S* = 4459. mm3mm 0 18 30 48x

0

6

55

y

41σc,τc

σm

u

v

Schema.stcm.043


Schema.stcm.043


Schema.stcm.043


Schema.srzp.044REAZIONI 919311 Suarez Pena Bryam Abraham


7/4F 7/4F7/4Fb

A B

5/4F

7/4F5/4Fb

5/4F

7/4F

B

C

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5/4F

3/2F

B D

2F

3/2F

2F

3/2F2Fb

D

E

2F

3/2F2Fb

2F

3/2F1/2Fb

EF

F

3/2F1/2Fb

3/2F

F

B

FFG

G

A

Schema.srzp.044AZIONI INTERNE 919311 Suarez Pena Bryam Abraham


0

7/4

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1

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Schema.srzp.044PROCEDIMENTO E RISULTATI 919311 Suarez Pena Bryam


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(-1/2 x2/b2 ) Fb 1/EJ dx = [-1/6 x3/b2 ]o

b Fb 1/EJ

= (-1/6 b ) Fb 1/EJ = -1/6 Fb2/EJ

LXoBA = ∫

o


b Fb 1/EJ

= (-1/2 b +1/2 b -1/6 b ) Fb 1/EJ = -1/6 Fb2/EJ

A = 618. mm2

Ju = 157731. mm4

Jv = 27774. mm4



τc = 3.893 N/mm2

σo = √σ2+3τ2 = 138.3 N/mm2

S* = 2834. mm3mm 0 12 18 30x

0

12

55

y

39σc,τc

σm

u

v

Schema.srzp.044


Schema.srzp.044


Schema.srzp.044


Schema.thid.045REAZIONI 868406 Taha Iad


7/4F 7/4F7/4Fb

A B

5/4F

7/4F5/4Fb

5/4F

7/4F

B

C

5/4F

3/2F3/2Fb

5/4F

3/2F

B D

2F

3/2F

F

3/2F3/2Fb

D

E

F

3/2F3/2Fb

F

3/2F

EF

3/2F

F

B

FFG

G

A

Schema.thid.045AZIONI INTERNE 868406 Taha Iad


0

7/4

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3/2

3/21

-3/2

1

0

F

7/4

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0

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00

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Schema.thid.045PROCEDIMENTO E RISULTATI 868406 Taha Iad


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoBC = ∫

o

b(1/2 - x/b +1/2 x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ

= [1/2 x -1/2 x2/b +1/6 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (1/2 b -1/2 b +1/6 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 7/6 Fb3/EJ

LXoCB = ∫

o

b(1/2 x2/b2 ) Fb2 1/EJ dx + 1 (-1) (-1) Fb3/EJ = [1/6 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (1/6 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 7/6 Fb3/EJ

A = 762. mm2

Ju = 174852. mm4

Jv = 74862. mm4

yg = 15.31 mmN = -887.5 NTy = -1065. NMx = 873300. Nmmxm = 24. mmym = 55. mmum = 3. mmvm = 39.69 mmσm = N/A-Mv/Ju = -199.4 N/mm2

xc = 21. mmyc = 38. mmvc = 22.69 mmσc = N/A-Mv/Ju = -114.5 N/mm2

τc = 3.229 N/mm2

σo = √σ2+3τ2 = 114.6 N/mm2

S* = 3181. mm3mm 0 18 24 42x

0

12

55

y

38σc,τc

σm

u

v

Schema.thid.045


Schema.thid.045


Schema.thid.045


Schema.tscr.046REAZIONI 829283 Tascau Radu Alexandru


31/16F 15/16F23/16Fb

A B

23/16F

15/16F23/16Fb

23/16F

15/16F

B

C

23/16F

FFb

23/16F

F

B D

F

F

F

FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

G

A

Schema.tscr.046AZIONI INTERNE 829283 Tascau Radu Alexandru


0 0

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1

1

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00

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Schema.tscr.046PROCEDIMENTO E RISULTATI 829283 Tascau Radu


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(1/2 x2/b2 -1/2 x3/b3 ) Fb2 1/EJ dx = [1/6 x3/b2 -1/8 x4/b3 ]o

b Fb2 1/EJ

= (1/6 b -1/8 b ) Fb2 1/EJ = 1/24 Fb3/EJ

LXoBA = ∫

o

b(1/2 x/b - x2/b2 +1/2 x3/b3 ) Fb2 1/EJ dx = [1/4 x2/b -1/3 x3/b2 +1/8 x4/b3 ]o

b Fb2 1/EJ

= (1/4 b -1/3 b +1/8 b ) Fb2 1/EJ = 1/24 Fb3/EJ

A = 804. mm2

Ju = 237762. mm4

Jv = 30384. mm4

yg = 23.11 mmN = -2516. NTy = -1750. NMx = 1540000. Nmmxm = 24. mmym = 55. mmum = 6. mmvm = 31.89 mmσm = N/A-Mv/Ju = -209.7 N/mm2

xc = 18. mmyc = 41. mmvc = 17.89 mmσc = N/A-Mv/Ju = -119. N/mm2

τc = 2.565 N/mm2

σo = √σ2+3τ2 = 119.1 N/mm2

S* = 4181. mm3mm 0 12 24 36x

0

6

55

y

41σc,τc

σm

u

v

Schema.tscr.046


Schema.tscr.046


Schema.tscr.046


Schema.ttrm.047REAZIONI 876617 Totaro Mario


5/4F 5/4F5/4Fb

A B

7/4F

1/4F7/4Fb

7/4F

1/4F

B

C

7/4F1/2Fb

7/4F

F

B D

F

F

F

FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

G

A

Schema.ttrm.047AZIONI INTERNE 876617 Totaro Mario


0

1/4

-7/4 -7/4

1

1

-1

1

0

F

5/4

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0-1

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JB

A b

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JC

B b

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00

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Schema.ttrm.047PROCEDIMENTO E RISULTATI 876617 Totaro Mario


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(- x2/b2 ) Fb2 1/EJ dx = [-1/3 x3/b2 ]o

b Fb2 1/EJ

= (-1/3 b ) Fb2 1/EJ = -1/3 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (- b + b -1/3 b ) Fb2 1/EJ = -1/3 Fb3/EJ

LXoBC = ∫

o


= [-3/2 x +3/2 x2/b -1/2 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ


LXoCB = ∫

o


b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-1/2 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 1/2 Fb3/EJ

Schema.ttrm.047PROCEDIMENTO E RISULTATI 876617 Totaro Mario


A = 1092. mm2

Ju = 292252. mm4

Jv = 116784. mm4



τc = 2.78 N/mm2

σo = √σ2+3τ2 = 128.8 N/mm2

S* = 5131. mm3mm 0 18 30 48x

0

12

55

y

40σc,τc

σm

u

v

Schema.ttrm.047


Schema.ttrm.047


Schema.vnnv.048REAZIONI 877057 Vennettilli Vittorio


23/16F 23/16F23/16Fb

A B

15/16F

23/16F23/16Fb

31/16F

23/16F

B

C

15/16F

FFb

15/16F

F

B D

F

F

F

FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

G

A

Schema.vnnv.048AZIONI INTERNE 877057 Vennettilli Vittorio


0

23/1

623

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-15/16

1

1

-1

1

0

F

23/16

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0

0

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27.0

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Mo(

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MxM

x/E

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AB

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BC

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b0

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00

00

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b0

Fx

00

FB

b0

00

00

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F b

00

00

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00

00

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00

00

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b0

00

00

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00

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Schema.vnnv.048PROCEDIMENTO E RISULTATI 877057 Vennettilli Vittorio


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoBC = ∫

o

b(1/2 x/b - x2/b2 +1/2 x3/b3 ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ

= [1/4 x2/b -1/3 x3/b2 +1/8 x4/b3 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ


LXoCB = ∫

o

b(1/2 x2/b2 -1/2 x3/b3 ) Fb2 1/EJ dx - 1 (-1) (-1) Fb3/EJ

= [1/6 x3/b2 -1/8 x4/b3 ]o

b Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ

= (1/6 b -1/8 b ) Fb2 1/EJ - 1 (-1) (-1) Fb3/EJ = -23/24 Fb3/EJ

A = 546. mm2

Ju = 162198. mm4

Jv = 37926. mm4



τc = 2.88 N/mm2

σo = √σ2+3τ2 = 131.3 N/mm2

S* = 2802. mm3mm 0 18 24 42x

0

6

55

y

39σc,τc

σm

u

v

Schema.vnnv.048


Schema.vnnv.048


Schema.vnnv.048


Schema.vgnd.049REAZIONI 890834 Vignati Davide


1/2F

3/4F

1/2F

3/4F3/4Fb

A B

9/4F

5/4F9/4Fb

9/4F

5/4F

B

C

7/4F

3/2F3/2Fb

7/4F

3/2F

B D

1/2F

3/2F

1/2F

3/2F1/2Fb

D

E

1/2F

1/2F1/2Fb

1/2F

1/2F

EF

1/2F

F

B

1/2F

F

1/2F1/2Fb

FG

1/2F1/2Fb

1/2F

G

A

Schema.vgnd.049AZIONI INTERNE 890834 Vignati Davide


1/2

-5/4

-7/4

-3/2

-1/2

-1/2

-1/2-1/2

0

F

3/4

-9/4

3/2

1/2

-1/2

0

-10

-1/2

F

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0

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01/

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1/2

0

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Schema.vgnd.049PROCEDIMENTO E RISULTATI 890834 Vignati Davide


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(3/2 x2/b2 ) Fb 1/EJ dx = [1/2 x3/b2 ]o

b Fb 1/EJ

= (1/2 b ) Fb 1/EJ = 1/2 Fb2/EJ

LXoBA = ∫

o

b(3/2 -3 x/b +3/2 x2/b2 ) Fb 1/EJ dx = [3/2 x -3/2 x2/b +1/2 x3/b2 ]o

b Fb 1/EJ

= (3/2 b -3/2 b +1/2 b ) Fb 1/EJ = 1/2 Fb2/EJ

A = 456. mm2

Ju = 127247. mm4

Jv = 25560. mm4

yg = 33.58 mmN = -1068. NTy = 915. NMx = -896700. Nmmxm = 18. mmum = -3. mmvm = -33.58 mmσm = N/A-Mv/Ju = -239. N/mm2


τc = 2.676 N/mm2

σo = √σ2+3τ2 = 140.4 N/mm2

S* = 2233. mm3mm 0 18 24 42x

0

48

52

y

14σc,τc

σm

u

v

Schema.vgnd.049


Schema.vgnd.049


Schema.vgnd.049


Schema.vrtd.050REAZIONI 898022 Vretenar Daniele


F

1/4F

F

1/4F1/4Fb

A B

11/4F

7/4F11/4Fb

11/4F

7/4F

B

C

7/4F

5/2F5/2Fb

7/4F

5/2F

B D

F

5/2F

F

5/2FFb

D

E

F

3/2FFb

F

1/2F

EF

1/2F

F

B

FFG

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F

G

A

Schema.vrtd.050AZIONI INTERNE 898022 Vretenar Daniele


1

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Schema.vrtd.050PROCEDIMENTO E RISULTATI 898022 Vretenar Daniele


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(5/2 x2/b2 ) Fb 1/EJ dx = [5/6 x3/b2 ]o

b Fb 1/EJ

= (5/6 b ) Fb 1/EJ = 5/6 Fb2/EJ

LXoBA = ∫

o


b Fb 1/EJ

= (5/2 b -5/2 b +5/6 b ) Fb 1/EJ = 5/6 Fb2/EJ

A = 672. mm2

Ju = 147014. mm4

Jv = 62496. mm4

yg = 37.25 mmN = -1050. NTy = 1500. NMx = -780000. Nmmxm = 18. mmum = -3. mmvm = -37.25 mmσm = N/A-Mv/Ju = -199.2 N/mm2


