Advanced Methods of Structural Analysis

Problems 197

y

l

x

P

A B

Fig. P6.4

Ans.EIy.x/D

Pl^3

12



3

x^2

l^2

 2

x^3

l^3



I EIy.l/D

Pl^3

12

.

6.5.A beam pinned with torsion spring at the left end and pinned at the right end
is subjected to uniformly distributed loadq. Torsion stiffness parameter equalskrot.
Calculate the reactionRAand slope 0. Derive an equation of the elastic curve. The
reactive moment and slope atAare related by expressionMADkrot.0/. Consider
limiting caseskrotD 0 ,andkrotD1. Find the range ofRAfor any stiffnesskrot.

y

l

x

q

x q^0 y(x)

krot

A B

Fig. P6.5

Ans.RAD

ql

2

1 C

5

12

krotl

EI

1 C

krotl

3 EI

; 0 DRA

l

krot



ql^2

2krot

;

0:5qlRA0:625qlfor any stiffnesskrot.

6.6.The fixed-pinned beam is subjected to uniformly distributed loadq(Fig.P6.6).
Derive an equation of elastic curve of the beam

y

l

x

q

x

A B

Fig. P6.6

Ans.EIy.x/D

ql^2

8

x^2

2



5

8

ql

x^3

6

C

qx^4

24

.