aula 04 - cisalhamentotransversal

8/18/2019 Aula 04 - CisalhamentoTransversal

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2

Professor Maurício P. Ferreira

Engenheiro Civil, M.Sc., D.Sc.Pós-doutorando - Universidade de BrasíliaPesquisador - Universidade Federal do Pará


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0. ( )

Definição: é a componente de tensão

que atua no plano da área seccionada.

Efeito: tende a provocar o

deslizamento (corte) entre seções

subseqüentes.

Limitações: casos de cisalhamento

simples ou direto, que ocorre em

ligações com pinos e parafusos.

τ =


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0. ( )


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0. ( , )

=

= ⋅ + +

= −

∑

=

+ ⋅ = ⋅ ⋅ + +

=

∑

= 0, =

= ,, = 0


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0. ( , )


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1. • E ( )

;

•

() ();

• (σ )

(τ

) ;• A .

.


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1. C

. :

1. (τ)

();

2.

();

3. ().

E τ

.


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1. D

:

1. A ;

2.

;

3. ,

.


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1. A

:

= = ± τ


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1.

A

:1. C 2 ;

2. ,

;

3. C

;

4.


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1.


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1.

• A , ,

;

• E .


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2.


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3.

• C ;

• A 2

,

;

• A , :

( )

⋅= −

+ ⋅= −

σ

σ


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3.

•

;

• C

;

•

;

•

τ

.


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3.

= ⋅ ⋅ ⋅

⋅

= ⋅ ⋅⋅

∫

∫

τ

τ

(E.1)= ⋅ = ⋅∫

•

:

⋅= ⋅

τ

• :

(E.2)


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4.

• A

() ;

• , (τ )

;

• , ( )

;

• ,

;

= ⋅ = ⋅∫

⋅=

⋅

τ


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0. ( )


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4.

= ⋅

= ⋅

= ⋅

= ⋅ −

∫

∫

• D:

(E.3)


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4.

= ⋅ ⋅ − ⋅

= ⋅ −

τ

τ (E.4)

• 3 2:

• τ = =

• τ = τ

=

⋅ ⋅= = ⋅ ∴

⋅ ⋅

τ

⋅=

⋅

τ

(E.5)


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4.


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5.

• E τ

;

•

;

• A

;

• A, τ

.


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5.


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5.


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6.

•

;

•

;

• A

.


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6.


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6.


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7. ()

• , ,

;

• , ,

13% (

);

• A

.


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7. ()

• ,

.


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• Exemplo 1: = 0,5 . E 100

150 . D

,

( ) 11

1,2 ( ).


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= ∴ = ⋅

• Exemplo 1:

=

⋅ ⋅=

⋅

σ

σ

⋅=⋅

⋅=

⋅

τ

τ

⋅ ⋅ ⋅ ⋅ ⋅ ⋅= = ∴ =

τ

⋅ ⋅ ⋅ ⋅= = ∴ =

⋅ ⋅

σ


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• Exemplo 2: A 3 . D: ) )

.


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• Exemplo 2:

= ⋅ −

⋅

= − ⋅ ⋅

=

τ

τ

τ

⋅=

⋅

⋅=

⋅ ⋅

=

τ

τ

τ


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• Exemplo 3: . 80 , : )

) .


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• Exemplo 3: = = = = =

( )

( )

= ⋅ ⋅ − ⋅ + ⋅

= ⋅ ⋅ − ⋅ + ⋅

= ⋅

( )

⋅ ⋅⋅= =

⋅ ⋅

⋅ ⋅ ⋅=

⋅ ⋅

=

τ

τ

τ

( )

⋅ ⋅⋅= =

⋅ ⋅

⋅ ⋅ ⋅=

⋅ ⋅

=

τ

τ

τ


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• Exemplo 3: = = = = =

( ) ( )

= ⋅ ⋅ + ⋅ ⋅

= ⋅

⋅=

⋅

⋅ ⋅=

⋅ ⋅

=

τ

τ

τ

( )

( )

⋅= ⋅ ⋅ +

⋅= ⋅ ⋅ +

=

τ τ


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• Exemplo 4: 2.000 . A

. D: ) ; )

) .


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• Exemplo 4:( ) ( )

= + ⋅ + ⋅ + ⋅

⋅ ⋅= + ⋅ ⋅ + ⋅ + ⋅ ⋅

=

( ) ( )

= ⋅ = ⋅ ⋅ + ⋅ ⋅ ⋅

=

∑

⋅ ⋅= =

⋅ ⋅ ⋅

=

τ

τ


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• Exemplo 4:

( )

= ⋅ = ⋅ ⋅ ⋅

=

∑

⋅ ⋅= =

⋅ ⋅ ⋅

=

τ

τ

⋅ ⋅= =

⋅ ⋅ ⋅

=

τ

τ

( )

= ⋅ = ⋅ ⋅ ⋅

=

∑

aula 04 - cisalhamentotransversal

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