τc = 4.775 N/mm2

σo = √σ2+3τ2 = 114.6 N/mm2

S* = 2808. mm3mm 0 18 24 42x

0

42

52

y

16σc,τc

σm

u

v

Schema.vrtd.050


Schema.vrtd.050


Schema.vrtd.050


Schema.wxng.051REAZIONI 832033 Wu Xiangyu


3/2F

3/4F

3/2F

3/4F3/4Fb

A B

9/4F

1/4F9/4Fb

9/4F

1/4F

B

C

3/4F

3/2F3/2Fb

3/4F

3/2F

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1/2F

3/2F

1/2F

3/2F1/2Fb

D

E

1/2F

1/2F1/2Fb

1/2F

1/2F

EF

1/2F

F

B

1/2FFG

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3/2F

G

A

Schema.wxng.051AZIONI INTERNE 832033 Wu Xiangyu


3/2

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Schema.wxng.051PROCEDIMENTO E RISULTATI 832033 Wu Xiangyu


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(-3/2 x2/b2 ) Fb2 1/EJ dx = [-1/2 x3/b2 ]o

b Fb2 1/EJ

= (-1/2 b ) Fb2 1/EJ = -1/2 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (-3/2 b +3/2 b -1/2 b ) Fb2 1/EJ = -1/2 Fb3/EJ

A = 768. mm2

Ju = 208192. mm4

Jv = 43776. mm4



τc = 3.732 N/mm2

σo = √σ2+3τ2 = 121.1 N/mm2

S* = 3744. mm3mm 0 18 30 48x

0

48

52

y

13σc,τc

σm

u

v

Schema.wxng.051


Schema.wxng.051


Schema.wxng.051


Schema.zhny.052REAZIONI 846641 Zhan Yuchen


F

3/4F

F

3/4F3/4Fb

A B

9/4F

1/4F9/4Fb

9/4F

1/4F

B

C

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3/2F3/2Fb

5/4F

3/2F

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D

E

1/2F1/2F1/2Fb

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F

1/2F1/2Fb

1/2F

F

B

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F

G

A

Schema.zhny.052AZIONI INTERNE 846641 Zhan Yuchen


1

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0

1/2

1/2

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F

3/4

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2

01/

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b0

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2

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03/

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00

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EF

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Schema.zhny.052PROCEDIMENTO E RISULTATI 846641 Zhan Yuchen


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(3/2 x2/b2 ) Fb 1/EJ dx = [1/2 x3/b2 ]o

b Fb 1/EJ

= (1/2 b ) Fb 1/EJ = 1/2 Fb2/EJ

LXoBA = ∫

o


b Fb 1/EJ

= (3/2 b -3/2 b +1/2 b ) Fb 1/EJ = 1/2 Fb2/EJ

A = 984. mm2

Ju = 244285. mm4

Jv = 98208. mm4



τc = 3.877 N/mm2

σo = √σ2+3τ2 = 129. N/mm2

S* = 4483. mm3mm 0 18 30 48x

0

42

52

y

14σc,τc

σm

u

v

Schema.zhny.052


Schema.zhny.052


Schema.zhny.052


Schema.zlln.053REAZIONI 878043 Zullo Nicola


F

3/4F

F

3/4F3/4Fb

A B

9/4F

1/4F9/4Fb

9/4F

1/4F

B

C

5/4F

3/2F3/2Fb

5/4F

3/2F

B D

3/2F

F

3/2F1/2Fb

D

E

F

1/2F1/2Fb

F

1/2F

EF

1/2F

F

B

FFG

FFb

F

G

A

Schema.zlln.053AZIONI INTERNE 878043 Zullo Nicola


1

-1/4

-5/4

-3/2

-3/2

-1

1/2

-1

0

F

3/4

-9/4

3/2

01

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0

0

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0 3/4

9/4

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00

FG

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Svi

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erst

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a

Schema.zlln.053PROCEDIMENTO E RISULTATI 878043 Zullo Nicola


LXXAB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBA = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXBC = ∫

