Advanced Methods of Structural Analysis

196 6 Deflections of Elastic Structures

y

B

l

q

A

x

Fig. P6.1

Ans.y.x/D

ql^4

30 EI



1 

5

4

x

l

C

x^5

4l^5



;yAD

ql^4

30 EI

;AD

ql^3

24 EI

.

6.2.The uniform beam is subjected to distributed loadqwithin the portionaD l,
as shown in Fig.P6.2. Derive an equation for elastic curve of the beam.

B

l

q

A

a = x l

y

x

Fig. P6.2

Ans.AD

qa^2 l

6 EI

.10:5  /^2.

6.3.The uniform simply supported beam is subjected to uniformly varying load
(Fig.P6.3). The maximum ordinate of load isq. Derive an equation of the elastic
curve. Determine the maximum vertical displacement, its location, and slope at the
supportsAandB.

l

A

q

B

y

x

Fig. P6.3

Ans.yxD

ql^4

360 EI



7

x

l

 10

x^3

l^3

C 3

x^5

l^5



;ymaxD

5

768

ql^4

EI

;

AD

7

360

ql^3

EI

;BD

8

360

ql^3

EI

.

6.4.Fixed-sliding beamA–B is subjected to action of concentrated forceP
(Fig.P6.4). Derive an equation of the elastic curve for the beam. Determine the
displacement of the beam at the right end.