Truss: Types and Classification

Theory of Structure - I

Lecture Outlines

• Common Types of Trusses

• Classification of Trusses

• Method of Joints

• Zero Force Members

• Method of Sections

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A truss is a structure comprising one or more triangular units constructed with straight members whose ends are connected at joints or nodes.

If all the bars lie in a plane, the structure is a planar truss.

The main parts of a planar truss.

TRUSS ANALYSISTRUSS ANALYSIS

In other words, Trusses are designed to form a stable structure.

Why are trusses strong?

Trusses derive their strength from the triangle.

The simplest of plane polygons, a triangle is unique in

that it is defined by the length of its sides. That is, one

and only one triangle can be drawn if the length of all

three sides is given.

TRUSS ANALYSISTRUSS ANALYSIS

Why are triangles used in trusses?

Rectangles and squares are not very strong because the middle of each side would tend to bend or buckle easily. And these are not used in truss.

A truss is a structure made up of triangles. Because triangles are strong because when you define the length of the three sides the relationship between the nodes is fixed. Similarly when you identify any two angles an a side or two sides and when you identify any two angles an a side or two sides and a common angle all other properties are fixed. In any other shape there are more degrees of rigidity required to create a fixed structure.

Triangles have sides that reinforce each other. They divide up the load.

Truss Bridges

A metal truss bridge is a bridge whose main structure comes from a triangular framework of structural steel or iron.

Iron and Steel

Due to their variety of designs, there is a system that is used to classify metal truss bridges by design.

Truss Basics

If the trusses run beside the deck, with no cross bracing above the deck, it is called a pony truss bridge.

Pony Truss

If cross-bracing is present above the deck of the bridge, then the bridge is referred to as a “through truss.”

Through Truss

Truss Basics

Deck Truss

Trusses may run under the deck: these are called simply Deck truss bridges.

Truss Bridge Forces

Tension

Compression

The chords and members of a truss bridge experience strain in the form of tension (stretching apart) and

compression (squeezing together). Engineers often picked different types of materials and designs for the different parts of a bridge based on these forces. An

example is shown above.

Truss Bridge Connections

The pieces of the framework of a truss bridge are held together by connections. Most connections on historic

bridges are either riveted or pinned.

Pinned Connections

Pinned connections can be identified by the bolt-like object called a pingoing through the loops of the members. They tend to show up on bridges from the first half of the truss bridge era.

Pin

Riveted connections are identified by a “gusset plate” which diagonals and vertical members are riveted to, and no pin is present.

These connections tend to show up in the second half of the truss bridge era.

Common Types of Trusses

gusset plate

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• Roof Trusses

top cord

roof

purlins

knee brace

bottom cord gusset plate

spanbay

Howe truss Pratt truss

howe truss Warren truss

saw-tooth trussFink truss

three-hinged arch

trough Pratt truss

deck Pratt truss

Warren truss

parker truss(pratt truss with curved chord)

Howe truss baltimore truss

K truss

Bridge Trusses

top cordsway bracing

top lateralbracing

portal

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deckstringers

portal end post

portalbracing

panel

floor beam

bottom cord

Assumptions for Design

• All members are connected at both ends by smooth frictionless pins.

• All loads are applied at joints (member weight is negligible).weight is negligible).

• Notes: – Centroids of all joint members coincide at the

joint.

– All members are straight.

– All load conditions satisfy Hooke’s law.

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Classification of Coplanar Trusses

• Simple Trusses

A B

C DP C D

A B

P P

A B

C

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a

b c

d (new joint)new members

• Compound Trusses

simple trusssimple truss

Type 1

simple trusssimple truss

Type 2

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secondary simple truss

secondary simple truss

main simple truss

Type 3

secondary simple truss

secondary simple truss

• Complex Trusses

• Determinacy

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• Determinacy

b + r = 2j statically determinateb + r > 2j statically indeterminate

In particular, the degree of indeterminacy is specified by the difference in thenumbers (b + r) - 2j.

• Stability

b + r < 2j unstableb + r 2j unstable if truss support reactions are concurrent or parallel

or if some of the components of the truss form a collapsiblemechanism

>

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External Unstable

Unstable-parallel reactions Unstable-concurrent reactions

C

F

O

Internal Unstable

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A BD E

O

8 + 3 = 11 < 2(6)

AD, BE, and CF are concurrent at point O

Example 3-1

Classify each of the trusses in the figure below as stable, unstable, statically determinate, or statically indeterminate. The trusses are subjected to arbitrary external loadings that are assumed to be known and can act anywhere on the trusses.