o


b b2 1/EJ

= ( b - b +1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXXCB = ∫

o

b( x2/b2 ) b2 1/EJ dx = [1/3 x3/b2 ]o

b b2 1/EJ

= (1/3 b ) b2 1/EJ = 1/3 b3/EJ

LXoAB = ∫

o

b(- x2/b2 ) Fb2 1/EJ dx = [-1/3 x3/b2 ]o

b Fb2 1/EJ

= (-1/3 b ) Fb2 1/EJ = -1/3 Fb3/EJ

LXoBA = ∫

o


b Fb2 1/EJ

= (- b + b -1/3 b ) Fb2 1/EJ = -1/3 Fb3/EJ

LXoBC = ∫

o


= [-5/2 x +5/2 x2/b -5/6 x3/b2 ]o

b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ


LXoCB = ∫

o


b Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ

= (-5/6 b ) Fb2 1/EJ + 1 (-1) (-1) Fb3/EJ = 1/6 Fb3/EJ

Schema.zlln.053PROCEDIMENTO E RISULTATI 878043 Zullo Nicola


A = 408. mm2

Ju = 112717. mm4

Jv = 9864. mm4



τc = 3.48 N/mm2

σo = √σ2+3τ2 = 135.6 N/mm2

S* = 1961. mm3mm 0 12 18 30x

0

48

52

y

13σc,τc

σm

u

v

Schema.zlln.053


Schema.zlln.053


Schema.xxxx.054REAZIONI Nome:


F

15/16F

F

1/16F7/16Fb

A B

39/16F

17/16F39/16Fb

39/16F

17/16F

B

C

23/16F

2F2Fb

23/16F

2F

B D

F

2F

F

2FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

FFb

F

G

A

Schema.xxxx.054AZIONI INTERNE Nome:


1 1

-17/

16

-23/16

-2

-1

1

-1

0

F

15/16-1/16

-39/

16

2

1

-1

0

0

-1

F

0 7/16

39/1

60

-20

01100

0

0010

Fb

Sch

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xxxx

.054

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27.0

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D

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G

W

F

X

X

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0-1

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27.0

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Qua

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per

iper

stat

ica

X=

WB

C

→M

x(x)

Mo(

x)M

xMo

MxM

x∫M

xMo/

EJd

x∫X

MxM

x/E

Jdx

AB

b-x

/b-3

/2F

x-1/

2qx2

3/2F

x2 /b+

1/2q

x3 /bx2 /b

2

5/8F

b2 /EJ

1/3X

b/E

JB

A b

1-x/

b2F

b-5/

2Fx+

1/2q

x22F

b-9/

2Fx+

3Fx2 /b

-1/2

qx3 /b

1-2x

/b+

x2 /b2

BC

b-1

+x/

b0

01-

2x/b

+x2 /b

2

01/

3Xb/

EJ

CB

bx/

b0

0x2 /b

2

BD

b0

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b+2F

x0

00

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B b

02F

x0

0

DE

b0

Fx

00

00

ED

b0

-Fb+

Fx

00

EF

b0

Fb-

Fx

00

00

FE

b0

-Fx

00

FB

b0

00

00

0B

F b

00

00

FG

b0

00

00

0G

F b

00

00

GA

b0

Fb-

Fx

00

00

AG

b0

-Fx

00

BC

elon

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Cε B

CL B

CF

b2 /EJ

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2/3X

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C-3

9/16

Fb

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Schema.xxxx.054PROCEDIMENTO E RISULTATI Nome:


LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(3/2 x2/b2 +1/2 x3/b3 ) Fb 1/EJ dx = [1/2 x3/b2 +1/8 x4/b3 ]o

b Fb 1/EJ

= (1/2 b +1/8 b ) Fb 1/EJ = 5/8 Fb2/EJ

LXoBA = ∫

o

b(2 -9/2 x/b +3 x2/b2 -1/2 x3/b3 ) Fb 1/EJ dx = [2 x -9/4 x2/b + x3/b2 -1/8 x4/b3 ]o

b Fb 1/EJ

= (2 b -9/4 b + b -1/8 b ) Fb 1/EJ = 5/8 Fb2/EJ

A = 552. mm2

Ju = 132127. mm4

Jv = 23256. mm4

yg = 35.13 mmN = -891.3 NTy = 1240. NMx = -892800. Nmmxm = 12. mmum = -3. mmvm = -35.13 mmσm = N/A-Mv/Ju = -239. N/mm2


