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SOLID MECHANICS ISOLID MECHANICS I(BDA 10402)

Lecture 4: Axial Loads

Dr. Waluyo Adi SiswantoUniversity Tun Hussein Onn Malaysia

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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

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BDA 10402 Dr. Waluyo Adi Siswanto 3

Sign Convention

Sign: tension and elongation

! Sign: com"ression and contraction

AA # $ %

& 4

&

!(

!)

*

)

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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

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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

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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

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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-

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BDA 10402 Dr. Waluyo Adi Siswanto 8

"riniple of S#perposition

L

R

=L

R=0

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$!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" #$%&

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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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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

@$