Transcript ENGR-36_Lec-13_Tipping_Determinancy_H13e

Engineering 36
Chp 5: Tipping,
Deteriminancy
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
[email protected]
Engineering-36: Vector Mechanics - Statics
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Statics of Tipping Over
 An Object resting on a
Support Structure will
TIP OVER when the
ΣM at the Pivot Point
results in a supporting
force Going to Zero
?
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
ForkLift Truck Tipping
 Analyze ForkLift Tipping
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Bruce Mayer, PE
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ForkLift Tipping
 Given Loading & Geometry
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Bruce Mayer, PE
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ForkLift Tipping
 The FBD
RA
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RB
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ForkLift Tipping
 At Tipping RB →0; Find the W1 that causes this
• The FBD Under These Conditions
 The ForkLift is
Teetering on the
Front Wheels; it’s
about to go Over
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RA
Bruce Mayer, PE
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ForkLift Tipping
 Take ΣMA = 0
0  aW 1  bW 2
 Solving for W1
Revals the
TIPPING LOAD
W 1 , tip 
b
a
W2
RA
 Maximize W1,tip by extending “b” by placing a
COUNTER-Wt at the back of the Truck
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Teeter-Totter Tipping
 Consider this Physical Situation
14kg
4.5kg
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Heavy
45kg
Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Teeter-Totter Tipping
 Loaded, and
Possibly Teetering,
SawHorse Shelf
 Loading Condition
• 14 kg = Plank Mass
– CG at Pt-G
• 4.5 kg = Box-B
• 45 kg = Box-D
 Problem: Find the
Mass of Box-A so
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 that that the plank
does NOT TIP
when Heavy Box-C
is Removed
Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
WhiteBoard Work
Temporary
Shelf as
TeeterTotter
4.5kg
14kg
Heavy
45kg
 Find Mass of Box-A to
prevent Tipping when
Box-C is taken off plank
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Equilibrium of a Rigid Body in 2D
 For all forces and moments
acting on a two-dimensional
structure, by 2D Criterion
Fz  0
M
x
M
y
0
M
z
 MO
 Then The Eqns of Equilibrium
F
x
0
F
y
0
M
z,A
0
• where A is ANY point in the
plane of the structure
 The 3 equations can be solved
for no more than 3 unknowns
• The 3 eqns can not be augmented
with added eqns, but
F 0
they can not be replaced  x
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M
A
0
M
B
0
Bruce Mayer, PE
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Statically Indeterminate Rcns

Fewer unknowns
than equations,
partially constrained
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
Equal number

unknowns and
equations but
improperly constrained
More unknowns than
equations
Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Determinacy and Stability
 Determinacy - provides both necessary
and sufficient conditions for equilibrium
• When all the forces in a structure can be
determined from the equations of equilibrium
then the structure is considered statically
determinate.
• If there are more unknowns than equations,
the structure is statically INdeterminate.
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Bruce Mayer, PE
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Determinacy
 For Planar structures, there are three
equations of equilibrium for each FBD,
so that for n-bodies and r-reactions
r  3n
Statically
DETERMINANANT
r  3n
Statically
INdeterminanant
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Determinacy
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Determinacy
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Determinacy and Stability
 Stability - Structures must be properly
held or constrained by their supports
• Partial Constraints - a structure or one of
its members with fewer reactive forces
than equations of equilibrium
• Improper Constraints - the number of
reactions equals the number of equations
of equilibrium, however, all the reactions
are concurrent.
– In this case, the moment equation is satisfied
and only two valid equations of equilibrium
remain
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Stability
 Another case is when all the
reactions are parallel
 In general, a structure is geometrically
unstable if there are fewer reactive
forces than equations of equilibrium.
r  3n
r  3n
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UNSTABLE
unstable if members reactions
are concurrent or parallel or
contains a COLLAPSIBLE
mechanism
Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Stability
 Unstable - Partial Constraints
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Stability
 Unstable - IMproper Constraints
F
D
F
M
D
0
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Bruce Mayer, PE
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Stability
F
 Stable → Reactions are
NonConcurrent and NonParallel
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Stability
M
A
0
A
FLOAD
 UNstable → The Three Reactions
are Concurrent
Engineering-36: Vector Mechanics - Statics
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Stability
F
 UNstable → The Three Reactions
are Parallel
• No ReAction for x-Directed Load
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Stability
F
 UNstable → r < 3n and member CD is
FREE TO MOVE horizontally while BC
rotates
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Table Top Tipping
 Consider the This Situation
G
Heavy
TableTop of
Weight W
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Table Top Tipping
 Loaded, and
Possibly Tilting,
Table Top
 Loading Condition
• W = Table Top
Weight
– Assume that the Table
Top CG coincides with
the Table Top
Geometry
 Problem: Find the
SMALLEST vertical
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 Force that when
applied to the table
Top will cause it to
TILT
Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
WhiteBoard Work
Unsecured
TableTop
Tilting
 Find minimum vertical
force need to tilt the
Table Top
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Engineering 36
Appendix
Bruce Mayer, PE
Registered Electrical & Mechanical Engineer
[email protected]
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
WhiteBoard Work
Let’s Work
some Equil
Problems
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
Engineering-36: Vector Mechanics - Statics
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
4.5kg
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14kg
Heavy
45kg
Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt
G
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-13_Tipping_Determinancy_H13e.pptx.ppt