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8/12/2019 Lecture Module 4 Axial Loads
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SOLID MECHANICS ISOLID MECHANICS I(BDA 10402)
Lecture 4: Axial Loads
Dr. Waluyo Adi SiswantoUniversity Tun Hussein Onn Malaysia
8/12/2019 Lecture Module 4 Axial Loads
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BDA 10402 Dr. Waluyo Adi Siswanto 2
Deformation Under Axial Load
From Hooke's Law
=E =
E=
F
A E
Since can be obtain from the elongation
=
L =
F L
A Ethen
If the bar is subjected to different axial forces
=F L
A E
Lo
Ao
FF
LA
FF
8/12/2019 Lecture Module 4 Axial Loads
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BDA 10402 Dr. Waluyo Adi Siswanto 3
Sign Convention
Sign: tension and elongation
! Sign: com"ression and contraction
AA # $ %
& 4
&
!(
!)
*
)
8/12/2019 Lecture Module 4 Axial Loads
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BDA 10402 Dr. Waluyo Adi Siswanto 4
Strain Relative
&
!(
!)
A # $ %
A /B=5 L
AB
AAB EB /C=
3LBC
ABCEC/D=
7LCD
ACDE
A /C=5 L
AB
AAB E
3LBC
ABCE
A /C=A/C
LAC
8/12/2019 Lecture Module 4 Axial Loads
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BDA 10402 Dr. Waluyo Adi Siswanto 5
More on Strain Energy Density
Strain +nerg, %ensit, is based on the straincalculation
Strain +nerg, %ensit, relates with the
corres"onding strains
+xam"les:A /B=
5 LAB
AAB E u A /B=
1
2 =
1
2
5
AAB
A/ B
L AB
=1
2
52
AABE
In general u i=1
2
Fi
2
AiE
8/12/2019 Lecture Module 4 Axial Loads
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BDA 10402 Dr. Waluyo Adi Siswanto 6
Approximation Approa!
A1
A2
F F
L1
L2
=FL
1
A1E
FL2
A2E
A2
A1
8/12/2019 Lecture Module 4 Axial Loads
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BDA 10402 Dr. Waluyo Adi Siswanto 7
Statially Indeterminay
Structures for which internal forces and reactions cannotbe determined from statics alone are said to be staticall,indeterminate-
A structure will be staticall, indeterminate whene.er it isheld b, more su""orts than are re/uired to maintain itse/uilibrium-
0edundant reactions are re"laced with unknown loadswhich along with the other loads must "roduce com"atibledeformations-
8/12/2019 Lecture Module 4 Axial Loads
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BDA 10402 Dr. Waluyo Adi Siswanto 8
"riniple of S#perposition
L
R
=L
R=0
8/12/2019 Lecture Module 4 Axial Loads
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BDA 10402 Dr. Waluyo Adi Siswanto 9
$!ermal Stress
A change in tem"erature can cause material to change its dimensions-
If the tem"erature increases 1 generall, the material ex"ands1 whereas if thetem"erature decreases1 the material will contract-
T= T L
T : the algebraic change in length of the member
: a "ro"ert, of the material1 referred to as the linear coefficient of thermal
ex"ansion
23 : the change in tem"erature of the member
L : the original length of the member
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BDA 10402 Dr. Waluyo Adi Siswanto 10
Example "ro%lem &'(
(-4
m
(-4m
3he A!( Steel column 5+67**89a is used tosu""ort the s,mmetric loads from the two floorsof a building-%etermine the loads 9; and 97 if A mo.esdownward ( mm and # mo.es downward 7-7&mm when the loads are a""lied-
3he column has a cross!sectional area of;4-7& mm7-
(Hibbeler, 7thd, !roble" #$%&
8/12/2019 Lecture Module 4 Axial Loads
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BDA 10402 Dr. Waluyo Adi Siswanto 11
Example "ro%lem &')
A reinforced concrete "edestal 5+67&*89aha.ing dimensions and loads as shown in the"icture-
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8/12/2019 Lecture Module 4 Axial Loads
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BDA 10402 Dr. Waluyo Adi Siswanto 14
Example "ro%lem &'+
3he two circular rod segments1 one ofaluminum and the other one co""er1 are fixedto the rigid walls such that there is a ga" of *-7mm between them when 3; 6 ;&o$-+ach rod has a diameter of (* mm1@
Al6 745;*!o$1 +
al6 )* 89a
@$