Draft

5.1Reactions 89

Figure5.4:GeometricInstability Causedby Concurrent Reactions

5.1.5 Examples

29 Examplesof reaction calculation willbe shown next. Each examplehas beencarefully

selectedas it bringsa dierent \twist"fromtheprecedingone. Someof thosesameproblems

willbe revisitedlaterforthedeterminationof theinternalforcesand/orde
ections.Many of

thoseproblemsaretakenfromProf.GerstletextbokBasicStructural Analysis.

Example5-1: SimplySupportedBeam

Determinethereactionsof thesimplysupportedbeamshownbelow.

Solution:

Thebeamhas3 reactions,we have 3 equationsof staticequilibrium, henceit is statically

determinate.

(+-) Fx= 0; ) Rax 36 k= 0

(+ 6 ) Fy= 0; ) Ray+Rdy 60 k(4)k/ft(12)ft= 0

(+


) M

c

z

= 0; ) 12 Ray 6 Rdy(60)(6)= 0

or throughmatrixinversion(onyourcalculator)

2

6

4

1 0 0

0 1 1

0 12 6

3

7

5

8

>

<

>

:

Rax

Ray

Rdy

9

>

=

>

;

=

8

>

<

>

:

36

108

360

9

>

=

>

;

)

8

>

<

>

:

Rax

Ray

Rdy

9

>

=

>

;

=

8

>

<

>

:

36 k

56 k

52 k

9

>

=

>

;

Alternativelywe couldhave usedanothersetof equations:

(+


) M

a

z

= 0; (60)(6)+ (48)(12)(Rdy)(18)= 0 ) Rdy= 52 k 6

(+


) M

d

z

= 0; (Ray)(18)(60)(12)(48)(6)= 0 ) Ray= 56 k 6