2. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
2
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Free Body Diagrams (FBDs)
A free-body diagram is a sketch of an object
of interest with all the surrounding objects
stripped away to reveal all of the forces
acting on the body
The purpose of a free-body force diagram is to
assist with determination of the Net Force
and/or Moment acting on a body
Space
Diagram
Free
Body
Diagram
3. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
3
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Constructing a free-body diagram
Select an object or group of objects to focus on as the "body“:
i.e., the system.
Sketch the body by itself, "free" of its surroundings
Draw only those forces/moments that are acting directly on the body.
• Include both the magnitude and the direction of these forces.
Do not include any forces that the body exerts on it surroundings,
they do NOT act ON the body.
• However, there is always an equal reaction force acting on the body.
For a compound body (e.g. Trusses, Machines) you do NOT need to
include any INTERNAL forces acting between the body's SUBPARTS
• these internal forces come in action-reaction pairs which cancel out each
other because of Newton's Third Law.
Choose a coordinate system and sketch it on the free-body diagram.
Often choose one of the axes to be parallel one or more forces
• it can sometimes simplify the equations to be solved.
4. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
4
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Structural Supports
NonMoving Structures are typically
Connected to Some Sort of
Supporting Base
The connection between the Structure
and Base are usually Called
“Structural Supports”
The Force and/or moments exerted on
the Structure Base are usually called
“Structural Reactions” (RCNs for Short)
5. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
5
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Structural Supports
A Support that Prevents Linear Motion
(sliding, translating) of the structure then
exerts a Force on the structure
A Support that Prevents Rotating
Motion (twisting, turning) of the structure
then exerts a Couple Moment on the
structure
6. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
6
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Recall SLIDING & FREE Vectors
Forces are SLIDING Vectors;
They can applied at
ANY-POINT on the
Vector Line of Action (LoA)
COUPLE-Moments are
FREE Vectors; They
can be applied at
ANY Point,
On or Off the Body
11. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
11
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Center of Gravity
If the Weight of the Rigid
Body is Not Negligible, then
the Entire Weight of the
Body can be concentrated
at a Single Point Called the
Center of Gravity (CG)
• Many times the CG location
is Given
– Can Calculate using Centroid
Methods which will be covered
later
12. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
12
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
2D Free-Body Diagram
First Steps for Static
Rigid-Body Equilibrium
Analysis
• Identification of All
Forces & Moments
Acting on the Body
• Formulation of the
Free-Body Diagram
Free Body Diagram
Construction Process
• See next slide
13. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
13
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
2D Free-Body Diagram cont
1. Select the extent of the
free-body and detach it
from the ground and other
bodies
2. Indicate for external loads:
• Point of application
• Magnitude & Direction Of
External Forces
– Including The Body Weight.
3. Indicate point of application
and ASSUMED direction of
UNKNOWN applied forces
14. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
14
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
2D Free-Body Diagram cont.2
• The Unknown Forces
Typically Include
REACTIONS through which
the GROUND and OTHER
BODIES oppose the possible
motion of the rigid body
4. Include All dimensions
Needed to Calculate the
Moments of the Forces
15. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
15
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Example: Truss Structure
Consider Rocker &
Pin Supported Truss
Analyze Loading
• Four External Force
Loads as shown
• Truss Weight, W
• RCN at Pt-A by
Rocker
– Expect NORMAL to
support Pad
• RCN at Pt-B by Pin
– Expect
in plane of Truss
Arbitrarily Directed
Draw the FBD for
this Structure
19. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
19
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
3D Support ReActions
This configuration is Commonly
Known as a
“Pillow Block Bearing”.
Type of support is (obviously)
designed to allow the shaft to
SPIN FREELY on its AXIS
24. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
24
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Example: Hinge & Rough-Surf
Given Bar supported
by Hinge at Pt-A
and rests on the
Rough x*y*z*
Surface at Pt-B
Analyze Rcn at Pt-A.
