1. 4. Rigid body Equilibrium
Su-Jin Kim
Gyeongsang National University
Fall 2017

2. OCW
Rigid Body Equilibrium Conditions
Rigid Body Equilibrium 2D
2 forces & 3 forces members
Rigid Body Equilibrium 3D

3. Index Equilibrium Conditions Rigid Body Equilibrium 2D

4. Equilibrium Conditions
Force : Σ F = 0
ΣFx =0
ΣFy =0
ΣFz =0
Moment : Σ M = 0
ΣMx =0
ΣMy =0
ΣMz =0 Mz My Mx

5. External force moment 2DFx Fy M
Fixed, Welded
String, wire T W
Gravity Fx Fy
Pin, Point Fy
Roller, Ball

6. Rigid Body Equilibrium 2D
Free body diagram (FBD)
Force vector, 3 unknown forces
3 Equilibrium equations ΣFx =0, ΣFy =0, ΣMo =0
FBD

7. Ex 2D
ΣFx =0, Fx + 5*1.41 = 0, Fx = -7.8 N
ΣFy =0 , Fy - 5*1.41 = 0, Fy = 7.8 N
ΣMo =0, Mo - 5*1.41*1 = 0, Mo = 7.8 Nm Mo Fx
45 ˚
1 m
10 N Fy

8. Ex) Two people Free body diagram (FBD) Force vector, 3 unknown forcesFx o m f1 f2 Fy N1 N2

9. Rigid Body Equilibrium 2D
ΣFx =0, Fx – P = 0
ΣFy =0, Fy – W = 0
ΣMo =0, P l = 0  P = 0 W P l Fx o Fy

10. Ex) Two people ΣFx =0, P - f1-f2 = 0  f1 = f2 = 50 N
ΣFy =0, N1+N2 – W = 0
ΣMo =0, -P l – W 0.5m + N2 m = 0
 N1 = 150 N, N2 = 450 N P
100 N W
600 N N1 N2 f1
f2=f1 L
1.5 m m
1 m o

11. Rigid Body Equilibrium 3D
Free body diagram (FBD) & Force vectors
6 unknown forces or moments
6 Equilibrium equations
Σ Fx =0, Σ Fy =0, Σ Fz =0
ΣMx =0 , ΣMy =0 , ΣMz =0

12. Ex1. Simple supported beam
60 kg
1.5 m
0.5
10 kg B A
Σ Fy = A + B – =0
ΣMo =0

13. Ex2. Scissor
400 N F
0.05
0.5 m
30°