Draft

Chapter 5

REVIEW of STATICS

To every action there is an equal

and opposite reaction.

Newton'sthirdlaw of motion

5.1 Reactions

1 In theanalysisof structures(handcalculations),it is ofteneasier(butnotalways necessary)

to startby determiningthereactions.

2 Once the reactions aredetermined, internalforces aredetermined next; nally, internal

stressesand/ordeformations(de
ectionsandrotations)aredeterminedlast

1

.

3 Reactionsarenecessaryto determinefoundationload.

4 Dependingonthetype of structures,therecanbe dierent types of supportconditions,Fig.

5.1.

Roller:providesa restraint in onlyonedirectionin a 2Dstructure,in 3Dstructuresa roller

may providerestraint in oneor two directions.A rollerwillallow rotation.

Hinge:allowsrotationbutnodisplacements.

FixedSupport:willprevent rotationanddisplacements in alldirections.

5.1.1 Equilibrium

5 Reactionsaredeterminedfromtheappropriateequationsof staticequilibrium.

6 Summationof forcesandmoments,in a staticsystemmustbe equalto zero

2

.

1

Thisis thesequenceof operationsin the

exibilitymethod which lendsitselfto handcalculation.In the

stinessmethod, we determinedisplacements rsts,theninternalforcesandreactions. Thismethod is most

suitableto computerimplementation.

2

In a dynamicsystemF=mawheremis themassandais theacceleration.