By 5.2-(9) the Single
Axially Constrained
Hinge will
• Provide Lateral (y &
z) and Axial (x)
Support
• Resist twisting about
the y and z axes
25. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
25
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Example: Hinge & Rough-Surf
PUSH (not PULL)
Normal to the
Surface
• In this case the y*
direction is normal to
the supporting plane
Resist Sliding in any
direction WITHIN
the supporting plane
Analyze Rcn at Pt-B.
Support Leg on a
rough surface will
27. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
27
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Symmetry City
If We’re Lucky enough to have a Plane of
Symmetry for BOTH Loading and Structural
GEOMETRY then we can treat real world 3D
problems as 2D
• OtherWise we need to Operate in full 3D
Can Treat as 2D Must Treat as 3D
No Symmetry
28. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
28
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Example: Utility Pole
Consider Leaning
Utility Pole
Determine the Loads
acting on the BASE
of the Pole
Analyze Rcn at Base
• This is a FIXED
support which is often
call a CantiLever
• Cantilever supports
resist both forces and
moments in ALL 3
Spatial Directions
29. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
29
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Example: Pole
Draw in the BASE
ReActions
FAz
FAy
FAx
MAz
MAy
This Diagram is
NOT a FBD as it
does not account for
these forces acting
on the pole
• Pole Weight
• Cable Tension
MAx
30. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
30
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Distributed Forces/Loads
In Some Cases Forces are concentrated
at Points; this is simplest case
Often times a Load cannot be identified
with a single point; Instead the Load is
Spread Out over a supporting surface
• Such Forces are Called “Distributed”
Distributed Loads
are indicated with
a Load Profile
31. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
31
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Distributed Force Profiles
A uniformily Dist Load
Has the same action
at every point on it’s
region of application.
• It’s profile is “Flat”
NonUniform Loads are also common
• They may be kinked, curved, or arbitrary
32. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
32
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Distributed-Force Equivalent
In Chp4 we discussed how to Replace a
Distributed-Load with an Equivalent
Point-Load placed at a Specific Location
Units for Distributed Forces
• 2D → Force per Length (lb/ft, lb/in N/m)
• 3D → Force Per Area (Pa, PSI, PSF)
33. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
33
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Example: Hydraulic Cylinder
The Hydraulic
Cylinder Pumps
Fluid in & out of the
Cylinder Reservoir
as Shown at Right
Draw The loads on
the Piston Assy
Game Plan:
• Isolate Piston Assy as Free Body
• CareFully Account for all Pt-Force and
PRESSURES acting on the Piston Assy
34. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
34
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Example – Cont.
9.81kN
Load-1 = 100 kg (220lb,
9.81kN) CounterWt
Load-2 = Weight of the
Piston Rod
WR
Load-3 = Weight of the
Piston
WP
Load-4 = Lateral Restraining
Forces Exerted by the
Cylinder Wall on the O-Ring
FOr
FOr
35. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
35
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Example – Cont.
9.81kN
Load-5 = The Air
Pressure on Top of the
Piston
Load-6 = The Hydraulic
Fluid Pressure on the
Bottom of the Cylinder
WR
WP
FOr
FOr
Pair
Pfluid
36. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
36
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Example – Cont.
9.81kN
We can SIMPLIFY the
analysis by making
assessments about the
relative significance of
the loads
• The Weight of the Rod
and Piston are likely
negligible compared to
the Counter Weight
WR
WP
FOr
FOr
Pair
Pfluid
37. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
37
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Example – Cont.
9.81kN
Additional
Symplifications
• The SideWall Forces on
the O-Ring must cancel
if the Cylinder is
Balanced
FOr
FOr
Pair
Pfluid
• The AIR pressure is
negligible compared to
the FLUID pressure
38. BMayer@ChabotCollege.edu • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx
38
Bruce Mayer, PE
Engineering-36: Engineering Mechanics - Statics
Example – Cont.
9.81kN
Thus in the NonMoving
Simplified System the
Fluid Pressure balances
the Counter Weight.
Mathematically
Pfluid
kN
Area
P piston
fluid 81
9.