Advanced Methods of Structural Analysis

198 6 Deflections of Elastic Structures

6.7.The uniform beam is subjected to vertical displacementof supportAas
shown in Fig.P6.7. Stiffness of elastic support isk. Determine the reactive moment
at the clamped supportAand vertical displacement at the elastic supportB.Re-
actionRBof elastic supportBand its vertical displacementBsatisfy equation
RBDkB.

l

D

A B

k

y

x

Fig. P6.7

Ans.MD

3 EI

l^2





1 C^3 klEI 3

;y.l/D

3 EI

kl^3





1 C^3 klEI 3

.

6.8.A beam is clamped at the left end and pinned with torsional spring support
at right end. Torsional stiffness parameter equalskrot. Derive an equation of the
elastic curve for the beam subjected to theunit angular displacement at the left end.
Calculate the reactions of supports. Moment at elastic supportBand stiffness are
related asMBD.l/krot. Analyze the limiting cases.krotD0; krotD1/.

q 0 =1

krot

l

y

MA RA

MB

A

B

Fig. P6.8

Ans.MAD

3iCkrot

1 C^14 kroti

;RAD

6 EI

l^2

1 

1

2



3iCkrot

iCk 4 rot

!

;iD

EI

l

.

Limiting cases:krotD 0 WMAD 3 EI=lI RAD 3 EI=l^2 I

krotD1WMAD 4 EI=lI RAD 6 EI=l^2.

Problems 6.9 through 6.16 should be solved by Maxwell–Mohr integral.

6.9.The simply supported beamABcarrying uniformly distributed loadqand con-
centrated forcePapplied at midspan pointC(Fig.P6.9). Determine the vertical
displacement atxDl=2and slope at supportA.