taller deformaciones

8/17/2019 Taller Deformaciones

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UNIVERSIDAD PEDAGÓGICA Y TECNOLÓGICA DE COLOMBIAINGENIERÍA ELECTROMECÁNICA

RESISTENCIA DE MATERIALES

Mg. Edgar torres Barahona 2015-2

=

=

This equation may be used only if the rod is homogeneous and has auniform cross section of area A.

If the rod is loaded at other points, or if it consist of several portions ofvarious cross section and possibly of different materials, then:

=

In the case of a rod of variable cross section, the strain ϵ depends upon the position of de point

Q where it is computed and is defined as

=

Then

= = And the total deformation is obtained as

= ∫

Examples

Two solid cylindrical rods are joined at B and loaded as shown. Road AB

is made of steel (E=200GPa), and rod BC of brass (laton) (E=105 GPa).Determine a) the total deformation of the composite rod ABC and b) thedeflection of point B.

Answer

For the equilibrium


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P1 = 178 kN in tensionP2 = 178 kN - 2(133 kN) = - 88 kN 88 kN in compression

a)

The total deformation of the composite rod ABC

=

Then

=

=

4

= 4() 4

() = 0.050

= 0.075

= 4() 4

()

= 4 ∗ 178 ∗ 1(0.05) ∗2006 4(88 )(0.75 )

(0.075) ∗ 1056 = 3 . 1 1 4

b)

The deflection of point B.

=4(88 )(0.75 )

(0.075) ∗1056

= 1.42 4 2.


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Answer

∑ = 0 0.18 ∗ 18 ∗ 0.44 = 0 = 44 ∑ = 0

18 = 0 = 26

The force in BE is compressiveThen

= = = 44 = 0.24 = 0.025 ∗ 0.035

= 2006

= 44 ∗ 0.24 0.025 ∗ 0.035 ∗2006 = 3.02 5

The force in BE is extensiveThen

= = = 26 = 0.24 = 0.025 ∗ 0.035 = 2006

= 26 ∗ 0.24 0.025 ∗ 0.035 ∗2006 = 1.783 5


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ASTATICALLY INDETERMINATE PROBLEMS

Problem data

= 0.18 = 0.12 = 0.10 = 0.10

= = 0.25 (0.04) = = 0.25 (0.03)

First method


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= = 0 =

= 0

( )

( )

( ) = 0

(

) =

( )

=

( )

Date:

= 3 ∗ 1 0−

8 = 0.25 = ∗ (0.036

0.028)4

= ∗0.025

4

= 706

= 1056

Analysis

= = = = = =

Then

=()

(+) = = ; =

= = = ; =

=


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taller deformaciones

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