Advanced Methods of Structural Analysis

11.2 Ancillary Diagrams 375

adbc

EI, a –24° h^ =^ 0.4m

a M1–0 M M3–4

M1–2 3–2

04123

b

c

M1–0 M1–2M3–2 M

3–4

d

1

Joint 1

3

Joint 3

Joint-load diagram

30 aEI 30 aEI

Fig. 11.6 (a,b) Design diagram of the beam and computation of the fixed-end moments;
(c,d) Joint-load diagram in case of temperature change

Figure11.6c presents the bending moments vicinity the joints 1 and 3. The joint
moments equal

Mj1DM 1  0 M 1  2 D90 ̨EI60 ̨EID30 ̨EI.kNm/counterclockwise;

Mj2D0; Mj3D90 ̨EI60 ̨EID30 ̨EI.kNm/clockwise:

The final joint-load diagram is shown in Fig.11.6d.

Example 11.2.The continuous beam is subjectedto the angular displacement'
of fixed support 0 and vertical displacementof rolled support 2 (Fig.11.7a).
Construct the joint-load diagram.

l 1 = 5m l 2 = 4m

j

D

1 2

0

j = 0.05rad D = 0.032m

a

M^0 P

b M1–0 M1–2

c

1

Joint 1

M1–0 M1–2

1

Joint-load

diagram

Mj 1 = 0.014EI (kNm)

d

Fig. 11.7 (a,b) Design diagram of the beam and computation of the fixed-end moments;
(c,d) Joint-load diagram in case of settlements of supports

Solution.The primary system of the displacement method and bending moment
diagram caused by given settlements of supports is shown in Fig.11.7b (first state).