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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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UNIVERSIDAD PEDAGÓGICA Y TECNOLÓGICA DE COLOMBIAINGENIERÍA ELECTROMECÁNICA
RESISTENCIA DE MATERIALES
Mg. Edgar torres Barahona 2015-2
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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UNIVERSIDAD PEDAGÓGICA Y TECNOLÓGICA DE COLOMBIAINGENIERÍA ELECTROMECÁNICA
RESISTENCIA DE MATERIALES
Mg. Edgar torres Barahona 2015-2
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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UNIVERSIDAD PEDAGÓGICA Y TECNOLÓGICA DE COLOMBIAINGENIERÍA ELECTROMECÁNICA
RESISTENCIA DE MATERIALES
Mg. Edgar torres Barahona 2015-2
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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UNIVERSIDAD PEDAGÓGICA Y TECNOLÓGICA DE COLOMBIAINGENIERÍA ELECTROMECÁNICA
RESISTENCIA DE MATERIALES
Mg. Edgar torres Barahona 2015-2
= = 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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UNIVERSIDAD PEDAGÓGICA Y TECNOLÓGICA DE COLOMBIAINGENIERÍA ELECTROMECÁNICA
RESISTENCIA DE MATERIALES
Mg. Edgar torres Barahona 2015-2