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Erie Canal Lift Bridge – Main Street, Brockport, NY©2007 Coon All Rights Reserved
SupportsA pinned support can support a structure in two dimensions.
A roller support can support a structure in only one dimension.
Static Determinacy Formula
RMJ 2
ReactionsofNumber R MembersofNumber Joints ofNumber
MJ
Statically Indeterminate
A truss is considered statically indeterminate when the static equilibriumequations are not sufficient to find the reactions on that structure. There are simply too many unknowns.
RMJ 2Try It
Did you notice the two pinned connections?
B
A CD
lbDF 500
Statically Determinate
A truss is considered statically determinate when the static equilibriumequations can be used to find the reactions on that structure.
RMJ 2Try It
Is the truss statically
determinate now?
B
A CD
lbDF 500
Static Determinacy Example
3838
3351922
RMJ
Each side of the main street bridge in Brockport, NY has 19 joints, 35 members and three reaction forces (pin and roller) making it a statically determinate truss.
What if these numbers were
different? ReactionsofNumber R MembersofNumber Joints ofNumber
:Remember
MJ
Equilibrium Equations
0 XFThe sum of all forces in the X- direction is zero.
0 YFThe sum of all forces in the Y- direction is zero.
0MThe sum of the moments about a given point is zero.
Momentary Review
RESISTANCE ARM
Lr
EFFORT ARMLe
Fe
EFFORT FORCE
Fr
RESISTANCE FORCE
A moment is a twisting or turning force sometime referred to as torque.
A moment arm is nothing more than a lever. The wheelbarrow pictured to the right is a third class lever.
Given the following information, you could calculate how much force would be needed to lift the handles of the wheelbarrow.
•Distance from the fulcrum (A) to the effort (C)
•Distance from the fulcrum (A) to the resistance (B).
•Resistance Load (B)
A
D C
RESISTANCE ARM
Lr
EFFORT ARMLe
Fe
EFFORT FORCE
Fr
RESISTANCE FORCE
Now lets replace the wheelbarrow with a truss. Likewise, joint A would be the fulcrum, the load is applied at joint D, and the reaction at joint C is counteracting force FD.
Remember the truss is in static equilibrium, therefore, all forces must sum to zero.
If we sum the moments about point A, we can find the reaction force RCY at point C.
Momentary Review
lbDF 500
B
A CAXR
AYR CYR
D
3’ 7’
Finding the Reaction Forces“For every action, there is an equal and opposite reaction”
- Sir Isaac Newton
Using Moments to Find RCYA force that would cause a clockwise moment is negative.
A force that causes a counterclockwise moment is positive.
lb
lbftft
ftlbft
ftftlb
ftft
150500,1)10(
0)10(500,10)10()3(5000)10()3(0
CY
CY
CY
CY
CYD
A
RRRRRF
MFD is negative because it
causes a clockwise moment.
RCY is positive because it causes a
counterclockwise moment.
B
A CAXR
AYR CYR
D
3’ 7’
lbDF 500
Sum the Y Forces to Find RAY
We know two out of the three forcesacting in the Y-direction. By simplysumming those forces together we
can find the unknown reaction at point A.
Please note that FB is a shown as a negative because of its direction.
See Cartesian coordinate system.
lbAY
AYlb
AYlblb
AYCYD
Y
RRRRRFF
3500350015050000
B
A CAXR
AYR
D
lbDF 500
Sum the X Forces to Find RAXBecause joint A is pinned, it could react
to a force applied in the X-direction.However, Since the only load applied to this truss (FB) has no X-component, RAX
must be zero.
00
AXRFx
B
A CAXR
AYR
D
lbDF 500
A
B
C
D
E F
If you can solve a truss using the Method of Joints, you can solve a
truss using the Method of Sections.
A
B
C
D
E F
RAY
RAX
RFY
Calculate Reaction Forces RAX, RAY & RFY
0 XF 0 YF 0M
A
B
C
D
E F
RAY
RAX
RFY
Let’s find the force in member CD.
F CD
known
known
known
A
B
C
D
E F
RAY
RAX
RFY
Cut across two or three members, but no more than three.
known
known
known
A
B
C
RAY
RAX
Treat this cut section as a RIDGID BODY.
known
known
A
B
C
RAY
RAX
Assume the forces on cut members act as external forces on the cut
FBD Assumed Compression
FCD Assumed Tension
FCEAssumed Tension
known
known
A
B
C
RAY
RAX
Treat left section as a RIDGID BODY.
FBD
FCD
FCE
0 XF
0 YF
0 CM
3 unknowns BD, CDX & BC
1 unknown CDy can be found
1 unknown FE can be found
known
known
0 XFThe sum of all forces in the X- direction is zero.
0 YFThe sum of all forces in the Y- direction is zero.
0MThe sum of the moments about a given point is zero.
Why can we only cut three members?
D
E F
RFY
You could use the right side of the truss as well. Start by cutting through two or three members.
FBD
FCD
FCE
Assumed Compression
Assumed Tension
Assumed Compression
known
D
E F
RFY
You could use the right side of the truss as well. Start by cutting through two or three members.
FBD
FCD
FCE
0 XF
0 YF
0 CM
3 unknowns BD, CDX & BC
1 unknown CDy can be found
1 unknown FE can be found
known
Erie Canal Lift Bridge – Main Street, Brockport, NY©2007 Coon All Rights Reserved