Engineering 36
Chp 6: FBD
Strategies
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
1 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
FBD Strategy
Synthesizing an FBD Space Diagram
entails three basic Steps
• A Space Diagram that
accurately Depicts the
Structural Concept
Physical Situation
• A Concept Diagram to
Identify and Idealize the
loads and support Structure Free Body Diagram
• The FBD which Shows the
Isolated Body of Interest
with Loads and Geometry
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
2 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
FBD Tactics
1. Ask “What is Going on Here?
• Study the Space Diagram to Assess
the PHYSICAL Operation of the System
– Where are the Forces/Moments (F/M) applied,
and what are the F/M Directions
• Can the System be approximated as 2D,
or is a full 3D analysis required
2. Define & Isolate the Body of interest
• Detach the Body from Any Support
• Locate CoOrd system at a “good” spot
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
3 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
FBD Tactics
3. Identify Loads Acting on
the Object/Body
• Include ALL known
Mags & Dirs
• If the body has NonNegligible
Weight, concentrate the
entire Wt at the Body’s
Center of Gravity (CG)
– More on CG Calcs in Chp8
• Label all Unknown F’s & M’s
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
4 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
FBD Tactics
4. Add Support ReAction Forces
• Analyze each Support for Each form of
Support Reaction and add to FBD
– Tables 6.1 & 6.2 are Excellent Resources
5. Identify any FLUID Boundaries
• Note that Fluids exert Pressure on the
Object of Interest
• Pressure Forces should be shown as
Distributed Loads with an appropriate
profile
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
5 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: Compression Cylinder
Step-1: Draw a
piston detached from
the device.
Step-2: Draw a force
vector (an arrow)
representing the
weight (mg) of the
piston.
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
6 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: Compression Cylinder
Step-3: Draw a force
vector (an arrow)
representing any force
exerted by the link on
the piston.
Step-4: Draw force
vectors (set of arrows)
representing the
distributed force (pAtm•A)
due to atmospheric
pressure on the piston.
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
7 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: Compression Cylinder
Step-5: Draw a force
vectors representing
the distributed force
(p•A) due to the
pressure inside.
Step-6: Check that
friction is negligible
• If Friction is NOT
small, then Add
Vertical Friction
forces at the Edges
of the Piston
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
8 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: Compression Cylinder
Step-7: Do a force
balance in the axial
direction to produce a
force balance equation.
Step-8: Note that the
force balance eqn of
Fig. 1 establishes that
a piston which is free to
move, i.e., F=0,
maintains a constant
pressure inside the
cylinder.
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
9 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: Cable Supported Pipe
Loading
• 300 lb at corner
• 200 ft•lb twist
Supports
• Cable at B
• NonThrust
Bearings at
Pt-A
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
10 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: Support Analysis
Cable
• Tension Only
• LoA Coincident
with geometry
Multiple Journal Brgs
• Ref. Tab 6.2.8B
– Prevent Up-&-Down and
Fwd-&Bkwd motions
• Brgs Cage
Pipe “T”, preventing
Side-to-Side Motion
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
11 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: FBD z
IsoLate Pipe FA2z
FA1z
Define CoOrd System
Add Known Loads
FAy
Add Tension Support y
200 TBC
Add Brg Planar ft•lb
x
Restraints
300 lb
Add Brg-Set
Axial Restraint
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
12 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: FBD z
MAz
Note the Brgs at the FA1z
FA2z
Caputured “T” resist
twisting about the X
and Z axes MAx
FAz FAy
Thus we can y
construct an 200 T
equivlaent RCN ft•lb
x
set at Pt-A that
includes These 300 lb
Resisting Moments
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
13 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: Platform Supports
Loading
• 400 lb at corner
Supports
• NonThrust
Bearing at Pt-A
• Ball at Pt-B
• “Captured Pin”
Hinge at Pt-C
– Pin Provides
Axial Restraint
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
14 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: FBD z
IsoLate PlatForm
400 lb
Define CoOrds FCz
Add FAz
Known MAx
Loads
x MCx FCy
MAz
Add Normal y
MCz
Support Provided
by the Ball FBz
Add Brg Restraints
Add Hinge Supports
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
15 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: FBD Simplification
z
Since the 400 lb induces
NO tendency for the 400 lb
the plate to FCz
twist, then FAz
NO Moments
are
generated xMAx MAz MAx FCy
at the Hinge or Brg MAz
y
The Hinge & Brg FBz
Moment RCNs can be
Removed without affecting
the analysis
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
16 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: Pipe Support
Loading
• 4 kN at End Pt-B
• 6 kN vertical
near MidSpan
Supports
• Thrust Brg at
Pt-A.
