13. 1 평형 (equilibrium) 13. 2 평형 조건 13. 3 중력 중심 (center of gravity) 13. 4 정적...
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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