Advanced Methods of Structural Analysis

Problems 207

Ans.y 1 D

637

9

P

EA

I y 2 D

1146

9

P

EA

I y 3 D

1274

9

P

EA

.

Problems 6.30 through 6.33 are to be solved using the reciprocal theorems

6.30.Calculate the angle of rotation of pointAcaused by given loadPand dis-
placement along thePcaused by momentMat pointA. The flexural stiffnessEIis
constant for all members.

A

P

l

h

b

A

P

l

h

a c

A

P

l

h

B

Fig. P6.30

Ans. (a)ADP

lh

EI

I yBDM

lh

EI

.

6.31.Show elastic curves for both states and displacementsı 21 for first state and
ı 12 for second state. Verify of reciprocal unit displacements theorem (Fig.P6.31).

P =1

P =1

l/2 l/2

State 1

State 2

Fig. P6.31

Ans.ı 12 Dı 21 D

5

48

l^3

EI

6.32.A fixed–fixed beam is subjected to unit vertical displacement of the right sup-
port (pointj). Calculate the vertical displacement of pointklocated atl=4from the
left support. The length of the beam island flexural stiffness isEI.(Hint:usethe
displacement and reactions reciprocal theorem)