– Ref Tab 6.2.9A
• Cable at Pt-B
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
17 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: FBD z
IsoLate Pipe
FAz
Define CoOrd System MAy
Add Known Loads
4 kN FAy
Add Cable
Tension MAz
y
TBC
6 kN
Add
Thrust-Bearing x
Supports
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
18 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: FBD z
The 6 kN load
generates primarily FAz
the MAy Reaction MAy
at the Bearing
The Off-Axis 4 kN FAy
4 kN and TBC y
TBC MAz
Forces generate
6 kN
the MAz Reaction
at the Bearing x
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
19 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: P6.6.9
ConCrete Hopper
• Mass of 400 kg
• Center of Gravity at G
Pulled UpWard at
CONSTANT Velocity by
Cable with Tension T
Draw FBD for
a. Hopper & Wheel Assys
b. Guide & Wheel Assy
at Pt-A
c. Hopper w/o Wheel Assys
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
20 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: P6.6.9a T
IsoLate Hopper and
Wheel Assemblies FC
y
Known Loads
FD
• Cable Pull at Pt-H
• Wt = mg = 400x9.81 = x
3924 N; at CG
FE
ReActions at A & B
• RCN Force is Normal to the
FF
Guide-Rails (Tab 6.1.11)
3.92 kN
– R[C&D] are to LEFT
– R[E&F] are to RIGHT
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
21 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: P6.6.9b y
IsoLate Upper Wheel
Assembly x
FAy
Known Loads FC
• Wheel Weight
• Pin at Pt-A on Bracket
FAx
– Pulls UP
– Pushes to RIGHT FD
ReActions at C&D Ww
• RCN Force is Normal to the
Guide-Rails (Tab 6.1.11) Wheel Assy
– Both Wheel RCNs to LEFT
At Pt-A
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
22 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: P6.6.9c T
IsoLate Hopper FAx
Known Loads y
• Cable Pull at Pt-H FAy
• Wt = mg = 400x9.81
= 3924 N; at CG
x
ReActions at A&B
• PINs connect the Wheel
Assys to the Hopper FBx
– By Tab 6.1.6 Pin RCNs are 2D FBy
RAx is to LEFT
RBx is to RIGHT
3.92 kN
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
23 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: P6.6.9c T
Note that the Loads FAy FAx
and FBy are due y
Soley to the Weight of
FAy
the Wheel Assemblies
It is quite likely that x
Wheel Assy wts are
negligible compared to
the 880lb hopper wt
FBx
In this case the Wheel FBy
wt can be neglected and
the FBD simplified 3.92 kN
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
24 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: P6.6.21
3D Bent Bar
Loaded with Wt W
at Pt-D
Supports
• Cantilever at Pt-A
• Spring Loaded Rod BE
Draw the FBD for the
Bent Bar
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
25 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Example: P6.6.21
IsoLate Bar & z
Set CoOrds MAx
FAx y
Known Load is
Wt W hanging x
FAy FAz
at Pt-B MAy
ReActions at A&B MAz FB
• RCN-A is a Cantilever
with 6 Degrees of
Restraint (Tab 6.2.5) W
• RCN-B is Solid Spring Which
can Push or Pull (Tab 6.2.3)
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
26 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
WhiteBoard Work
None Today;
Did by
PowerPoint
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
27 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
28 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
29 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt
Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE
30 BMayer@ChabotCollege.edu • ENGR-36_Lec-10_Drawing_FBDs.ppt