13. 1 평형 (Equilibrium)

13. 2 평형 조건

13. 3 중력 중심 (Center of Gravity)

13. 4 정적 평형의 예

13. 5 불확실한 (Indeterminate) 구조

13. 6 탄성 (Elasticity)

CHAPTER 13. 평형과 탄성

constP

Equilibrium ( 평형 )

: Static Equilibrium ( 정적 평형 ) Section 8-5

13-1 평형 (Equilibrium)13-1 평형 (Equilibrium)

const L

0L0P

&

0 const.ext

FdtPd

P

병진운동 :

회전운동 :

(balance of force)

(balance of torques)

) // ( zτ

2 차원

일정한 속도로 미끄러지는 Hockey puck

13-2 평형 조건13-2 평형 조건

0Fext

0 const.ext

τdtLd

L

0 ext

τ

0F

0F

0F

z

y

x

13-3 중력 중심 (Center of Gravity)13-3 중력 중심 (Center of Gravity)

Center of Mass = Center of Gravity

0x

F

13-4 정적 평형의 예13-4 정적 평형의 예

0mgMFFFrey

0LFL

mgL

Mg0Frez 24

τ

Scale readings?

0x

F

0mgMgFTFy

0dTDmgLMg0Fτz

0 pxwx FFF

gysgxFF μ

0)( gmMFF pyy

032

1 amgaMghFτ wz

a

mMgbT

bmgmgbaT

τ

c

c

z

)(

02

:

2

1

0

0chx TFF

222

22

gmMT

FFF

gmMF

mgMgFF

c

vh

v

vy

)(

)(

0

Find Tc and F on the hinge.

0x

F

mgN

mgN

NfNf

mgffFy

5607011 21

21

22

11

21

. ,. and .For

0

N

mdgw

N

mgdNw

N

mgdwfh

mgdNhwf

τ z

111

1

0

0

Rock climber resting

Find N, and h.

Best position to rest.

13-5 Indeterminate Structure13-5 Indeterminate Structure

For 2-dimensional problems,

2 Fx, Fy

1 z

3 unknowns solvable

What if we have 4 unkowns?

indeterminate

Need elasticity to solve them!

(a) Tensile stress ( 인장 변형력 )

(b) Shearing stress ( 층 밀리기 변형력 )

(c) hydraulic stress

13-6 탄성 (Elasticity) 13-6 탄성 (Elasticity)

Spring model of atomic “lattice”

MaterialDensity

(Kg/m3)

Young'sModulus E(106N/m2)

UltimateStrength Su

(106N/m2)

YieldStrength Sy

(106N/m2)

Steel 7860 200 400 250

Aluminum 2710 70 110 95

Glass 2190 65 50 -

Concrete 2320 30 40 -

Wood 525 13 50 -

Bone 1900 9 170 -

Polystyrene 1050 3 48 -

Ultimate Strength 의 차이 : 콘크리트 : 압축 ( 강 ) 장력 ( 약 )

Tension and Compression ( 인장과 압축 )

modulus sYoung' : A

F Stress E

L

LE

Stress = modulus x strain

constant of proportionality = modulus of elasticity

modulusBulk : Stress Hydrolic BV

VBp

층 밀리기 :

modulusShear : StressShear GL

XG

A

F

체적의 변형 :

At the bottom of the Pacific Ocean, p = ~ 4107 N/m2 (~ 4000 m 깊이 )B(water) = 2.2109 N/m2 and B(steel) = 161010 N/m2

81 cm R=9.5 mm

F = 6.2 104 N

F

mm 89.01

Elongation LA

F

EL

282

N/m 102.2 Stress R

F

A

F

% 025.0160

2.2 % 8.1 : Steel

% 8.1 :Water

V

ΔVV

ΔV

Find Stress, elongation and strain of the rod.

% 11.0Strain

L

L