τc = 3.89 N/mm2

σo = √σ2+3τ2 = 137.8 N/mm2

S* = 2487. mm3mm 0 12 18 30x

0

42

52

y

15σc,τc

σm

u

v

Schema.xxxx.054


Schema.xxxx.054


Schema.xxxx.054




F

1/4F

F

1/4F1/4Fb

A B

11/4F

7/4F11/4Fb

11/4F

7/4F

B

C

7/4F

3F5/2Fb

7/4F

2F

B D

F

2F

F

2FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

FFb

F

G

A



1

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-7/4 -7/4

-2

-1

1

-1

0

F

1/4

-11/

4

3 2

1

-1

0

0

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F

0 1/4

11/4

0

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01100

0

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27.0

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B C

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F

X

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27.0

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Qua

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iper

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X=

WB

C

→M

x(x)

Mo(

x)M

xMo

MxM

x∫M

xMo/

EJd

x∫X

MxM

x/E

Jdx

AB

b-x

/b-5

/2F

x5/

2Fx2 /b

x2 /b2

5/6F

b2 /EJ

1/3X

b/E

JB

A b

1-x/

b5/

2Fb-

5/2F

x5/

2Fb-

5Fx+

5/2F

x2 /b1-

2x/b

+x2 /b

2

BC

b-1

+x/

b0

01-

2x/b

+x2 /b

2

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CB

bx/

b0

0x2 /b

2

BD

b0

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Fb+

3Fx-

1/2q

x20

00

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B b

02F

x+1/

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b0

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00

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b0

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00

00

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00

00

FG

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00

00

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CF

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ica

X=

WB

C-1

1/4F

b

Svi

lupp

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alco

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LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(5/2 x2/b2 ) Fb 1/EJ dx = [5/6 x3/b2 ]o

b Fb 1/EJ

= (5/6 b ) Fb 1/EJ = 5/6 Fb2/EJ

LXoBA = ∫

o


b Fb 1/EJ

= (5/2 b -5/2 b +5/6 b ) Fb 1/EJ = 5/6 Fb2/EJ

A = 720. mm2

Ju = 188659. mm4

Jv = 22464. mm4



τc = 2.878 N/mm2

σo = √σ2+3τ2 = 117.2 N/mm2

S* = 3341. mm3mm 0 12 24 36x

0

48

52

y

12σc,τc

σm

u

v

Schema.xxxx.055


Schema.xxxx.055


Schema.xxxx.055




F

7/16F

F

7/16F7/16Fb

A B

31/16F

9/16F39/16Fb

47/16F

9/16F

B

C

15/16F

2F2Fb

15/16F

2F

B D

F

2F

F

2FFb

D

E

F

FFb

F

F

EF

F

F

B

FFG

FFb

F

G

A



1

-9/1

6-9

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-15/16

-2

-1

1

-1

0

F

7/16

-31/

16-4

7/16

2

1

-1

0

0

-1

F

0 7/16

39/1

60

-20

01100

0

0010

Fb

Sch

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.056

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OC

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I Nom

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dolfo

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27.0

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06.0

9.19

A

B C

D

EF

G

W

F

X

X

q

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di c

alco

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0-2

0 0-20

01

10 0 0

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0-1

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27.0

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Qua

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X=

WB

C

→M

x(x)

Mo(

x)M

xMo

MxM

x∫M

xMo/

EJd

x∫X

MxM

x/E

Jdx

AB

b-x

/b-2

Fx

2Fx2 /b

x2 /b2

2/3F

b2 /EJ

1/3X

b/E

JB

A b

1-x/

b2F

b-2F

x2F

b-4F

x+2F

x2 /b1-

2x/b

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2

BC

b-1

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x2-1

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x+F

x2 /b-1

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3 /b1-

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CB

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FB

b0

00

00

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F b

00

00

FG

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00

00

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00

00

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Fx

00

00

AG

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Cε B

CL B

CF

b2 /EJ

tota

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2/3X

b/E

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X=

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C-3

9/16

Fb

Svi

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alco

lo ip

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a



LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(2 x2/b2 ) Fb 1/EJ dx = [2/3 x3/b2 ]o

