Trusses and Frames

• Frames and trusses are the structures consisting of bars, roads,angle section, channel section etc. pinned/hinged/rivetted/weldedtogether to form a rigid structures.

• The function of the frame/truss is to support loads and transmit thesame to the support through the various members of theframe/truss.frame/truss.

• Three categories of engineering structures are considered:

a) Frames: contain at least one multi-force member, i.e., memberacted upon by 3 or more forces.

b) Trusses: formed from two-force members, i.e., straight memberswith end point connections

c) Machines: structures containing moving parts designed totransmit and modify forces.

• A truss consists of straight members connectedat joints. No member is continuous through ajoint.

• Most structures are made of several trussesjoined together to form a space framework.Each truss carries those loads which act in itsplane and may be treated as a two-dimensionalstructure.

Truss - Definition

structure.

• Bolted or welded connections are assumed tobe pinned together. Forces acting at themember ends reduce to a single force and nocouple. Only two-force members areconsidered.

• When forces tend to pull the member apart, itis in tension. When the forces tend to compressthe member, it is in compression.

Frames Frames --DefinitionDefinition

• Frames are structures that always

contain at least one member acted on

by forces at three or more points.

Frames are constructed and supported

so as to prevent any motion.so as to prevent any motion.

Comparison of Truss and Frames

Truss Frames

• In truss forces act only along the axis of

the members. Members are having

tension or compression.

• Each member is acted upon by two equal

and opposite forces having line of action

• In frames forces are acting along the axis

of the member. In addition to transverse

forces.

• One or more than one member of frame

is subjected to more than two forcesand opposite forces having line of action

along the centre of members. i.e. every

member of truss is a two force member.

• Member does not bend.

• Forces are applied at the joints only.

• Used for large loads.

is subjected to more than two forces

(multiple force members).

• Members may bend/may not bend.

• Forces may act anywhere on the

member.

• Used for small and medium loads.

Types of Truss Connections

Pinned

Connection

Gusset Plate

Connection

Truss - Definition

• A framework composed of members joined at their ends to

form a rigid structure is called a truss.

• i.e bridges, roof supports

• When the members of truss lie in a single plane, the truss is

called a plane truss.called a plane truss.

Structural Member

Solid Rod

Solid Bar

Hollow Tube

-Shape

Solid Rod

Solid Bar

Hollow Tube

-Shape

Members of a truss are slender and not capable of

supporting large lateral loads.

Loads must be applied at the joints.

The combined weights of roadway and vehicle is transferred to the

longitudinal stringers, then to the cross beams, and finally, to the

upper joints of two plane trusses which form the vertical sides of

structure.

Uses of truss

• Roof of factory shade.

• Ware house

• Railway platform

• Garage shed

• Transmission towers• Transmission towers

• Crane truss

• Bridge Truss

• Sport Stadium Truss

Types of Truss

• Perfect/stable/sufficient Truss

• Imperfect/unstable/Deficient Truss

• The truss which does not collapse (i.e. which

does not change in shape) when loaded isdoes not change in shape) when loaded is

called a perfect/stable/sufficient truss.

• The truss which collapse (i.e. which do change

in shape) when loaded is called a

imperfect/unstable/deficient truss.

Stability and Determinacy of Trusses

m=2j-3j- number of joints.

m- number of members.

3- number of support reaction

m<2j-3 Truss unstable

(Deficient truss)

m>2j-3 Statically indeterminate

(Redundant truss)

m=2j-3 Statically determinate

(Perfect truss)

Loads on Truss

• Weight of the roof

• Wind load acting on the roof

• Travelling loads of cars, trucks, trains etc. On the bridge

structure

• Weight of the structure it self. ( Generally Neglected)• Weight of the structure it self. ( Generally Neglected)

• Reactions at the supports.

Internal Stresses in the Members

• Members of the truss transmit the load acting on it to the

support. In transmitting the loads, members are subjected to

either compressive stresses or tensile stresses.

• Member subjected to compression is called

a strut.a strut.

• Member subjected to tensile is called a Tie.

Assumptions for Analysis of Truss

• Truss joints are frictionless pin joints. They cannot resist

moments.

• Load are applied only at the joints.

• Truss members are straight and uniform in section.

• Each member of the truss is subjected to axial force only.• Each member of the truss is subjected to axial force only.

• The truss is assumed perfect.(i.e. m= 2j-3)

• Members of truss has negligible weight as compare to the

loads applied.

• Each member of the truss is two force member.

• The truss is rigid and does not change in shape.

Methods of analysis of Truss

1. Method of joints

2. Method of sections

Method of Joints

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

equilibrium.

• The method of joints consists of satisfying the equilibrium

equations for forces acting on each joint.

Σ Fx = 0, Σ Fy = 0, Σ M = 0 Σ Fx = 0, Σ Fy = 0, Σ M = 0

• Methods of joint is most suited when forces in all the

members are required to be obtained.

Method of Joints• Steps • Decide whether a truss is perfect or not, using equation; m = 2j-3.

• Find support reactions for simply supported truss, using three conditionsof equilibrium.

– Considering entire truss as a single unit.

• Force acting at all the joints are coplanar concurrent and assumed to be instatic equilibrium and hence

– (i) apply (a) Σ H= 0 and (b) Σ V= 0 for the purpose of analysis.– (i) apply (a) Σ H= 0 and (b) Σ V= 0 for the purpose of analysis.

– Or (ii) since the forces acting at the joints are in equilibrium, plot allthe forces in magnitude and direction to get either a closed forcetriangle or closed force polygon .

• Each members of the truss is assumed to be in equilibrium hence applyequal, opposite and collinear forces at the two ends along the centre lineof the member.

• Start the analysis only with a joint where there are only two unknowns.Do not start the analysis with a joint where unknowns are more than two.– Since, Σ H= 0 and (b) Σ V= 0 provide only two equations to solve the

unknowns.

Method of Joints

• Dismember the truss and create afree body diagram for eachmember and pin.

• The two forces exerted on eachmember are equal, have themember are equal, have thesame line of action, and oppositesense.

• Forces exerted by a member onthe pins or joints at its ends aredirected along the member andequal and opposite.

Method of Joints

Method of Joints

Method of Joints

• Example - Consider the following truss

Method of Joints

Method of Joints

Methods of Sections

• The method of joints is most effective when the forces in all

the members of a truss are to be determined.

• If however, the force is only one or a few members are

needed, then the method of sections is more efficient.

Methods of Sections

• In this method section is taken to

divide the truss into two parts,

cutting the truss along the members

in which the forces are required to

be found out.be found out.

• After cutting the truss into two parts

external forces are drawn on each

part of the truss and forces are also

drawn acting in the cut members.

• Apply the equilibrium condition:

• Fx = 0, Σ Fy = 0, Σ M = 0

Methods of Sections

• Cutting a truss care should be taken, not to cut more than

three members of the truss at one time in which the forces

are not known.

The Method of Sections

100 N

A

B C D

EFG

2 m

2 m 2 m 2 m

Ex

Dx

Dya

a

+ ΣMG = 0:

C

100 N

A

B

G

2 m

45o

FGF

FGC

FBC

+ ΣMG = 0:

100(2) - FBC(2) = 0

FBC = 100 N (T)

ΣFy = 0:+

-100 + FGCsin45o = 0

FGC = 141.42 N (T)

+ ΣMC = 0:

100(4) - FGF(2) = 0

FGF = 200 N (C)

Any Question?Any Question?

Thank youThank you