Advanced Methods of Structural Analysis

312 8 The Displacement Method

8.18.Resolve a given load into symmetrical and antisymmetrical components. Axis
of symmetry (AS) is shown by dotted line (Fig.P8.18).

a q b

q

d

q

c

q 1 q^2

Fig. P8.18

8.19.Symmetrical portal frame is loaded by the forceP, as shown in Fig.P8.19.
Resolve the given load into symmetrical and antisymmetrical components and cal-
culate the bending moments at specified points for corresponding loading. Calculate
the horizontal reactionH. Determine the horizontal displacement of the crossbar
and show the elastic curve.

AS

P

l

EI 1 h

EI 2

A

B

C

D

H H

Fig. P8.19

Ans.MBD

3k

2.1C6k/

PhIMAD

1 C3k

2.1C6k/

PhI HD

P

2

I kD

I 2

I 1



h

l

:

8.20.The portal frame in Fig.P8.20is subjected to horizontal uniformly distributed
loadq. Construct the bending moment diagram by the Combined method. De-
termine the horizontal displacement of the crossbar and show the elastic curve.
EIDconstant for all members;lD 4 m,hD 8 m.

h

l

q

B

AC

D

Fig. P8.20

Ans.MAsymD3:335qI MBsymD1:335qIMCtotalD7:746qI MDtotalD6:257q: