e14 - applied mechanics: staticsbiomechanics.stanford.edu/e14/e14_s11.pdfe14 - applied mechanics:...
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1mon/wed/fri, 12:50-2:05pm, 370-370
e14 - applied mechanics: statics
2syllabus
e14 - applied mechanics: statics
fourth homework
due
35. equilibrium of a rigid body
• to develop equations of equilibrium for a rigid body• to introduce the concept of a free body diagram for a rigid body• to show how to solve rigid body equilibrium problems
today‘s objectives
45.3 equations of 2d equilibrium
three alternative sets of eqns
MO = 0 Fx = 0 Fy = 0• two force & one moment equilibrium equations
MB = 0 F = 0• one force & two moment equilibrium equations
MA = 0
MC = 0• no force & three moment equilibrium equations
MB = 0 MA = 0
line through A and B must be ! to x-axis
A, B and C must not be on one line
55.3 equations of 2d equilibrium
procedure for drawing a FBD
I. isolate the system of interestII. identify all forces & moments
applied loadingreactions @support & contactweight of the body
III. label forces & give dimensions
65.3 equations of 2d equilibrium
procedure for drawing a FBD
I. isolate the system of interestII. identify all forces & moments
applied loadingreactions @support & contactweight of the body
III. label forces & give dimensions
75.3 equations of 2d equilibrium
procedure for drawing a FBD
I. isolate the system of interestII. identify all forces & moments
applied loadingreactions @support & contactweight of the body
III. label forces & give dimensions
W
d1
AH2
H1
d2
85.3 equations of 2d equilibrium
equilibrium analysis
MO = 0 :
Fx = 0 :
Fy = 0 :
H2 = -H1
A - W = 0 A = W
H1d2 - Wd1=0 H1 = W d1/d2
for d1= 2d2, both arms have to support twice the weight
W
d1
AH2
H1
d2O
H1 + H2 =0
tension
com-pression
95.4 two- and three-force members
• pin-connected at both ends• weightless• no extra forces acting on it
two-force members
FAB and FBA are equal andopposite FAB = FBA,, resultingfrom Fx=0 and Fy=0, andlie along the same line ofaction, resulting from MO=0
105.4 two- and three-force members
three-force members
MO=0 requires that thethree forces form aconcurrent (meeting at acommon point O) or parallel(meeting at ") force system
115.4 two- and three-force members
three-force members
MO=0 requires that the three forces form a concurrentforce system, their lines of action interset at a common point
W
F1F2
125.4 two- and three-force members
three-force members
MO=0 requires that the three forces form a concurrentforce system, their lines of action interset at a common point
W
F2
F1100N
800N
600N
450Ngraphic solution using vector addition
W
F1F2
135.5 free body diagram
procedure for drawing a FBD
I. isolate the system ofinterest
II. identify all forces &momentsapplied loadingreactions
support, contact forcesweight of the body
III. label each force & givedimensions
Fhr
Fhl
Ffr
Ffl
W
145.5 free body diagram
support reactions in 2d - memorize!
roller pin fixed
no motion # force / no rotation # moment
155.5 free body diagram
support reactions in 2d - memorize!
no motion # force / no rotation # moment
pin-like
roller-like
W
BH
A
BV
165.5 free body diagram
support reactions - example 04
ball-and-socket joint
175.5 free body diagram
support reactions - example 05
journal bearing
185.5 free body diagram
support reactions - example 08
single smooth pin
195.6 equations of 3d equilibirum
force and moment equilibrium
(MR)O = MO = 0
• forces sum up to zero
• moments at point O sum up to zero
FR = F = 0 Fz = 0 Fx = 0 Fy = 0
Mz = 0 Mx = 0 My = 0
205.6 equations of 3d equilibirum
example 5.15
215.6 equations of 3d equilibirum
example 5.15
225.6 equations of 3d equilibirum
example 5.15
235.7 constraints & statical determinacy
too much support
2d3 equations
3d6 equations
245.7 constraints & statical determinacy
too much support
2d3 equations
3d6 equations
2d5 unknowns
3d8 unknowns
W
F
N1
T3
M
T1
N3
T2
N2
statically indeterminate
255.7 constraints & statical determinacy
too much support
2d3 equations
2d8 unknowns
265.7 constraints & statical determinacy
not enough support
2d3 equations
2d3 equations
275.7 constraints & statical determinacy
not enough support
2d3 equations
2d2 unknowns
2d3 equations
2d3 unknowns
MA = 0 moment is not supported # system will rotate!
Fy = 0 force is not supported # system will translate!
285.7 constraints & statical determinacy
not enough support
MA = 0 moment is not supported # system will rotate!
M
the system is improperly supported if all reaction forces areparallel
F1 F2 F3
2d3 equations
2d3 unknowns
296. structural analysis
equilibrium of structural systems
306. structural analysis
equilibrium of structural systems
W1
W2
F
N
F
N T
FH
FVM