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SOLUTION

b = 19,r = 3, j = 11, then b + r = 2j or 22 = 22. Therefore, the truss is statically determinate.By inspection the truss is internally stable.

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b = 15, r = 4, j = 9, then b + r > 2j or 19 > 18. The truss is statically indeterminate to the first degree. By inspection the truss is internally stable.

Since b = 9, r = 3, j = 6, then b + r = 2j or 12 = 12. The truss is statically determinate. By inspection the truss is internally stable.

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b = 12, r = 3, j = 8, then b + r < 2j or 15 < 16. The truss is internally unstable.

Method of Joints

• If a truss is in equilibrium, then each of its joints must also be in equilibrium

• The method of joints consists of satisfying the • The method of joints consists of satisfying the equilibrium conditions for the forces exerted “on the pin” at each joint of the truss

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• Truss members are all straight two-force members lying in the same plane

– The force system acting at each pin is coplanar and concurrent (intersecting)and concurrent (intersecting)

– Rotational or moment equilibrium is automatically satisfied at the joint, only need to satisfy ∑ Fx = 0, ∑ Fy = 0

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Procedure for Analysis

• Draw the free-body diagram of a joint having at least one known force and at most two unknown forces (may need to first determine unknown forces (may need to first determine external reactions at the truss supports)

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• Establish the sense of the unknown forces

– Always assume the unknown member forces acting on the joint’s free-body diagram to be in tension (pulling on the “pin”)tension (pulling on the “pin”)

– Assume what is believed to be the correct sense of an unknown member force

– In both cases a negative value indicates that the sense chosen must be reversed

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• Orient the x and y axes such that the forces can be easily resolved into their x and y components

• Apply ∑ Fx = 0 and ∑ Fy = 0 and solve for the • Apply ∑ Fx = 0 and ∑ Fy = 0 and solve for the unknown member forces and verify their correct sense

• Continue to analyze each of the other joints, choosing ones having at most two unknowns and at least one known force

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• Members in compression “push” on the joint and members in tension “pull” on the joint

• Mechanics of Materials and building codes are • Mechanics of Materials and building codes are used to size the members once the forces are known

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2 m

2 m

500 N

45oA

B

C

The Method of Joints

Cy = 500 N

Ax = 500 N

Ay = 500 N

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FBA

FBC

500 NB

45o

Joint B

x

ySFx = 0:+

500 - FBCsin45o = 0FBC = 707.11 N (C)

SFy = 0:+

- FBA + FBCcos45o = 0FBA = 500 N (T)

2 m

2 m

500 N

45oA

B

C

Cy = 500 N

Ax = 500 N

Ay = 500 N

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Joint A

500 N

500 N

500 N

FAC

SFx = 0:+

500 - FAC = 0FAC = 500 N (T)

Zero Force Members

• Truss analysis using the method of joints is greatly simplified if one is able to determine those members which support no loading (zero-force members)(zero-force members)

• These zero-force members are used to increase stability of the truss during construction and to provide support if the applied loading is changed

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• If only two members form a truss joint and no external load or support reaction is applied to the joint, the members must be zero-force members. members.

• If three members form a truss for which two of the members are collinear, the third member is a zero-force member provided no external force or support reaction is applied.

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Zero-force members• Frequently the analysis can be simplified by identifying

members that carry no load– two typical cases are found

• When only two members form a non-collinear joint and there is no external force or reaction at that joint, then both members must be zero-force

P If either T or T ≠

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PA B

C

D

E

TCB

TCD

C

If either TCB or TCD ≠ 0, then C cannot be in equilibrium, since there is no restoring force towards the right.

Hence both BC and CD are zero-load members here.

• When three members form a truss joint for which two members are collinear and the third is at an angle to these, then this third member must be zero-force– in the absence of an external force or reaction from a support

P

A BHere, joint B has only

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A BC

D

E

TBCTAB

TBD

B

Here, joint B has only one force in the vertical direction.

Hence, this force must be zero or B would move (provided there are no external loads/reactions)

Also TAB = TBC

• While zero-force members can be removed in this configuration, care should be taken– any change in the loading can lead to the member carrying a load

– the stability of the truss can be degraded by removing the zero-force member

P

A BC

You may think that we can remove AD and BD to make a triangle …

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C

D

E

triangle …

This satisfies the statics requirements

However, this leaves a long CE member to carry a compressive load. This long member is highly susceptible to failure by buckling.

P

A

B C

DEDx

DyEy

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C

FCD

FCB SFx = 0: FCB = 0+

SFy = 0: FCD = 0+

FAE

FAB

Aq

SFy = 0: FABsinq = 0, FAB = 0 +

SFx = 0: FAE + 0 = 0, FAE = 0+

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