b Fb 1/EJ

= (2/3 b ) Fb 1/EJ = 2/3 Fb2/EJ

LXoBA = ∫

o

b(2 -4 x/b +2 x2/b2 ) Fb 1/EJ dx = [2 x -2 x2/b +2/3 x3/b2 ]o

b Fb 1/EJ

= (2 b -2 b +2/3 b ) Fb 1/EJ = 2/3 Fb2/EJ

LXoBC = ∫

o

b(-1/2 x/b + x2/b2 -1/2 x3/b3 ) Fb 1/EJ dx + 1 (-1) (-1) Fb2/EJ

= [-1/4 x2/b +1/3 x3/b2 -1/8 x4/b3 ]o

b Fb 1/EJ + 1 (-1) (-1) Fb2/EJ

= (-1/4 b +1/3 b -1/8 b ) Fb 1/EJ + 1 (-1) (-1) Fb2/EJ = 23/24 Fb2/EJ

LXoCB = ∫

o

b(-1/2 x2/b2 +1/2 x3/b3 ) Fb 1/EJ dx + 1 (-1) (-1) Fb2/EJ

= [-1/6 x3/b2 +1/8 x4/b3 ]o

b Fb 1/EJ + 1 (-1) (-1) Fb2/EJ

= (-1/6 b +1/8 b ) Fb 1/EJ + 1 (-1) (-1) Fb2/EJ = 23/24 Fb2/EJ



A = 864. mm2

Ju = 219048. mm4

Jv = 44928. mm4

yg = 31.83 mmN = -806.3 NTy = 1720. NMx = -1427600. Nmmxm = 12. mmum = -6. mmvm = -31.83 mmσm = N/A-Mv/Ju = -208.4 N/mm2


τc = 2.73 N/mm2

σo = √σ2+3τ2 = 117.3 N/mm2

S* = 4172. mm3mm 0 12 24 36x

0

42

52

y

14σc,τc

σm

u

v

Schema.xxxx.056


Schema.xxxx.056




1/2F

3/4F

1/2F

3/4F3/4Fb

A B

9/4F

5/4F9/4Fb

9/4F

5/4F

B

C

11/4F

3/2F3/2Fb

11/4F

3/2F

B D

1/2F

3/2F

1/2F

3/2F1/2Fb

D

E

1/2F

1/2F1/2Fb

1/2F

1/2FFb

EF

1/2F

F

B

1/2F

F

1/2F1/2Fb

FG

1/2F1/2Fb

1/2F

G

A



-1/2

-5/4

-11/4

-3/2

1/2

-1/2

1/21/2

0

F

3/4

-9/4

3/2

-1/2

-1/2

0

-10

1/2

F

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9/4

0

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0-1

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0

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27.0

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G

W

F

X

X

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27.0

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Qua

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WB

C

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Mo(

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MxM

x∫M

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MxM

x/E

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2x/b

+x2 /b

2

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b0

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1/2F

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J2/

3Xb/

EJ

iper

stat

ica

X=

WB

C-9

/4F

b

Svi

lupp

i di c

alco

lo ip

erst

atic

a



LXXAB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXXBA = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXBC = ∫

o


b 1/EJ

= ( b - b +1/3 b ) 1/EJ = 1/3 b/EJ

LXXCB = ∫

o

b( x2/b2 ) 1/EJ dx = [1/3 x3/b2 ]o

b 1/EJ

= (1/3 b ) 1/EJ = 1/3 b/EJ

LXoAB = ∫

o

b(3/2 x2/b2 ) Fb 1/EJ dx = [1/2 x3/b2 ]o

b Fb 1/EJ

= (1/2 b ) Fb 1/EJ = 1/2 Fb2/EJ

LXoBA = ∫

o


b Fb 1/EJ

= (3/2 b -3/2 b +1/2 b ) Fb 1/EJ = 1/2 Fb2/EJ

A = 912. mm2

Ju = 222885. mm4

Jv = 52416. mm4

yg = 19.68 mmN = -3190. NTy = 1740. NMx = -1531200. Nmmxm = 24. mmym = 52. mmum = 6. mmvm = 32.32 mmσm = N/A-Mv/Ju = 218.5 N/mm2


τc = 2.62 N/mm2

σo = √σ2+3τ2 = 129.3 N/mm2

S* = 4027. mm3mm 0 12 24 36x

0

12

52

y

39σc,τc

σm

u

v

Schema.xxxx.057


Schema.xxxx.057


Schema.xxxx.057


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