Transcript Chapter #6, Section 6.6 - Pennsylvania State University

Chapter 6 Structural Analysis
Section 6.6 FRAMES AND MACHINES
Today’s Objectives:
Students will be able to:
a) Draw the free body diagram of a
frame or machine and its members.
b) Determine the forces acting at the
joints and supports of a frame or
machine.
READING QUIZ
1. Frames and machines are different as compared to trusses since they
have ___________.
A) Only two-force members
B) Only multiforce members
C) At least one multiforce member D) At least one two-force
member
2. Forces common to any two contacting members act with _______
on the other member.
A) Equal magnitudes but opposite sense
B) Equal magnitudes and the same sense
C) Different magnitudes but opposite sense
D) Different magnitudes but the same sense
APPLICATIONS
Frames are commonly used
to support various external
loads.
How is a frame different than a
truss?
To be able to design a frame,
you need to determine the
forces at the joints and
supports.
APPLICATIONS (continued)
“Machines,” like those above, are used in a variety of
applications. How are they different from trusses and frames?
How can you determine the loads at the joints and supports?
These forces and moments are required when designing the
machine members.
FRAMES AND MACHINES: DEFINITIONS
Frame
Machine
Frames and machines are two common types of structures that
have at least one multi-force member. (Recall that trusses have
nothing but two-force members).
Frames are generally stationary and support external loads.
Machines contain moving parts and are designed to alter the
effect of forces.
STEPS FOR ANALYZING A FRAME OR MACHINE
1. Draw a FBD of the frame or machine and its
members, as necessary.
Hints:
a) Identify any two-force members, b) forces
on contacting surfaces (usually between a pin
and a member) are equal and opposite, and,
c) for a joint with more than two members or an
external force, it is advisable to draw a FBD of
the pin.
FAB
2. Develop a strategy to apply the equations of
equilibrium to solve for the unknowns.
Problems are going to be challenging since there
are usually several unknowns. A lot of practice
is needed to develop good strategies.
EXAMPLE
Given: The frame supports an
external load and moment
as shown.
Find: The horizontal and vertical
components of the pin
reactions at C and the
magnitude of reaction at B.
Plan:
a) Draw FBDs of the frame member BC. Why pick this
part of the frame?
b) Apply the equations of equilibrium and solve for the
unknowns at C and B.
EXAMPLE
800 N m
400 N
CX
CY
1m
1m
2m
B
45°
FBD of member BC
FAB
Please note that member AB is a two-force member.
Equations of Equilibrium:
+  MC = FAB sin45° (1) – FAB cos45° (3) + 800 N m + 400 (2) = 0
FAB = 1131 N
EXAMPLE
800 N m
400 N
CX
CY
1m
1m
2m
B
45°
FBD of member BC
FAB
Now use the x and y direction Equations of Equilibrium:
 +  FX = – CX + 1131 sin 45° = 0
CX = 800 N
 +  FY = – CY + 1131 cos 45° – 400 = 0
CY = 400 N
CONCEPT QUIZ
1. The figures show a frame and its FBDs. If an additional couple
moment is applied at C, then how will you change the FBD of
member BC at B?
A)
B)
C)
D)
No change, still just one force (FAB) at B.
Will have two forces, BX and BY, at B.
Will have two forces and a moment at B.
Will add one moment at B.
CONCEPT QUIZ (continued)
D
2. The figures show a frame and its FBDs. If an additional force is
applied at D, then how will you change the FBD of member BC
at B?
A)
B)
C)
D)
No change, still just one force (FAB) at B.
Will have two forces, BX and BY, at B.
Will have two forces and a moment at B.
Will add one moment at B.
GROUP PROBLEM SOLVING
Given: A frame supports
a 50-kg cylinder.
Find: The reactions that
the pins exert on the
frame at A and D.
Plan:
a) Draw a FBD of member ABC and another one for CD.
b) Apply the equations of equilibrium to each FBD to solve for
the six unknowns. Think about a strategy to easily solve for
the unknowns.
GROUP PROBLEM SOLVING (continued)
FBDs of members ABC and CD
CY
CX
50(9.81) N
0.7 m
1.2 m
1.6 m
DX
Applying E-of-E to member ABC:
DY
+  MA = CY (1.6) – 50 (9.81) (0.7) – 50 (9.81) (1.7) = 0 ;
CY = 735.8 N
+  FY = AY – 735.8 – 50 (9.81) – 50 (9.81) = 0 ; AY = 245 N
+  FX = CX – AX = 0 ; CX = AX
GROUP PROBLEM SOLVING (continued)
FBDs of members ABC and CD
CY
CX
50(9.81) N
0.7 m
1.2 m
1.6 m
DX
Applying E-of-E to member CD:
DY
+  MD = CX (1.2) + 50 (9.81) (0.7) – 735.8(1.6) = 0 ; CX = 695 N
+  FY = DY – 735.8 + 50 (9.81) = 0 ; DY = 245 N
+  FX = DX – 695 = 0 ; DX = 695 N
AX = CX = 695 N
ATTENTION QUIZ
1. When determining the reactions
at joints A, B, and C, what is the
minimum number of unknowns
for solving this problem?
A) 3
B) 4
C) 5
D) 6
2. For the above problem, imagine that you have drawn a FBD
of member AB. What will be the easiest way to write an
equation involving unknowns at B?
A)  MC = 0
B)  MB = 0
C)  MA = 0
D)  FX = 0
Example 4: The 500 kg engine is suspended from the boom crane as
shown. Determine resultant internal loadings acting on the cross section
of the boom at point E.
Statics: Example 1 - Pliers
Given: Typical
household pliers as
shown.
Find: Force applied to
wire and force in pin
that connects the two
parts of the pliers.
.
See solution Link
Side: what is the shear
stress in pin and bending
stress in handle? SofM
Statics: Example 2 – Crane Structure
Given: Crane structure
as shown.
Find: Forces and FBD’s
for cables A-B and A-E,
boom DEF and post
AFC.
See solution Link
Side: what is the normal stress
in cables (average normal
only) and normal stress in
boom and post (combined
loading)? SofM
Example 3 (6.67) – Pulleys
Determine the force P required
to hold the 100 lb weight in
equilibrium.
Example 4 (6.114) – Front End Loader
Question 1: The tractor shovel carries a
500 kg load of soil having a center of
mass at G. Compute the forces
developed in the hydraulic cylinder BC
and reaction forces at A due to this
loading.
Question 2: Compute the force at F (=
force in link FH) and reaction forces at
D.
Example 5 (6.115) – Clamping Device
If a force of P = 100 N is
applied to the handle of
the toggle clamp,
determine the horizontal
clamping force Ne that
the clamp exerts on the
smooth wooden block at
E.