Draft

5.1Reactions 87

StructureType Equations

Beam,noaxialforces Fy Mz

2DTruss,Frame,Beam Fx Fy Mz

Grid Fz Mx My

3DTruss,Frame Fx Fy Fz Mx My Mz

AlternateSet

Beams,noaxialForce M

A

z

M

B

z

2 D Truss,Frame,Beam Fx M

A

z

M

B

z

M

A

z M

B

z M

C

z

Table5.1:Equationsof Equilibrium

2. Assumea directionfortheunknownquantities


3. Theright handsideof theequationshouldbe zero

If yourreactionis negative, thenit willbe in a directionoppositefromtheoneassumed.

16 Summationof externalforcesis equal andoppositetothe internalones. Thusthe net

force/moment is equalto zero.

17 Theexternalforcesgive riseto the(non-zero)shearandmoment diagram.

5.1.2 Equationsof Conditions

18 If a structurehasaninternalhinge(which may connecttwo or moresubstructures),then

thiswillprovideanadditionalequation(M = 0 atthehinge)which can be exploitedto

determinethereactions.

19 Thoseequationsareoftenexploitedin trusses(whereeach connectionis a hinge)to determine

reactions.

20 In aninclinedrollersupportwithSxandSyhorizontalandverticalprojection,thenthe

reactionR wouldhave, Fig.5.2.

Rx

Ry

=

Sy

Sx

(5.3)

Figure5.2:InclinedRollerSupport