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