Advanced Methods of Structural Analysis

Problems 311

h

P

EI EI EI

EI = ∞

Fig. P8.15

Ans.M 0 DPh=3,R 0 DP=3.

8.16.A design diagram of a frame with columns having a step-variable cross sec-
tion is presented in Fig.P8.16. The frame is subjected to uniformly distributed load
qD 5 kN=m within the first span. Construct the bending moment diagram using the
displacement method in canonical form (use TablesA.7andA.8).

l = 12m l = 12m

H

=^

10m

7m

3m EI

A

B C

D

E

EI

2 EI 2 EI

4 EI 4 EI

Fig. P8.16

Ans.MAD12:41kN m;MBD21:02; MDD8:83; MCBD47:24;

MCDD14:95; MCED32:29.

8.17.A design diagram of a two-storey frame is presented in Fig.P8.17.The
crossbars are absolutely rigid. Connections between the vertical members and the
crossbars are rigid. Construct the internal force diagrams. Determine the reactions
of support.

2 EI

2 P

h

2 EI

EI = ∞

EI = ∞

h

P

A B

l

Fig. P8.17

Ans.QAD1:5P; NleftDNrightD

2:5P h

l

;MAD0:75P h: