kuliah statika

7/18/2019 Kuliah Statika

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Civil Engineering Department, Faculty of Engineering, Sriwijaya University1Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

LECTURELECTURE

"y # ! Dr. Ir. Anis Saggaff, MSCE

Civil Engineering DepartmentFaculty of Engineering

Sriwijaya University $U%S&I'E(tension ! )lg

I%*&+DUC*I+% *+ S*EE




Material of StructuresMaterial of Structures

Woods / Timbers

Structures

Compositeor Fibers

ReinforcedConcrete (R/C)

Traditional and Low Weight

Structures

Modern Structures

(Middle and High Strength Structures)

Light Weight

Steel Structures




Important Design Considerations

Mecanical )roperties• Compressive Strengt

• Stress-Strain curve

• *ensile strengt

• Sear strengt• Moulus of Elasticity

• )oisson/s ratio




Introuction $0'Introuction $0'

Determining External Forces ActingOn A Structure

– Loads !eactions

" Determining Forces #$ic$ %old &oget$er&$e 'arious (em)ers O* A Structure

– &russes (ac$ines

+ext, Learn %o- to Determine &$e

Internal Forces #$ic$ %old &oget$er

&$e 'arious .arts O* A /i0en (em)er



Civil Engineering Department, Faculty of Engineering, Sriwijaya UniversityDr. Ir. Anis Saggaff, MSCE Mecanics ! Statics


&$e Four &pes o* I+&E!+AL Forces.resent in Structural (em)ers

" &ension or Compression

" S$ear" ending

" &orsion&-isting

&$e Su)s5uent Analses do +ot

Consider &orsion Loads

" For (ore torsion In*o See E+/!4





Examine in Detail &-o Important&pes O* Engineering Structures7

18 EA(S 9 usuall long, straig$t, prismatic

mem)ers designed to support loads

applied at 0arious points along t$e

mem)er

28 CALES 9 *lexi)le mem)ers capa)le o*

-it$standing only tension, designed tosupport concentrated or distri)uted loads


http://slidepdf.com/reader/full/kuliah-statika 7/40Civil Engineering Department, Faculty of Engineering, Sriwijaya University:

Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

Internal Forces in Mem3ers $0'Internal Forces in Mem3ers $0'

;a< Straig$t t-o9*orce mem)er AB is

in e5uili)rium under

application o*

F and 9F 8 ;)< Internal Forces

e5ui0alent to F and

9F

are re5uired *ore5uili)rium o* *ree9

)odies AC and CB8 'I!&=AL

Section



Civil Engineering Department, Faculty of Engineering, Sriwijaya University>Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics


(ulti*orce mem)er ABCD is in e5uil9

i)rium under t$e

application o* ca)le

and mem)er contact*orces8

I+&E!+AL *orces e5ui0alent

to a FO!CE9CO=.LE ;'9(<

sstem are necessar *or

e5uili)rium o* *ree9)odies JD

and ABCJ

F"D

'I!&=AL

Section J



Civil Engineering Department, Faculty of Engineering, Sriwijaya University?Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics


An internal FO!CE9CO=.LE ;'9(< sstem isre5uired *or e5uili)rium o* &#O9FO!CE

mem)ers -$ic$ are +O& S&!AI/%&



Civil Engineering Department, Faculty of Engineering, Sriwijaya University1@Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

E(ample )ro3lem 0E(ample )ro3lem 0

/i0en 39(em)erStructure at !ig$t

Determine t$e

I+&E!+AL *orces

in

a< mem)er ACF at

point J

)< mem)er BCD at K




" Cut mem)er ACF at J 8

– &$e internal *orces at arerepresented ) e5ui0alent*orce9couple ;'9(< sstem-$ic$ is determined )considering e5uili)rium o*

eit$er cut part8" Cut mem)er BCD at K 8

– Determine *orce9couple ;'9(< sstem e5ui0alent tointernal *orces at B )

appling e5uili)riumconditions to eit$er cut part8

Solution .lan7

" Compute !cns andForces atconnections *oreac$ mem)er



Civil Engineering Department, Faculty of Engineering, Sriwijaya University12 Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

First Determine External !cns Connection9Forces

Consider t$e E+&I!E Frame

as a Free od

( ) ( ) ( )

N1800

0m8.m!." N#000

=⇒

=+−==∑ F

F M E

N!000 N1800 N#000

=⇒=++−==∑

y

y y

E E F

00 =⇒=∑ x x E F




Consider Lin (em)er BCD as a Free od

( ) ( ) ( )

N"!00

0m.#m!." N#00

0

=⇒

=+−

⇒=∑

y

y

B

C

C

M

( )( ) ( )

N1#00

0m.#m#.1 N#00

0

=⇒

=+−

⇒=∑

y

y

C

B

B

M

0

0

=+−

⇒=∑ x x

x

C B

F Dont Bno- ;et<




Consider ABE as a Free od

$0=∑ A M ( ) 0m%.# = x B 0= x B

∑ = $0 x F 0=− x x A B 0= x A

∑ = $0 y F 0 N!00 =++− y y B A N1800= y A

!ecall *rom (em)er BCD

00 =+−⇒=∑ x x x C B F

" ut *rom A)o0e x @0=∴ xC

N"!00

0

N1800

0

ALL Forces on ACF are

no- B+O#+




Cut mem)er ACF at J

" &$e internal *orces at J are represented ) e5ui0alent *orce9couple sstem

Consider Free od AJ

$0=∑ J M

( ) ( ) 0m#.1 N1800 =+− M m N#1!0 ⋅= M

$0=∑ x F

( ) 0%.1cos N1800 =°− F N1"= F

$0=∑ y F

( ) 0%.1sin N1800 =°+−V N11&%=V




Cut mem)er BCD at K

" Determine a *orce9couple sstem e5ui0alent to internal *orces at K

Consider Free od BK

$0=∑ K M

( ) ( ) 0m'.1 N1#00 =+ M m N1800 ⋅−= M

$0=∑ x F 0= F

$0=∑ y F

0 N1#00 =−− V N1#00−=V



Civil Engineering Department, Faculty of Engineering, Sriwijaya University1: Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

"eam - 4at is "eam5"eam - 4at is "eam5

"eam ≡ Structural mem)erdesigned to support loads applied

at 0arious points along its lengt$

eams can )e su)ected to

CO+CE+&!A&ED loads orDIS&!I=&ED loads or a

CO(I+A&IO+ o* )ot$8

"eam Design is 29Step .rocess

18 Determine S$earing Forces And ending (oments .roduced Applied Loads

28 Select Structural Cross9section est Suited &o !esistS%EA!I+/9Forces and E+DI+/9(oments



Civil Engineering Department, Faculty of Engineering, Sriwijaya University1> Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

"eam oaing an Supports"eam oaing an Supports

eams are classi*ied according to t$e Support(et$od;s<G e8g8, Simpl9Supported, Cantile0er

!eactions at )eam supports are Determinatei* t$e in0ol0e exactl &%!EE unno-ns8

" Ot$er-ise, t$e are Staticall I+determinate



Civil Engineering Department, Faculty of Engineering, Sriwijaya University1? Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

Sear 6 "ening!MomentSear 6 "ening!Moment /oal determine )ending

moment and s$earing *orce atan point in a )eam su)ected

to concentrated and

distri)uted loads Determine reactions at

supports ) treating -$ole)eam as *ree9)od8

Cut )eam at C and dra- *ree9)od diagrams *or AC and CB

exposing '9( Sstem

From e5uili)riumconsiderations, determine( ' or ( '8



Civil Engineering Department, Faculty of Engineering, Sriwijaya University2@ Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

7 6 M Sign Conventions7 6 M Sign Conventions

Consider aCon0entionall

;/ra0it< Loaded

Simpl9Supported

eam -it$ t$e H9 Axis Origin

Con0entionall

Located at t$e LEF&

+ext Consider a'irtual Section

Located at C

C

DEFI+E t$is Case as .OSI&I'E

" S$ear, '

– &$e 'irtual (em)er LEF& o* t$e Cut is pus$ed DO#+ )

t$e !ig$t 'irtual (em)er

" (oment, (

– &$e eam O#S

=.-ard




M 6 7 Sign ConventionsM 6 7 Sign Conventions

Simpl9Supported eam -it$ t$e H9Axis Origin Con0entionall

(

)

C

.ositi0e S$ear

" !ig$t (em)er .us$esDO#+ on Le*t (em)er

.ositi0e ending

" eam o-s =.-ard

.OSI&I'E Internal

Forces, ' (" +ote t$at at a 'irtual

Section t$e 's (s(=S& alance




7 6 M Diagrams7 6 M Diagrams

#it$ t$e Signs o*'( De*ined -e

Can no- Determine

t$e (A/+I&=DE

and SE+SE *or '(at A+ ar)itrar

'irtual9Cut Location

.LO&&I+/ '( 0s8

x ields t$e Staced

Load9S$ear9(oment

;L'(< Diagram

LOAD Diagram

S%EA! Diagram

(O(E+& Diagram

JBinsK at Load9

Application .oints




"uil M67 Diagram"uil M67 Diagram)< Determine reactions at supports

c< Cut )eam at C and consider le*tmem)er AC

## Px M P V +=+=d< Cut )eam at E and consider rig$t

mem)er E( ) ( ) x L P M P V −=−= #*#*

e< .lot ' 0s x

*< .lot ( 0s x

%ote7 For a )eam su)ected to

CO+CE+&!A&ED LOADS, s$ear

is CO+S&A+& )et-een loading

points and moment 0aries

LI+EA!L

Uli L d i




Example of SS:

wW W

a a

LRL RR

Ultimate Load comprises:

• self-weight (DL) of G, and

• concentrated LL’s of Q

USFD

UBMD

Vmax

Vmax

Mmax

G = 1.4w

Q = 1.6W

RL* = RR*

= G . L / 2 + Q

Vmax = RL* = RR*

Mmax

= Q a + G L2

/8So M* = Mmax for

our design purpose





For t$e /i0en Load /eometr, Dra-

t$e s$ear and)ending momentdiagrams *or t$e)eam A

Solution .lan" &aing entire )eamas *ree9)od,calculate reactions at

A and 8

" Determine e5ui0alentinternal *orce9couplesstems at sectionscut -it$in segments

AC, CD, and D

" .lot !esults




&aing entire )eam as a

*ree9)od, calculatereactions at A and 8

" +ote &$e 4@@ l) load at E ma )e !E.LACED ) a

4@@ l) *orce and 16@@ l)9in8 couple at D

$0=∑ A M

( ) ( ) ( ) ( ) ( ) 0in.##lb00in.!lb80in."# =−− y B

lb"!'= y B

$0=∑ B M

( ) ( ) ( ) ( ) ( ) 0in."#in.10lb00in.#!lb80 =−+ A

lb'1'= A

$0=∑ x F 0= x B



Civil Engineering Department, Faculty of Engineering, Sriwijaya University2: Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

E0aluate e5ui0alent internal

*orce9couple sstems atsections cut -it$in segments

AC, CD, and D

" From A9C use Cut91

∑ = $0 y F 00'1' =−− V x

xV 0'1'−=

$01 =∑ M ( ) 00'1' #1 =++− M x x x

##0'1' x x M −=



Civil Engineering Department, Faculty of Engineering, Sriwijaya University2> Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

E0aluate e5ui0alent internal*orce9couple sstems at

sections cut -it$in segments

AC, CD, and D

" From C9D use Cut92

$0# =∑ M ( ) 0!80'1' =+−+− M x x

( ) in.lb"'#880 ⋅+= x M

∑ = $0 y F 080'1' =−− V

lb"'=V



Civil Engineering Department, Faculty of Engineering, Sriwijaya University2? Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

E0aluate e5ui0alent internal*orce9couple sstems at

sections cut -it$in segments

AC, CD, and D

" From D9 =se Cut93

$0" =∑ M ( ) ( ) 018001!00!80'1' =+−+−−+− M x x x

( ) in.lb"!'!80+11 ⋅−= x M

∑ = $0 y F 00080'1' =−−− V

lb"!'−=V



Civil Engineering Department, Faculty of Engineering, Sriwijaya University3@ Dr. Ir. Anis Saggaff, MSCE Mecanics ! Statics

.lot !esults

" From A to C7 xV 0'1'−=

##0'1' x x M −=

" From C to Dlb"'=V

( ) in.lb"'#880 ⋅+= x M

" From D to

lb"!'−=V

( ) in.lb"!'!80+11 ⋅−= x M – +ote t$at o0er A9C &$e ending9(oment E5uation is

SECO+D Order, and Conca0e DO#+




&elations "etween an 7&elations "etween an 7

On Element o* Lengt$ x*rom C to CG MFx @

( )

w x

V

dx

dV

xwV V V

x

−=∆

∆=

=∆−∆+−

→∆ 0

lim

0

Separating t$e 'aria)les and

Integrating *rom Ar)itrar

.oints C D

( )cur,e-/underre−=

=−=−= ∫ ∫ D

C

D

C

x

x

C D

V

V

dxwV V dV




&elations "etween an M&elations "etween an M

+o- on C9C tae M(CD @

Separating t$e 'aria)les andIntegrating *rom Ar)itrar

.oints C D

( )

( ) V xwV x

M

dx

dM

x xw xV M M M

x x=∆−=

∆

∆=

=∆

∆+∆−−∆+

→∆→∆ #

1

00limlim

0#

( )cur,eS23R underre==− ∫ D

C

x

x

C D dxV M M

0




Summary# , 7, M &elationsSummary# , 7, M &elations

&$e 1st

Deri0ati0e o*' is t$e +egati0e o*

t$e Load

( )0

0

xwdx

dV

x x

−==

&$e S$ear is t$e

+egati0e o* t$e Area

under t$e Ld9Cur0e

( )∫ −= dx xwV

&$e 1st

Deri0ati0e o*( is t$e S$ear

( )0

0

xV dx

dM

x x

==

&$e (oment is t$e

Area under t$e '9

Cur0e

( )∫ = dx xV M





For t$e /i0en Load

/eometr, Dra-

t$e s$ear and

)ending momentdiagrams *or t$e

)eam AE

Solution .lan" &aing entire )eamas *ree9)od,calculate reactions atSupport A and D8

" et-eenconcentrated loadapplication points,d'dx 9- @, and&$us t$e S$ear isCO+S&A+&




Solution .lan ;cont8<

" #it$ =+IFO!(

loading )et-een D

and E , t$e s$ear0ariation is LI+EA!

" et-een concentratedload application points,

d(dx ' const8 &$eC%A+/E I+ (O(E+&

)et-een load applicationpoints is e5ual to A!EA=+DE! S%EA! C=!'E)et-een Load9App points

" #it$ a LI+EA! s$ear

0ariation )et-een D andE, t$e )ending momentdiagram is a .A!AOLA;i8e8, 2nd order in x<8




&aing entire )eam as a

*ree9)od, determinereactions at supports

∑ = $0 A M

( ) ( ) ( ) ( ) ( )

( ) ( ) 0ft8#4ips1#

ft14ips1#ft!4ips#0ft#

=−

−− D

4ips#!= D$0∑ = y F

04ips1#4ips#!4ips1#4ips#0 =−+−− y A

4ips18= y A



Civil Engineering Department, Faculty of Engineering, Sriwijaya University3:


&$e 'E!&ICAL !eactions

et-een concentrated load

application points, d'dx @,and t$us s$ear is Constant

4ips#!= D4ips18= y A

#it$ uni*orm loading

)et-een D and E , t$e s$ear0ariation is LI+EA!8



Civil Engineering Department, Faculty of Engineering, Sriwijaya University3>


et-een concentrated loadapplication points, d(dx '

Const8 &$us t$e c$ange in

moment )et-een load application

points is e5ual to A!EA under t$e

S%EA! C=!'E )et-een points8

ft4ip810

ft4ip&#1!

ft4ip108108

⋅−=−=−

⋅+=−=−

⋅+=+=−

DC D

C BC

B A B

M M M

M M M

M M M

ft ! ft 8 ft 10 ft 8



Civil Engineering Department, Faculty of Engineering, Sriwijaya University3?


#it$ a Linear S$ear 0ariation)et-een D and E , t$e

)ending moment diagram is

.A!AOLIC8

08

ft4ip8

=+=−⋅−=

E D E

D

M M M

M

+ote t$at t$e F!EE End o* aCantile0er eam CannotSupport A+ S$ear orending9(oment

ft ! ft 8 ft 10 ft 8




All Done for *oayAll Done for *oay

Statics

"eam an Supports

Bulia$Bulia$S*S*

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