What is a Truss?• A structure composed of members connected

together to form a rigid framework.

• Usually composed of interconnected triangles.

• Members carry load in tension or compression.

Component Parts

Vertical Bottom Chord

Diagonal

End Post

Hip Vertical

Deck

Top Chord

Vertical Bottom Chord

Diagonal

End Post

Hip Vertical

Deck

Top Chord

Support (Abutment)

Standard Truss Configurations

Pratt Parker

Double Intersection Pratt

Howe Camelback

K-Truss

Fink

Warren

Bowstring Baltimore

Warren (with Verticals)

Waddell “A” Truss Pennsylvania

Double Intersection Warren

Lattice

Pratt Parker

Double Intersection Pratt

Howe Camelback

K-Truss

Fink

Warren

Bowstring Baltimore

Warren (with Verticals)

Waddell “A” Truss Pennsylvania

Double Intersection Warren

Lattice

Types of Structural Members

Solid Rod

Solid Bar

Hollow Tube

-Shape

Solid Rod

Solid Bar

Hollow Tube

-Shape

These shapes are calledcross-sections.

These shapes are calledcross-sections.

Types of Truss ConnectionsPinnedConnection

Gusset PlateConnection

Most modern bridges use gusset plate connectionsMost modern bridges use gusset plate connections

Forces, Loads, & Reactions

• Force – A push or pull.• Load – A force applied to a structure.

• Reaction – A force developed at the support of a structure to keep that structure in equilibrium.

Self-weight of structure, weight of vehicles, pedestrians, snow, wind, etc.Self-weight of structure, weight of vehicles, pedestrians, snow, wind, etc.

Forces are represented mathematically asVECTORS.

Forces are represented mathematically asVECTORS.

Equilibrium

An object at rest will remain at rest, provided it is not acted upon by an unbalanced force.

A Load... ...and Reactions

Newton’s First Law:

Tension and CompressionAn unloaded member experiences no deformation

Tension causes a member to get longer

Compression causes a member to shorten

Tension and Compression

EXTERNAL FORCES and INTERNAL FORCES Must be in equilibrium with each other.

EXTERNAL FORCES and INTERNAL FORCES Must be in equilibrium with each other.

Structural Analysis• For a given load, find the internal forces

(tension and compression) in all members.• Why?• Procedure:

– Model the structure:• Define supports• Define loads• Draw a free body diagram.

– Calculate reactions.– Calculate internal forces using

“Method of Joints.”

Model the Structure

15 cm

15 cm 15 cm

A CB

D

mass=5 kg

=2.5 kg per truss

Draw a Free Body Diagram

15 cm

15 cm 15 cm

A CB

D

mass=2.5 kg

RA RC

x

y

N5.24secm81.9kg5.2 2 maF

24.5N

Calculate Reactions• Total downward force is 24.5

N.• Total upward force must be

24.5 N.• Loads, structure, and reactions

are all symmetrical.

RA and RC must be equal.RA and RC must be equal.

SOUP

SCALE SCALE

Centerline

Centerline

SOUP

SCALE SCALE

Centerline

Centerline

SOUP

SCALE SCALE

Centerline

Centerline

SOUPSOUP

SCALE SCALE

Centerline

Centerline

Calculate ReactionsN 25.12

2

N 5.24 CA RR

A

RA

x

y

15 cm

15 cm 15 cm

CB

D

RC

24.5 N12.25 N 12.25 N

12.3 N

Method of Joints• Isolate a Joint.

A

x

y

15 cm

15 cm 15 cm

CB

D

RC

24.5 N12.25 N12.25 N

Method of Joints Isolate a Joint. Draw a free body diagram of

the joint. Include any external loads of

reactions applied at the joint. Include unknown internal forces

at every point where a member was cut. Assume unknown forces in tension.

Solve the Equations of Equilibrium for the Joint.

12.25 N

A

x

y

FAD

FAB

EXTERNAL FORCES and INTERNAL FORCES Must be in equilibrium with each other.

EXTERNAL FORCES and INTERNAL FORCES Must be in equilibrium with each other.

Equations of Equilibrium• The sum of all forces acting in

the x-direction must equal zero.

• The sum of all forces acting in the y-direction must equal zero.

• For forces that act in a diagonal direction, we must consider both the x-component and the y-component of the force.

12.25 N

A

x

y

FAD

FAB0 xF

0 yF

Components of ForceFAD

Ax

y

• If magnitude of FAD is represented as the hypotenuse of a right triangle...

• Then the magnitudes of (FAD)x and (FAD)y are represented by the lengths of the sides.

A

(FAD)y

(FAD)x

Trigonometry Review

H

y

hypotenuse

oppositesin

H

x

hypotenuse

adjacentcos

Therefore:

sinHy

cosHx

x

y

Definitions:

H

Components of Force

FAD(FAD)y

Ax

y

A(FAD)x

Therefore:

sinHy

cosHx

45o 45o

ADADxAD FFF 707.045cos

ADADyAD FFF 707.045sin

Equations of Equilibrium

12.3 N

A

x

y

FAD

FAB

0 xF

0 yF

0.707 FAD

0.707 FAD

0707.0 ADAB FF

0707.0N 25.12 ADF

N 25.12707.0 ADF

N 3.17707.0

N 25.12

ADF

ADAB FF 707.0

N 25.12)N 3.17(707.0 ABF

FAD=17.3 N (compression)

FAB=12.25 N (tension)

?

Method of Joints...Again• Isolate another Joint.

x

y

12.25 N

A

15 cm

15 cm 15 cm

C

D

RC12.25 N

B

24.5 N

Equations of Equilibrium

x

y

B

24.5 N

FBD

FBCFAB

0 xF

0 yF

05.24 BDF

N5.24BDF

FBD=24.5 N (tension)

0 BCAB FF

N 25.12 ABBC FF

FBC=12.25 N (tension)

Results of Structural Analysis

12.25 N

A C

D

12.25 N

B

24.5 N

12.25 N (T) 12.25 N (T)24

.5 N

(T)

17.3 N (C

)17.3 N (C)

Do these results make sense?Do these results make sense?

Results of Structural Analysis

In our model, what kind of members are used for tension? for compression?In our model, what kind of members are used for tension? for compression?

12.25 N

A C

D

12.25 N

B

24.5 N

12.25 N (T) 12.25 N (T)24

.5 N

(T)

17.3 N (C

)17.3 N (C)